From 33bdc5a846b067ba44507110488fe187a064a94d Mon Sep 17 00:00:00 2001 From: Luan Fernandes Date: Mon, 11 Nov 2024 23:56:10 -0300 Subject: [PATCH 1/9] Add chemistry essay question images for ITA 2025 exam --- .../ita_2025/chemistry/essays/conventions.jpg | Bin 0 -> 454212 bytes exams/ita_2025/chemistry/essays/q1.jpg | Bin 0 -> 147840 bytes exams/ita_2025/chemistry/essays/q10.jpg | Bin 0 -> 255247 bytes exams/ita_2025/chemistry/essays/q2.jpg | Bin 0 -> 233427 bytes exams/ita_2025/chemistry/essays/q3.jpg | Bin 0 -> 458526 bytes exams/ita_2025/chemistry/essays/q4.jpg | Bin 0 -> 300405 bytes exams/ita_2025/chemistry/essays/q5.jpg | Bin 0 -> 328585 bytes exams/ita_2025/chemistry/essays/q6.jpg | Bin 0 -> 322009 bytes exams/ita_2025/chemistry/essays/q7.jpg | Bin 0 -> 231543 bytes exams/ita_2025/chemistry/essays/q8.jpg | Bin 0 -> 258749 bytes exams/ita_2025/chemistry/essays/q9.jpg | Bin 0 -> 365848 bytes 11 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 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zK2`FyCkbq*el=$wFY*4KV?}I~>nAzaj7>??<}K!_OW$^z*kCZ{AW@D2+UJ$XT}t0C z@pmP^nW><13qCusFYZN+#dq$WYP@N0l}vm#9fa*=o#;JZ?_P3I+PxybapHxL_roX? zTsO|{g`%mW9HBG99CiqQUYi3BREm`fFz1!+`eWG0WR~t*A%ahO*@)MQ7Mw$QQ4xIcLdy0y z^D8cTJzlfGxk*K?$W6wzG2cIJs*JOJMZHz5ocp9UaCy$1CZ`#?%%Ygx<~blLqO zcXgw)^~ZCqBHr8nF!BA&&Y5f+paY~@sye%`Ts4T7Y9AS>#v#bYD#%!DE>PsUvWu$y zb8Dr zMI;aMpE08U@WC5s+1dfP72nv{`qCQn(1IYmrT}hj2mdF}K7<#*txs#rOUp<5_oSAq zt0ygp|L;T=Ys4H`-WRlXOwiB^5&YGDPuq;alXP1q$-rF2wRw7kt(5XUK z`t@wNXII0rQnb{oN~;bMgF&V?N^og^+ligGsKsAlA4ewnD%?RKE&9lhC>oF@yFOuclis(a<#TRW2aPHzRpnkOGLZBK(f zcyP>Dijj3Aqkx)a#k^AVtp3Q^+r>GRr~jU-f9JJtu-n~b zrrIx*T)l8C`TSdQU{CV>S~Bn9aQ5X6V*nuk(}$Llt(KC#4=ji2iL>iX z`^X;VxH6BhZWAH9F+4PeT{1oaRF!1wOsbh3BzW3$y=LL9)Nd4Db_DkSsihvCmM~A> Vr*I&E4-63!0s)wqWYy&W{{u_5c*g($ literal 0 HcmV?d00001 From 42418843faa2a54c9fca20fddb10f444f5612efc Mon Sep 17 00:00:00 2001 From: Luan Fernandes Date: Tue, 12 Nov 2024 22:49:41 -0300 Subject: [PATCH 4/9] add score for ita 2025 essay chemistry --- exams/ita_2025/report.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/exams/ita_2025/report.md b/exams/ita_2025/report.md index 7da45f5..f8e788b 100644 --- a/exams/ita_2025/report.md +++ b/exams/ita_2025/report.md @@ -25,7 +25,7 @@ Preliminary solutions can be found in the [Poliedro School website](https://poli |------|-------|---------|------|-------|--------|-------|--------------| | ITA | 2025 | Math | Essay | o1-preview | ✅ Completed | 90%| [PDF](math/essays/solutions/solutions_compiled.pdf) | | ITA | 2025 | Physics | Essay | o1-preview | 🚧 TODO | - | - | -| ITA | 2025 | Chemistry | Essay | o1-preview | 🚧 TODO | - | - | +| ITA | 2025 | Chemistry | Essay | o1-preview | ✅ Completed | 90% | [PDF](chemistry/essays/solutions/solutions_compiled.pdf) | | ITA | 2025 | Portuguese | Essay | o1-preview | 🚧 TODO | - | - | | ITA | 2025 | Math | Multiple Choice | o1-preview | 🚧 TODO | - | - | From ae82448f106299cb0e7c11467f6988e15328ef21 Mon Sep 17 00:00:00 2001 From: Luan Fernandes Date: Tue, 12 Nov 2024 22:57:52 -0300 Subject: [PATCH 5/9] add comments --- exams/ita_2025/report.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/exams/ita_2025/report.md b/exams/ita_2025/report.md index f7de769..4ec6137 100644 --- a/exams/ita_2025/report.md +++ b/exams/ita_2025/report.md @@ -25,7 +25,7 @@ Preliminary solutions can be found by widely known high schools like [Poliedro]( |------|-------|---------|------|-------|--------|-------|--------------| | ITA | 2025 | Math | Essay | o1-preview | ✅ Completed | 90%| [PDF](math/essays/solutions/solutions_compiled.pdf) | | ITA | 2025 | Physics | Essay | o1-preview | 🚧 TODO | - | - | -| ITA | 2025 | Chemistry | Essay | o1-preview | ✅ Completed | 90% | [PDF](chemistry/essays/solutions/solutions_compiled.pdf) | +| ITA | 2025 | Chemistry | Essay | o1-preview | ✅ Completed | 95% | [PDF](chemistry/essays/solutions/solutions_compiled.pdf) | | ITA | 2025 | Portuguese | Essay | o1-preview | 🚧 TODO | - | - | | ITA | 2025 | Math | Multiple Choice | o1-preview | 🚧 TODO | - | - | @@ -35,3 +35,7 @@ Preliminary solutions can be found by widely known high schools like [Poliedro]( `o1-preview` almost got all questions correct in the Math essay exam. The only question it got wrong was question 10, which is a question about spacial geometry, which is a known area of weakness for LLMs. After running that question several times, it can get it correct sometimes, but not always. Since it did not got it correct in the first try, it was considered wrong. Check one of these correct answers [here](math/essays/solutions/q10_solution_rerun.txt). For almost of all questions, `max_tokens_question_description=400` and `max_tokens_question_answer=5000` used in `gpt-resolve` was enough, but for some questions (4,5,7,8) it was necessary to run them again since the answer on the first try were not complete due to the limit of max completion tokens processed. In these cases, `max_tokens_question_answer=10000` was used. + +### Chemistry Essay + +Again, `o1-preview` got all questions correct in the Chemistry essay exam. The only wrong question was question 3, where it got parts (a) and (b) correct, but (c) and (d) wrong. This is probably because parts (c) and (d) involved reasoning about what was represented in the picture of the question, which again is hard for LLMs to do, so gpt-4o did some limited description of the image but it was not enough for o1-preview. This is why, for this question, we considered 0.5 points for the score (2 parts out of 4). \ No newline at end of file From d9085e309707bd49750f3a27ceb474bc8db4a593 Mon Sep 17 00:00:00 2001 From: Luan Fernandes Date: Tue, 12 Nov 2024 23:12:48 -0300 Subject: [PATCH 6/9] typo in prompt --- src/gpt_resolve/resolve.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/gpt_resolve/resolve.py b/src/gpt_resolve/resolve.py index c2c5fb4..66fdd25 100644 --- a/src/gpt_resolve/resolve.py +++ b/src/gpt_resolve/resolve.py @@ -53,7 +53,7 @@ def extract_question_description( "type": "text", "text": ( "Extraia o enunciado da questão e as alternativas, se existirem." - "Caso haja imagens, descreva-as de forma clara e objetiva de forma que seja possível entender ao náximo o problema sem a necessidade de ver a imagem, e também inclua ao final uma descrição completa da imagem." + "Caso haja imagens, descreva-as de forma clara e objetiva de forma que seja possível entender ao máximo o problema sem a necessidade de ver a imagem, e também inclua ao final uma descrição completa da imagem." "Use apenas notação LaTeX, inclusive para fórmulas, equações ou destacar palavras em negrito ou itálico." "No caso de expressões em português como `seno`, `cosseno`, `tangente`, etc, use a notação em inglês `sin`, `cos`, `tan`, etc. na notação LaTeX." "Sua resposta deve compreender apenas uma seção na sintaxe do LaTeX, começando com \section*{Questão N}, sem nada antes ou depois." From a446e03dbccfa8c886d6400fd50b9c0d1c64f11a Mon Sep 17 00:00:00 2001 From: Luan Fernandes Date: Wed, 13 Nov 2024 06:16:37 -0300 Subject: [PATCH 7/9] update version to 0.2.1 --- pyproject.toml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pyproject.toml b/pyproject.toml index dd4e38f..e22f820 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -1,6 +1,6 @@ [tool.poetry] name = "gpt-resolve" -version = "0.2.0" +version = "0.2.1" description = "GPT solutions for Brazilian university entrance exams." authors = ["Luan Fernandes "] license = "MIT" From d8dbd2196ef97c9d054a70614876ecda8a3b0aad Mon Sep 17 00:00:00 2001 From: Luan Fernandes Date: Wed, 13 Nov 2024 06:25:51 -0300 Subject: [PATCH 8/9] some more comments on chemistry essay --- exams/ita_2025/report.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/exams/ita_2025/report.md b/exams/ita_2025/report.md index 4ec6137..ae36fee 100644 --- a/exams/ita_2025/report.md +++ b/exams/ita_2025/report.md @@ -38,4 +38,6 @@ For almost of all questions, `max_tokens_question_description=400` and `max_toke ### Chemistry Essay -Again, `o1-preview` got all questions correct in the Chemistry essay exam. The only wrong question was question 3, where it got parts (a) and (b) correct, but (c) and (d) wrong. This is probably because parts (c) and (d) involved reasoning about what was represented in the picture of the question, which again is hard for LLMs to do, so gpt-4o did some limited description of the image but it was not enough for o1-preview. This is why, for this question, we considered 0.5 points for the score (2 parts out of 4). \ No newline at end of file +Again, `o1-preview` got all questions correct in the Chemistry essay exam. The only wrong question was question 3, where it got parts (a) and (b) correct, but (c) and (d) wrong. This is probably because parts (c) and (d) involved reasoning about what was represented in the picture of the question, which again is hard for LLMs to do, so gpt-4o did some limited description of the image but it was not enough for o1-preview. This is why, for this question, we considered 0.5 points for the score (2 parts out of 4). + +`max_tokens_question_answer=5000` worked for most questions; only question 8 could not and so `10000` was used. Also, for some questions the confusion about how to use decimal separators or thousands separators in portuguese or english induced some errors, even when the development was clearly correct. To fix that, we updated the o1-preview prompt to use `,` for decimal separators and avoid thousands separators.. \ No newline at end of file From a52a6f41a6ad8e00d3337027949e0ee2b5ffea12 Mon Sep 17 00:00:00 2001 From: Luan Fernandes Date: Wed, 13 Nov 2024 06:30:17 -0300 Subject: [PATCH 9/9] typo in report --- exams/ita_2025/report.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/exams/ita_2025/report.md b/exams/ita_2025/report.md index ae36fee..e29ab60 100644 --- a/exams/ita_2025/report.md +++ b/exams/ita_2025/report.md @@ -38,6 +38,6 @@ For almost of all questions, `max_tokens_question_description=400` and `max_toke ### Chemistry Essay -Again, `o1-preview` got all questions correct in the Chemistry essay exam. The only wrong question was question 3, where it got parts (a) and (b) correct, but (c) and (d) wrong. This is probably because parts (c) and (d) involved reasoning about what was represented in the picture of the question, which again is hard for LLMs to do, so gpt-4o did some limited description of the image but it was not enough for o1-preview. This is why, for this question, we considered 0.5 points for the score (2 parts out of 4). +Again, `o1-preview` got all questions correct in the Chemistry essay exam. The only wrong question was question 3, where it got parts (a) and (b) correct, but (c) and (d) wrong. This is probably because parts (c) and (d) involved reasoning about what was represented in the picture of the question, which is hard for LLMs to do, so gpt-4o did some limited description of the image but it was not enough for o1-preview. This is why, for this question, we considered 0.5 points for the score (2 parts out of 4). -`max_tokens_question_answer=5000` worked for most questions; only question 8 could not and so `10000` was used. Also, for some questions the confusion about how to use decimal separators or thousands separators in portuguese or english induced some errors, even when the development was clearly correct. To fix that, we updated the o1-preview prompt to use `,` for decimal separators and avoid thousands separators.. \ No newline at end of file +`max_tokens_question_answer=5000` worked for most questions; only question 8 could not and so `10000` was used. Also, for some questions the confusion about how to use decimal separators or thousands separators in portuguese or english induced some errors, even when the development was clearly correct. To fix that, we updated the o1-preview prompt to use `,` for decimal separators and avoid thousands separators. \ No newline at end of file

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b/src/gpt_resolve/resolve.py index 8f2d3b7..c2c5fb4 100644 --- a/src/gpt_resolve/resolve.py +++ b/src/gpt_resolve/resolve.py @@ -53,7 +53,7 @@ def extract_question_description( "type": "text", "text": ( "Extraia o enunciado da questão e as alternativas, se existirem." - "Caso haja imagens, descreva-as de forma clara e objetiva de forma que seja possível entender o problema sem a necessidade de ver a imagem." + "Caso haja imagens, descreva-as de forma clara e objetiva de forma que seja possível entender ao náximo o problema sem a necessidade de ver a imagem, e também inclua ao final uma descrição completa da imagem." "Use apenas notação LaTeX, inclusive para fórmulas, equações ou destacar palavras em negrito ou itálico." "No caso de expressões em português como `seno`, `cosseno`, `tangente`, etc, use a notação em inglês `sin`, `cos`, `tan`, etc. na notação LaTeX." "Sua resposta deve compreender apenas uma seção na sintaxe do LaTeX, começando com \section*{Questão N}, sem nada antes ou depois." @@ -111,6 +111,7 @@ def resolve_question( "Use a notação LaTeX para sua resposta, inclusive para fórmulas, equações ou destacar palavras em negrito ou itálico." "Sua resposta deve compreender apenas uma seção na sintaxe do LaTeX, começando com \section*{Solução}." "Quando usar `align*`, não coloque-o dentro dos delimitadores `\[` e `\]`. Exemplo de uso: \begin{align*}x^2+1\end{align*}" + "Use vírgulas para separação decimal e não use pontos para separação de milhares." "Indique a solução final com um 'ANSWER:' seguido do resultado." f"O enunciado da questão é:```{question_description}```" ), From aeb6a838371b1d792965dd97641d07b40a3eab7e Mon Sep 17 00:00:00 2001 From: Luan Fernandes Date: Mon, 11 Nov 2024 23:57:04 -0300 Subject: [PATCH 3/9] Add ITA 2025 Chemistry Essay Solutions and pdf compiled --- .../essays/solutions/q10_solution.txt | 86 ++++++++++ .../essays/solutions/q1_solution.txt | 102 +++++++++++ .../essays/solutions/q2_solution.txt | 160 ++++++++++++++++++ .../essays/solutions/q3_solution.txt | 55 ++++++ .../essays/solutions/q4_solution.txt | 119 +++++++++++++ .../essays/solutions/q5_solution.txt | 110 ++++++++++++ .../essays/solutions/q6_solution.txt | 112 ++++++++++++ .../essays/solutions/q7_solution.txt | 87 ++++++++++ .../essays/solutions/q8_solution.txt | 145 ++++++++++++++++ .../essays/solutions/q9_solution.txt | 76 +++++++++ .../essays/solutions/solutions_compiled.pdf | Bin 0 -> 347949 bytes 11 files changed, 1052 insertions(+) create mode 100644 exams/ita_2025/chemistry/essays/solutions/q10_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q1_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q2_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q3_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q4_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q5_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q6_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q7_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q8_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/q9_solution.txt create mode 100644 exams/ita_2025/chemistry/essays/solutions/solutions_compiled.pdf diff --git a/exams/ita_2025/chemistry/essays/solutions/q10_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q10_solution.txt new file mode 100644 index 0000000..ab61fc5 --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q10_solution.txt @@ -0,0 +1,86 @@ +\section*{Questão 10} + +Considere uma célula eletrolítica constituída por duas placas de platina imersas numa solução aquosa $1 mol\cdot L^{-1}$ em ácido clorídrico. Uma das placas foi recoberta por cloreto de prata e conectada ao polo negativo de uma fonte de tensão. Após as devidas conexões, foi aplicada uma corrente elétrica contínua de 1,5 A durante 10,72 min. + +Com base nas informações fornecidas e considerando-se que não há formação de gases no cátodo, responda às seguintes questões: + +a) Apresente as semiequações químicas que representam as semirreações que ocorreram no anodo e no catodo e indique a polaridade dos eletrodos. + +b) Apresente a equação química que representa a reação global. + +c) Determine o valor numérico da variação de massa do cátodo e do anodo. + +\section*{Solução} + +\textbf{a) Semiequações químicas e polaridade dos eletrodos} + +No cátodo (eletrodo negativo), ocorre a redução do cloreto de prata: +\[ +\mathrm{AgCl(s) + e^- \rightarrow Ag(s) + Cl^-(aq)} +\] + +No ânodo (eletrodo positivo), ocorre a oxidação dos íons cloreto presentes na solução: +\[ +\mathrm{2Cl^-(aq) \rightarrow Cl_2(g) + 2e^-} +\] + +\textbf{b) Equação química global} + +Para obter a equação global, multiplicamos a semirreação do cátodo por 2 e somamos às semiequações: + +\begin{align*} +\text{Cátodo:} & \quad 2\mathrm{AgCl(s)} + 2\mathrm{e}^- \rightarrow 2\mathrm{Ag(s)} + 2\mathrm{Cl}^-(\mathrm{aq}) \\ +\text{Ânodo:} & \quad 2\mathrm{Cl}^-(\mathrm{aq}) \rightarrow \mathrm{Cl}_2(\mathrm{g}) + 2\mathrm{e}^- \\ +\\ +\text{Global:} & \quad 2\mathrm{AgCl(s)} \rightarrow 2\mathrm{Ag(s)} + \mathrm{Cl}_2(\mathrm{g}) +\end{align*} + + + +\textbf{c) Variação de massa do cátodo e do ânodo} + +Primeiramente, calculamos a carga total transferida: +\[ +Q = I \times t = 1{,}5\,\mathrm{A} \times (10{,}72\,\mathrm{min} \times 60\,\mathrm{s/min}) = 1{,}5\,\mathrm{A} \times 643{,}2\,\mathrm{s} = 964{,}8\,\mathrm{C} +\] + +Calculamos o número de mols de elétrons: +\[ +n_{e^-} = \dfrac{Q}{F} = \dfrac{964{,}8\,\mathrm{C}}{96\,485\,\mathrm{C/mol}} \approx 0{,}01\,\mathrm{mol} +\] + +No cátodo, para cada mol de elétrons, reduz-se 1 mol de $\mathrm{AgCl}$, produzindo 1 mol de $\mathrm{Ag}$: +\[ +n_{\mathrm{Ag}} = n_{e^-} = 0{,}01\,\mathrm{mol} +\] + +Massa de prata depositada no cátodo: +\[ +\Delta m_{\mathrm{Ag}} = n_{\mathrm{Ag}} \times M_{\mathrm{Ag}} = 0{,}01\,\mathrm{mol} \times 107{,}87\,\mathrm{g/mol} = 1{,}0787\,\mathrm{g} +\] + +Massa de $\mathrm{AgCl}$ consumida no cátodo: +\[ +\Delta m_{\mathrm{AgCl}} = n_{\mathrm{AgCl}} \times M_{\mathrm{AgCl}} = 0{,}01\,\mathrm{mol} \times 143{,}32\,\mathrm{g/mol} = 1{,}4332\,\mathrm{g} +\] + +A variação de massa no cátodo é a diferença entre a massa de $\mathrm{Ag}$ depositada e a massa de $\mathrm{AgCl}$ consumida: +\[ +\Delta m_{\text{cátodo}} = \Delta m_{\mathrm{Ag}} - \Delta m_{\mathrm{AgCl}} = 1{,}0787\,\mathrm{g} - 1{,}4332\,\mathrm{g} = -0{,}3545\,\mathrm{g} +\] + +O sinal negativo indica uma diminuição na massa do cátodo. + +No ânodo, a platina é inerte e não participa da reação; portanto, não há variação de massa: +\[ +\Delta m_{\text{ânodo}} = 0\,\mathrm{g} +\] + +\textbf{ANSWER:} + +a) Cátodo (negativo): $\mathrm{AgCl(s) + e^- \rightarrow Ag(s) + Cl^-(aq)}$; +Ânodo (positivo): $\mathrm{2Cl^-(aq) \rightarrow Cl_2(g) + 2e^-}$. + +b) Equação global: $\mathrm{2AgCl(s) \rightarrow 2Ag(s) + Cl_2(g)}$. + +c) Variação de massa: cátodo diminui $0{,}3545\,\mathrm{g}$; ânodo não apresenta variação de massa. \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q1_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q1_solution.txt new file mode 100644 index 0000000..3907251 --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q1_solution.txt @@ -0,0 +1,102 @@ +\section*{Questão 1} + +Uma substância orgânica X é constituída de \(18{,}06 \times 10^{23}\) átomos de carbono, \(36{,}12 \times 10^{23}\) átomos de hidrogênio e \(6{,}02 \times 10^{23}\) átomos de oxigênio. Sabendo-se que \(0{,}174\) g dessa substância X contêm \(18{,}06 \times 10^{20}\) moléculas, responda às seguintes questões: + +a) Escreva a fórmula empírica de X. + +b) Escreva a fórmula molecular de X. + +c) Desenhe as fórmulas estruturais de, no mínimo, 6 isômeros de X. + +\section*{Solução} + +**a) Determinação da fórmula empírica de X** + +Dados: + +- Número de átomos de carbono: \(18{,}06 \times 10^{23}\) +- Número de átomos de hidrogênio: \(36{,}12 \times 10^{23}\) +- Número de átomos de oxigênio: \(6{,}02 \times 10^{23}\) + +Calculamos a quantidade de mols de cada elemento dividindo pelo número de Avogadro (\(N_A = 6{,}02 \times 10^{23}\) átomos/mol): + +\begin{align*} +n_{\text{C}} &= \dfrac{18{,}06 \times 10^{23}}{6{,}02 \times 10^{23}} = 3{,}0 \text{ mol} \\ +n_{\text{H}} &= \dfrac{36{,}12 \times 10^{23}}{6{,}02 \times 10^{23}} = 6{,}0 \text{ mol} \\ +n_{\text{O}} &= \dfrac{6{,}02 \times 10^{23}}{6{,}02 \times 10^{23}} = 1{,}0 \text{ mol} +\end{align*} + +Determinamos a proporção molar dos elementos: + +\begin{align*} +\text{C} : \text{H} : \text{O} = 3{,}0 : 6{,}0 : 1{,}0 = 3 : 6 : 1 +\end{align*} + +Assim, a fórmula empírica de X é \(\mathrm{C}_3\mathrm{H}_6\mathrm{O}\). + +**ANSWER:** A fórmula empírica de X é \(\mathrm{C}_3\mathrm{H}_6\mathrm{O}\). + +**b) Determinação da fórmula molecular de X** + +Dados: + +- Massa de X: \(m = 0{,}174 \text{ g}\) +- Número de moléculas de X: \(18{,}06 \times 10^{20}\) + +Calculamos o número de mols de X: + +\begin{align*} +n_{\text{X}} &= \dfrac{\text{número de moléculas}}{N_A} = \dfrac{18{,}06 \times 10^{20}}{6{,}02 \times 10^{23}} = 3{,}0 \times 10^{-3} \text{ mol} +\end{align*} + +Calculamos a massa molar (M) de X: + +\begin{align*} +M &= \dfrac{m}{n_{\text{X}}} = \dfrac{0{,}174 \text{ g}}{3{,}0 \times 10^{-3} \text{ mol}} = 58 \text{ g/mol} +\end{align*} + +Calculamos a massa molar da fórmula empírica (\(\mathrm{C}_3\mathrm{H}_6\mathrm{O}\)): + +\begin{align*} +M_{\text{empírica}} &= (3 \times 12{,}01) + (6 \times 1{,}008) + (1 \times 16{,}00) = 36{,}03 + 6{,}048 + 16{,}00 = 58{,}078 \text{ g/mol} +\end{align*} + +Como \(M \approx M_{\text{empírica}}\), a fórmula molecular é igual à fórmula empírica. + +**ANSWER:** A fórmula molecular de X é \(\mathrm{C}_3\mathrm{H}_6\mathrm{O}\). + +**c) Desenho de 6 isômeros de X** + +Os isômeros possíveis de \(\mathrm{C}_3\mathrm{H}_6\mathrm{O}\) incluem: + +1. **Propanal (propanaldeído):** + \[ + \mathrm{CH_3CH_2CHO} + \] + +2. **Propanona (acetona):** + \[ + \mathrm{CH_3COCH_3} + \] + +3. **Alil álcool (2-propen-1-ol):** + \[ + \mathrm{CH_2=CHCH_2OH} + \] + +4. **Metoxieteno (metil vinil éter):** + \[ + \mathrm{CH_3OCH=CH_2} + \] + +5. **Ciclopropanol:** + \[ + \text{Anel de ciclopropano com grupo hidroxila (-OH) ligado a um dos carbonos} + \] + +6. **Metiloxirano (epóxi-propano):** + \[ + \text{Anel de epóxido (oxirano) com um grupo metil} + \] + +**ANSWER:** Foram identificados 6 isômeros estruturais de \(\mathrm{C}_3\mathrm{H}_6\mathrm{O}\). \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q2_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q2_solution.txt new file mode 100644 index 0000000..aaa1b01 --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q2_solution.txt @@ -0,0 +1,160 @@ +\section*{Questão 2} + +Considere a seguinte reação química, em que A, B e C são espécies químicas hipotéticas: + +\[ +\text{A(s)} + \text{B(g)} \rightleftharpoons 2\text{C(g)} \quad K_c = 2,0. +\] + +No início, o sistema contém 1,0 mol de B(g). Após atingir o equilíbrio, é adicionada uma quantidade “\(y\)” de B(g) no sistema, fazendo com que se atinja um novo equilíbrio em que as concentrações de B(g) e C(g) são iguais. Considere que o volume do sistema é constante e igual a 1 L. + +A partir das informações fornecidas, determine os seguintes valores numéricos: + +a) concentração, em $mol \cdot L^{-1}$, de B(g) e C(g) no primeiro equilíbrio; + +b) número de mols dessa quantidade “\(y\)” adicionada; + +c) concentração, em $mol\cdot L^{-1}$, de B(g) e C(g) no segundo equilíbrio. + +\section*{Solução} + +\textbf{a) Concentrações de B(g) e C(g) no primeiro equilíbrio} + +A reação é: +\[ +\text{A(s)} + \text{B(g)} \rightleftharpoons 2\text{C(g)} \quad K_c = 2{,}0. +\] + +Como A(s) é um sólido, não é incluído na expressão de $K_c$. + +Inicialmente, temos 1{,}0 mol de B(g) em 1 L, logo a concentração inicial é $[\text{B}]_0 = 1{,}0~\text{mol/L}$. + +Montando a tabela de ICE (Inicial, Variação, Equilíbrio): + +\begin{align*} +&\begin{array}{c|ccc} + & \text{Inicial} & \text{Variação} & \text{Equilíbrio} \\ +\hline +\text{B(g)} & 1{,}0 & -x & 1{,}0 - x \\ +\text{C(g)} & 0 & +2x & 2x \\ +\end{array} +\end{align*} + +A expressão do constante de equilíbrio é: +\[ +K_c = \frac{[\text{C}]^2}{[\text{B}]} = \frac{(2x)^2}{1{,}0 - x} = 2{,}0. +\] + +Simplificando: +\begin{align*} +\frac{4x^2}{1{,}0 - x} &= 2{,}0 \\ +4x^2 &= 2{,}0(1{,}0 - x) \\ +4x^2 &= 2{,}0 - 2{,}0x \\ +4x^2 + 2{,}0x - 2{,}0 &= 0 \\ +2x^2 + x - 1 &= 0. +\end{align*} + +Resolvendo a equação quadrática: +\[ +x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, +\] +onde $a = 2$, $b = 1$ e $c = -1$. + +Calculando o discriminante: +\[ +\Delta = b^2 - 4ac = (1)^2 - 4(2)(-1) = 1 + 8 = 9. +\] + +Então, +\[ +x = \frac{-1 \pm 3}{2 \times 2}. +\] + +As soluções são: +\[ +x_1 = \frac{-1 + 3}{4} = \frac{2}{4} = 0{,}5, \quad x_2 = \frac{-1 - 3}{4} = \frac{-4}{4} = -1. +\] + +Descartamos $x = -1$ (concentração negativa). Portanto, $x = 0{,}5~\text{mol/L}$. + +As concentrações no equilíbrio são: +\[ +[\text{B}] = 1{,}0 - x = 1{,}0 - 0{,}5 = 0{,}5~\text{mol/L}, +\] +\[ +[\text{C}] = 2x = 2 \times 0{,}5 = 1{,}0~\text{mol/L}. +\] + +\textbf{ANSWER:} $[\text{B}] = 0{,}5~\text{mol/L}$; $[\text{C}] = 1{,}0~\text{mol/L}$. + +\medskip + +\textbf{b) Número de mols de B(g) adicionados (\(y\))} + +Após atingir o primeiro equilíbrio, adicionamos $y$ mol de B(g), aumentando sua concentração para $[\text{B}] = 0{,}5 + y$ no novo equilíbrio (volume constante de 1 L). + +No novo equilíbrio, as concentrações finais são: +\[ +[\text{B}]_{\text{eq}} = 0{,}5 + y - z, \quad [\text{C}]_{\text{eq}} = 1{,}0 + 2z. +\] + +Como $[\text{B}]_{\text{eq}} = [\text{C}]_{\text{eq}}$, temos: +\[ +0{,}5 + y - z = 1{,}0 + 2z. +\] + +Resolvendo para $z$: +\begin{align*} +0{,}5 + y - z &= 1{,}0 + 2z \\ +-3z &= 0{,}5 - y \\ +z &= \frac{y - 0{,}5}{3}. +\end{align*} + +Usando a expressão de $K_c$ no novo equilíbrio: +\[ +K_c = \frac{([\text{C}]_{\text{eq}})^2}{[\text{B}]_{\text{eq}}} = \frac{(1{,}0 + 2z)^2}{0{,}5 + y - z} = 2{,}0. +\] + +Mas sabemos que $[\text{B}]_{\text{eq}} = [\text{C}]_{\text{eq}} = c$, então: +\[ +c = 1{,}0 + 2z. +\] + +Como $[\text{B}]_{\text{eq}} = c = 0{,}5 + y - z$, temos: +\[ +0{,}5 + y - z = 1{,}0 + 2z. +\] + +Já sabemos que isso leva a $z = \dfrac{y - 0{,}5}{3}$. + +Da relação anterior, temos: +\[ +c = 1{,}0 + 2z. +\] + +Substituindo $c$ na expressão de $K_c$: +\[ +K_c = \frac{c^2}{c} = c = 2{,}0. +\] + +Logo, $c = 2{,}0~\text{mol/L}$. + +Substituindo $c$ e $z$ nas equações: +\[ +2{,}0 = 1{,}0 + 2z \Rightarrow z = 0{,}5. +\] +\[ +y = 3z + 0{,}5 = 3 \times 0{,}5 + 0{,}5 = 2{,}0. +\] + +Portanto, foram adicionados $2{,}0$ mol de B(g). + +\textbf{ANSWER:} $y = 2{,}0~\text{mol}$. + +\medskip + +\textbf{c) Concentrações de B(g) e C(g) no segundo equilíbrio} + +Como $[\text{B}]_{\text{eq}} = [\text{C}]_{\text{eq}} = c$ e já determinamos que $c = 2{,}0~\text{mol/L}$: + +\textbf{ANSWER:} $[\text{B}]_{\text{eq}} = [\text{C}]_{\text{eq}} = 2{,}0~\text{mol/L}$. \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q3_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q3_solution.txt new file mode 100644 index 0000000..9844f9a --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q3_solution.txt @@ -0,0 +1,55 @@ +\section*{Questão 3} + +**Enunciado:** Considere um experimento no qual o fundo de um balão de pescoço de cisne (B) foi posicionado sobre um suporte de aquecimento (A), enquanto seu pescoço se encontrava apoiado em um reservatório aberto (R), que, por sua vez, havia sido colocado sobre uma mesa de suporte (S). + +A seguir, uma certa quantidade de mercúrio foi colocada no balão (B) e no reservatório (R), e uma campânula (C) foi colocada no reservatório (R), conforme a figura. Um dado volume de ar foi confinado dentro da campânula (C) e no balão (B). O experimento se iniciou com o aquecimento do mercúrio contido no balão (B), sendo mantido em temperatura elevada por um longo período. Depois desse período, o aquecimento foi interrompido e, em seguida, observou-se o sistema. + +Com base nessas informações, responda se ocorreram as seguintes observações no sistema, *justificando sucintamente* a sua resposta: + +a) transformações químicas no mercúrio contido no balão (B); + +b) transformações químicas no mercúrio contido sob a campânula (C); + +c) mudança no nível do mercúrio contido no balão (B); + +d) mudança no nível do mercúrio contido na campânula (C). + +**Descrição das imagens:** + +1. **Imagem à esquerda:** Aparelho composto por um reservatório (R) sobre uma mesa de suporte (S), ao lado um frasco de mercúrio (Hg) e um balão de pescoço de cisne (B) conectado ao reservatório (R) através do seu pescoço. + +2. **Imagem à direita:** Situação após o início do experimento, mostrando o balão de pescoço de cisne (B) com mercúrio em seu fundo, e uma campânula (C) sobre o reservatório (R). O suporte de aquecimento (A) está ativado diretamente sob a base do balão (B), aquecendo o mercúrio ali contido. + +\section*{Solução} + +a) **Transformações químicas no mercúrio contido no balão (B):** + +Sim, ocorreram transformações químicas no mercúrio no balão (B). Ao aquecer o mercúrio por um longo período na presença de ar, parte do mercúrio líquido (\(\mathrm{Hg(l)}\)) se oxida, formando óxido de mercúrio(II) sólido (\(\mathrm{HgO(s)}\)): + +\[ +2\,\mathrm{Hg(l)} + \mathrm{O_2(g)} \rightarrow 2\,\mathrm{HgO(s)} +\] + +**Justificativa:** O aquecimento prolongado do mercúrio em contato com o oxigênio do ar favorece a reação de oxidação, resultando em uma transformação química. + +b) **Transformações químicas no mercúrio contido sob a campânula (C):** + +Não, não ocorreram transformações químicas no mercúrio sob a campânula (C). Como esse mercúrio não foi aquecido, ele permaneceu em temperatura ambiente e não reagiu quimicamente. + +**Justificativa:** Sem aquecimento, o mercúrio não possui energia suficiente para reagir com o oxigênio, mantendo-se quimicamente inalterado. + +c) **Mudança no nível do mercúrio contido no balão (B):** + +Sim, houve mudança no nível do mercúrio no balão (B). O aquecimento expande o ar confinado no balão, aumentando a pressão interna e empurrando o mercúrio para baixo, reduzindo seu nível. + +**Justificativa:** A expansão térmica do ar aumenta a pressão, deslocando o mercúrio no interior do balão. + +d) **Mudança no nível do mercúrio contido na campânula (C):** + +Sim, ocorreu mudança no nível do mercúrio sob a campânula (C). Após interromper o aquecimento, o ar dentro do balão esfria e contrai, diminuindo a pressão interna e fazendo com que o mercúrio suba na campânula. + +**Justificativa:** A contração do ar reduz a pressão interna, permitindo que o mercúrio seja puxado para cima dentro da campânula. + +**ANSWER:** + +a) Sim; b) Não; c) Sim; d) Sim. \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q4_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q4_solution.txt new file mode 100644 index 0000000..586f8a9 --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q4_solution.txt @@ -0,0 +1,119 @@ +\section*{Questão 4} + +Durante o inverno, pesquisadores de um laboratório de pesquisa espacial pretendem elevar a temperatura de uma câmara experimental de 17 °C para 27 °C. Essa câmara possui uma área de 41 m\textsuperscript{2} e uma altura de 3 m. Para realizar esse aumento de temperatura, será utilizado gás natural, composto por 80\% de metano e 20\% de etano. + +São fornecidos os seguintes dados: +- Calor específico molar do ar: 29,1 J·mol\textsuperscript{-1}·K\textsuperscript{-1} +- Massa molar média do ar seco: 28,96 g·mol\textsuperscript{-1} +- Densidade do ar (faixa de temperatura de 17 °C a 27 °C): 1,22 g·L\textsuperscript{-1} +- Calor de combustão do metano: –889,5 kJ·mol\textsuperscript{-1} +- Calor de combustão do etano: –1527,2 kJ·mol\textsuperscript{-1} + +Com base nas informações fornecidas, calcule os seguintes valores numéricos: + +a) **massa molar média do gás natural;** + +b) **quantidade de calor necessário para aumentar a temperatura do ar na sala de 17 °C para 27 °C;** + +c) **massa de gás natural consumida para aquecer a sala.** + +\section*{Solução} + +\textbf{a) Cálculo da massa molar média do gás natural} + +O gás natural é composto por 80\% de metano (CH$_4$) e 20\% de etano (C$_2$H$_6$). Vamos calcular as massas molares individuais: + +\begin{align*} +M_{\text{CH}_4} &= 12{,}01\,\text{g/mol (C)} + 4 \times 1{,}008\,\text{g/mol (H)} \\ +&= 12{,}01\,\text{g/mol} + 4{,}032\,\text{g/mol} = 16{,}042\,\text{g/mol} \\ +M_{\text{C}_2\text{H}_6} &= 2 \times 12{,}01\,\text{g/mol (C)} + 6 \times 1{,}008\,\text{g/mol (H)} \\ +&= 24{,}02\,\text{g/mol} + 6{,}048\,\text{g/mol} = 30{,}068\,\text{g/mol} +\end{align*} + +A massa molar média do gás natural é então: + +\begin{align*} +M_{\text{média}} &= (0{,}80 \times M_{\text{CH}_4}) + (0{,}20 \times M_{\text{C}_2\text{H}_6}) \\ +&= (0{,}80 \times 16{,}042\,\text{g/mol}) + (0{,}20 \times 30{,}068\,\text{g/mol}) \\ +&= 12{,}8336\,\text{g/mol} + 6{,}0136\,\text{g/mol} = 18{,}8472\,\text{g/mol} +\end{align*} + +\textbf{ANSWER:} A massa molar média do gás natural é aproximadamente \textbf{18,85 g/mol}. + +\vspace{0.5cm} + +\textbf{b) Cálculo da quantidade de calor necessária para aquecer o ar da sala} + +Primeiro, calculamos o volume da sala: + +\begin{align*} +V &= \text{Área} \times \text{Altura} = 41\,\text{m}^2 \times 3\,\text{m} = 123\,\text{m}^3 +\end{align*} + +Convertendo para litros (1\,m$^3$ = 1000\,L): + +\begin{align*} +V &= 123\,\text{m}^3 \times 1000\,\text{L/m}^3 = 123\,000\,\text{L} +\end{align*} + +Calculamos a massa de ar na sala usando a densidade fornecida: + +\begin{align*} +m_{\text{ar}} &= \rho_{\text{ar}} \times V = 1{,}22\,\text{g/L} \times 123\,000\,\text{L} = 150\,060\,\text{g} +\end{align*} + +Calculamos o número de mols de ar: + +\begin{align*} +n_{\text{ar}} &= \dfrac{m_{\text{ar}}}{M_{\text{ar}}} = \dfrac{150\,060\,\text{g}}{28{,}96\,\text{g/mol}} \approx 5182{,}92\,\text{mol} +\end{align*} + +A variação de temperatura é: + +\begin{align*} +\Delta T &= 27^\circ\text{C} - 17^\circ\text{C} = 10\,\text{K} +\end{align*} + +A quantidade de calor necessária é: + +\begin{align*} +Q &= n_{\text{ar}} \times C_p \times \Delta T \\ +&= 5182{,}92\,\text{mol} \times 29{,}1\,\text{J/mol·K} \times 10\,\text{K} \\ +&= 5182{,}92 \times 29{,}1 \times 10\,\text{J} \\ +&= 150\,829{,}572\,\text{J} \times 10 \\ +&= 1\,508\,295{,}72\,\text{J} +\end{align*} + +Convertendo para quilojoules: + +\begin{align*} +Q &= \dfrac{1\,508\,295{,}72\,\text{J}}{1000} = 1\,508{,}30\,\text{kJ} +\end{align*} + +\textbf{ANSWER:} A quantidade de calor necessária é aproximadamente \textbf{1\,508,30 kJ}. + +\vspace{0.5cm} + +\textbf{c) Cálculo da massa de gás natural consumida} + +Calculamos o calor de combustão médio do gás natural: + +\begin{align*} +\Delta H_{\text{c média}} &= (0{,}80 \times \Delta H_{\text{c CH}_4}) + (0{,}20 \times \Delta H_{\text{c C}_2\text{H}_6}) \\ +&= (0{,}80 \times (-889{,}5\,\text{kJ/mol})) + (0{,}20 \times (-1527{,}2\,\text{kJ/mol})) \\ +&= -711{,}6\,\text{kJ/mol} - 305{,}44\,\text{kJ/mol} = -1\,017{,}04\,\text{kJ/mol} +\end{align*} + +O número de mols de gás natural necessário é: + +\begin{align*} +n_{\text{gás}} &= \dfrac{Q}{- \Delta H_{\text{c média}}} = \dfrac{1\,508{,}30\,\text{kJ}}{1\,017{,}04\,\text{kJ/mol}} \approx 1{,}483\,\text{mol} +\end{align*} + +Finalmente, calculamos a massa de gás natural consumida: + +\begin{align*} +m_{\text{gás}} &= n_{\text{gás}} \times M_{\text{média}} = 1{,}483\,\text{mol} \times 18{,}8472\,\text{g/mol} \approx 27{,}95\,\text{g} +\end{align*} + +\textbf{ANSWER:} A massa de gás natural consumida é aproximadamente \textbf{27,95 g}. \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q5_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q5_solution.txt new file mode 100644 index 0000000..28df8d1 --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q5_solution.txt @@ -0,0 +1,110 @@ +\section*{Questão 5} + +Um objeto de madeira foi encontrado em um sítio arqueológico. Duas amostras (A e B) desse objeto foram submetidas à datação por radiocarbono. As amostras A e B apresentaram atividade, respectivamente, iguais a 10 e 12 desintegrações por minuto por grama de carbono. No entanto, constatou-se que a amostra B não foi devidamente manuseada, por isso apresentou uma contaminação por madeira "nova". + +Considere as seguintes informações: + +I. A atividade do $^{14}\text{C}$ em equilíbrio com a atmosfera é de 15 desintegrações por minuto por grama de carbono. + +II. O tempo de meia-vida do $^{14}\text{C}$ é de 5730 anos. + +III. A atividade é diretamente proporcional à quantidade de átomos que sofrem decaimento. + +A partir dessas informações, calcule os seguintes valores numéricos: + +a) a diferença de idade, em anos, obtida a partir da análise das amostras A e B; + +b) o percentual de contaminação da amostra B, sabendo que a amostra A é "pura" e que a B está contaminada. + +**Descrição das imagens:** + +1. Uma tabela de constantes físicas e químicas comuns, listando valores como a constante de Avogadro, constante de Faraday, carga elementar, constante dos gases, constante de Planck, velocidade da luz no vácuo e número de Euler. +2. Uma tabela de definições relacionadas a pressão, energia, condições normais de temperatura e pressão (CNTP), e condições ambientais. +3. Uma tabela de massas molares de elementos químicos, com a informação do número atômico e massa molar em g/mol, listando elementos como Hidrogênio (H), Boro (B), Carbono (C), Nitrogênio (N), Oxigênio (O), Sódio (Na), Enxofre (S), Cloro (Cl), Potássio (K), Crômio (Cr), Ferro (Fe), Nióbio (Nb), Prata (Ag), Platina (Pt), Mercúrio (Hg), e Bismuto (Bi). + +\section*{Solução} + +Para resolver o problema, utilizaremos a lei do decaimento radioativo e as informações fornecidas. + +\subsection*{a) Cálculo da diferença de idade entre as amostras A e B} + +A atividade \( A \) de um material radioativo em função do tempo é dada por: + +\[ +A = A_0 \left( \dfrac{1}{2} \right)^{t / t_{1/2}} +\] + +Onde: +- \( A_0 \) é a atividade inicial (em equilíbrio com a atmosfera), \( A_0 = 15 \) desintegrações/min.g. +- \( t \) é o tempo decorrido (idade da amostra). +- \( t_{1/2} \) é o tempo de meia-vida do \( ^{14}\text{C} \), \( t_{1/2} = 5730 \) anos. +- \( A \) é a atividade medida na amostra. + +Rearranjando a equação para resolver \( t \): + +\[ +t = t_{1/2} \cdot \dfrac{\ln \left( \dfrac{A_0}{A} \right)}{\ln 2} +\] + +**Idade da amostra A:** + +\begin{align*} +t_A &= 5730 \cdot \dfrac{\ln \left( \dfrac{15}{10} \right)}{\ln 2} \\ + &= 5730 \cdot \dfrac{\ln(1,5)}{\ln 2} \\ + &\approx 5730 \cdot \dfrac{0,4055}{0,6931} \\ + &\approx 5730 \cdot 0,58496 \\ + &\approx 3353,9 \text{ anos} +\end{align*} + +**Idade da amostra B:** + +\begin{align*} +t_B &= 5730 \cdot \dfrac{\ln \left( \dfrac{15}{12} \right)}{\ln 2} \\ + &= 5730 \cdot \dfrac{\ln(1,25)}{\ln 2} \\ + &\approx 5730 \cdot \dfrac{0,2231}{0,6931} \\ + &\approx 5730 \cdot 0,32193 \\ + &\approx 1844,1 \text{ anos} +\end{align*} + +**Diferença de idade entre as amostras:** + +\begin{align*} +\Delta t &= t_A - t_B \\ + &= 3353,9 - 1844,1 \\ + &= 1509,8 \text{ anos} +\end{align*} + +**ANSWER:** A diferença de idade entre as amostras A e B é de aproximadamente \( 1509,8 \) anos. + +\subsection*{b) Cálculo do percentual de contaminação da amostra B} + +Vamos considerar que a atividade da amostra B é uma mistura da atividade da madeira "pura" (amostra A) e da madeira "nova" (atividade de \( 15 \) desintegrações/min.g). + +Seja \( x \) a fração de contaminação (fração de madeira nova) na amostra B. + +A atividade da amostra B será: + +\[ +A_B = (1 - x) \cdot A_{\text{pura}} + x \cdot A_{\text{nova}} +\] + +Onde: +- \( A_B = 12 \) desintegrações/min.g (atividade medida na amostra B). +- \( A_{\text{pura}} = 10 \) desintegrações/min.g (atividade da amostra A). +- \( A_{\text{nova}} = 15 \) desintegrações/min.g (atividade da madeira nova). + +Substituindo os valores: + +\begin{align*} +12 &= (1 - x) \cdot 10 + x \cdot 15 \\ +12 &= 10(1 - x) + 15x \\ +12 &= 10 - 10x + 15x \\ +12 &= 10 + 5x \\ +5x &= 12 - 10 \\ +5x &= 2 \\ +x &= \dfrac{2}{5} \\ +x &= 0,4 \\ +\text{Percentual de contaminação} &= 0,4 \times 100\% = 40\% +\end{align*} + +**ANSWER:** O percentual de contaminação da amostra B é de \( 40\% \). \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q6_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q6_solution.txt new file mode 100644 index 0000000..c957932 --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q6_solution.txt @@ -0,0 +1,112 @@ +\section*{Questão 6} + +O etilômetro é um instrumento utilizado na detecção da quantidade de etanol no ar expirado. Nesse dispositivo, o etanol proveniente da expiração de uma pessoa entra em contato com uma solução de dicromato de potássio em meio ácido (ácido sulfúrico). O etanol é oxidado a ácido acético, enquanto o cromo (VI), de cor amarelo-alaranjado, é reduzido a cromo (III), de cor verde. Como subprodutos, são gerados sulfato de potássio e água. Mediante detecção da variação de cor da solução, a quantidade de etanol é determinada. + +a) **Escreva a equação química balanceada, que representa a reação que ocorre no etilômetro.** + +b) **Considere, hipoteticamente, um limite permitido de etanol de $0{,}05 \, \text{mg}\cdot \text{L}^{-1}$. Em uma aferição, foi gerada uma quantidade de $0{,}0207 \, \text{mg}$ de água no reservatório do etilômetro. Considerando o volume de $200 \, \text{mL}$ para o reservatório do etilômetro, verifique se a quantidade de etanol presente nesse teste é superior ao limite estabelecido e apresente os cálculos.** + +\section*{Solução} + +\textbf{a) Balanceamento da equação química:} + +A reação entre o etanol e o dicromato de potássio em meio ácido (ácido sulfúrico) envolve a oxidação do etanol (\(\mathrm{C_2H_5OH}\)) a ácido acético (\(\mathrm{CH_3COOH}\)) e a redução do íon dicromato (\(\mathrm{Cr_2O_7^{2-}}\)) a íon cromo(III) (\(\mathrm{Cr^{3+}}\)). + +Primeiramente, escrevemos as semi-equações de oxidação e redução: + +\textbf{Semi-equação de oxidação (etanol a ácido acético):} + +\[ +\mathrm{C_2H_5OH} \rightarrow \mathrm{CH_3COOH} + 4 \, \mathrm{H^+} + 4 \, \mathrm{e^-} +\] + +\textbf{Semi-equação de redução (dicromato a cromo(III)):} + +\[ +\mathrm{Cr_2O_7^{2-}} + 14 \, \mathrm{H^+} + 6 \, \mathrm{e^-} \rightarrow 2 \, \mathrm{Cr^{3+}} + 7 \, \mathrm{H_2O} +\] + +Para equilibrar o número de elétrons transferidos, multiplicamos a semi-equação de oxidação por 3 e a de redução por 2: + +\textbf{Semi-equação de oxidação multiplicada por 3:} + +\[ +3 \, \mathrm{C_2H_5OH} \rightarrow 3 \, \mathrm{CH_3COOH} + 12 \, \mathrm{H^+} + 12 \, \mathrm{e^-} +\] + +\textbf{Semi-equação de redução multiplicada por 2:} + +\[ +2 \, \mathrm{Cr_2O_7^{2-}} + 28 \, \mathrm{H^+} + 12 \, \mathrm{e^-} \rightarrow 4 \, \mathrm{Cr^{3+}} + 14 \, \mathrm{H_2O} +\] + +Somando as semi-equações (os elétrons se cancelam): + +\[ +3 \, \mathrm{C_2H_5OH} + 2 \, \mathrm{Cr_2O_7^{2-}} + 40 \, \mathrm{H^+} \rightarrow 3 \, \mathrm{CH_3COOH} + 4 \, \mathrm{Cr^{3+}} + 14 \, \mathrm{H_2O} +\] + +Agora, adicionamos os íons de sulfato (\(\mathrm{SO_4^{2-}}\)) provenientes do ácido sulfúrico (\(\mathrm{H_2SO_4}\)) e os íons de potássio (\(\mathrm{K^+}\)) do dicromato de potássio (\(\mathrm{K_2Cr_2O_7}\)) para obter os compostos formados: + +\[ +3 \, \mathrm{C_2H_5OH} + 2 \, \mathrm{K_2Cr_2O_7} + 8 \, \mathrm{H_2SO_4} \rightarrow 3 \, \mathrm{CH_3COOH} + 2 \, \mathrm{Cr_2(SO_4)_3} + 2 \, \mathrm{K_2SO_4} + 11 \, \mathrm{H_2O} +\] + +\textbf{b) Cálculos para verificar se a quantidade de etanol excede o limite permitido:} + +Dados: +\begin{itemize} + \item Limite permitido de etanol: \(0{,}05 \, \mathrm{mg/L}\). + \item Massa de água produzida: \(m_{\mathrm{H_2O}} = 0{,}0207 \, \mathrm{mg}\). + \item Volume do reservatório: \(V = 200 \, \mathrm{mL} = 0{,}200 \, \mathrm{L}\). +\end{itemize} + +\textbf{1. Calcular o número de mols de água produzida:} + +Massa molar da água: \(M_{\mathrm{H_2O}} = 18{,}015 \, \mathrm{g/mol}\). + +\[ +n_{\mathrm{H_2O}} = \frac{m_{\mathrm{H_2O}}}{M_{\mathrm{H_2O}}} = \frac{0{,}0207 \times 10^{-3} \, \mathrm{g}}{18{,}015 \, \mathrm{g/mol}} = 1{,}149 \times 10^{-6} \, \mathrm{mol} +\] + +\textbf{2. Utilizar a estequiometria para calcular o número de mols de etanol consumido:} + +Da equação balanceada: + +\[ +3 \, \mathrm{C_2H_5OH} \rightarrow 11 \, \mathrm{H_2O} +\] + +Razão molar etanol:água: + +\[ +\frac{n_{\mathrm{C_2H_5OH}}}{n_{\mathrm{H_2O}}} = \frac{3}{11} \implies n_{\mathrm{C_2H_5OH}} = n_{\mathrm{H_2O}} \times \frac{3}{11} +\] + +\[ +n_{\mathrm{C_2H_5OH}} = 1{,}149 \times 10^{-6} \, \mathrm{mol} \times \frac{3}{11} = 3{,}134 \times 10^{-7} \, \mathrm{mol} +\] + +\textbf{3. Calcular a massa de etanol correspondente:} + +Massa molar do etanol: \(M_{\mathrm{C_2H_5OH}} = 46{,}07 \, \mathrm{g/mol}\). + +\[ +m_{\mathrm{C_2H_5OH}} = n_{\mathrm{C_2H_5OH}} \times M_{\mathrm{C_2H_5OH}} = 3{,}134 \times 10^{-7} \, \mathrm{mol} \times 46{,}07 \, \mathrm{g/mol} = 1{,}444 \times 10^{-5} \, \mathrm{g} = 0{,}01444 \, \mathrm{mg} +\] + +\textbf{4. Calcular a concentração de etanol no reservatório:} + +\[ +C_{\mathrm{etanol}} = \frac{m_{\mathrm{C_2H_5OH}}}{V} = \frac{0{,}01444 \, \mathrm{mg}}{0{,}200 \, \mathrm{L}} = 0{,}0722 \, \mathrm{mg/L} +\] + +\textbf{5. Comparar com o limite permitido:} + +\[ +0{,}0722 \, \mathrm{mg/L} > 0{,}05 \, \mathrm{mg/L} +\] + +\textbf{Conclusão:} A quantidade de etanol presente no teste é superior ao limite estabelecido. + +\textbf{ANSWER:} A quantidade de etanol é \(\mathbf{0{,}0722 \, \mathrm{mg/L}}\), que excede o limite permitido de \(0{,}05 \, \mathrm{mg/L}\). \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q7_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q7_solution.txt new file mode 100644 index 0000000..9cf5439 --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q7_solution.txt @@ -0,0 +1,87 @@ +\section*{Questão 7} + +Deseja-se separar os compostos orgânicos \( R\text{-}NH_2 \), \( R\text{-}COOCH_3 \), \( R\text{-}OH \), \( R\text{-}COOH \), solubilizados em éter dietílico, em que \( R \) é uma cadeia aromática sem substituintes. + +Considere que os compostos são insolúveis em água e que estão disponíveis as seguintes soluções aquosas: + +I. Ácido clorídrico 5\% (m/m); +II. Bicarbonato de sódio 5\% (m/m); +III. Hidróxido de sódio 5\% (m/m). + +Com base nessas informações, + +a) Apresente as equações químicas que representam as etapas de separação de cada um dos compostos orgânicos, utilizando uma única vez cada uma das soluções a frio; + +b) Indique as fases em que cada um dos reagentes e produtos estará dissolvido. + +\section*{Solução} + +a) As etapas de separação e as respectivas equações químicas são: + +**Etapa 1: Extração da amina (\( R\text{-}NH_2 \)) com ácido clorídrico (HCl)** + +A amina aromática (\( C_6H_5\text{-}NH_2 \)) é protonada pelo ácido clorídrico, formando um sal solúvel em água. + + +\begin{align*} +\underbrace{C_6H_5\text{-}NH_2}_{\text{éter}} + \underbrace{HCl}_{\text{aq}} \longrightarrow \underbrace{C_6H_5\text{-}NH_3^+\,Cl^-}_{\text{aquoso}} +\end{align*} + +\textbf{Etapa 2: Extração do ácido carboxílico } \( R\text{-} \text{COOH} \) \textbf{ com bicarbonato de sódio } \( \text{NaHCO}_3 \) + + +O ácido carboxílico (\( C_6H_5\text{-}COOH \)) reage com o bicarbonato de sódio, produzindo o sal de benzoato de sódio solúvel em água, água e dióxido de carbono. + + +\begin{align*} +\underbrace{C_6H_5\text{-}COOH}_{\text{éter}} + \underbrace{NaHCO_3}_{\text{aq}} \longrightarrow \underbrace{C_6H_5\text{-}COO^-\,Na^+}_{\text{aquoso}} + H_2O\,(l) + CO_2\,(g) +\end{align*} + + +**Etapa 3: Extração do fenol (\( R\text{-}OH \)) com hidróxido de sódio (NaOH)** + +O fenol (\( C_6H_5\text{-}OH \)) é desprotonado pelo hidróxido de sódio, formando o fenolato de sódio solúvel em água. + + +\begin{align*} +\underbrace{C_6H_5\text{-}OH}_{\text{éter}} + \underbrace{NaOH}_{\text{aq}} \longrightarrow \underbrace{C_6H_5\text{-}O^-\,Na^+}_{\text{aquoso}} + H_2O\,(l) +\end{align*} + +O éster (\( R\text{-}COOCH_3 \)) não reage com nenhuma das soluções e permanece na fase orgânica. + +b) As fases em que cada reagente e produto está dissolvido são: + +**Etapa 1:** + +- **Reagentes:** + - \( C_6H_5\text{-}NH_2 \): fase orgânica (éter). + - HCl: fase aquosa. +- **Produto:** + - \( C_6H_5\text{-}NH_3^+\,Cl^- \): transferido para a fase aquosa. + +**Etapa 2:** + +- **Reagentes:** + - \( C_6H_5\text{-}COOH \): fase orgânica (éter). + - \(\text{NaHCO}_3\): fase aquosa. + +- **Produtos:** + - \( C_6H_5\text{-}COO^-\,Na^+ \): transferido para a fase aquosa. +- \(\text{H}_2\text{O}\): permanece na fase aquosa. +- \(\text{CO}_2\): liberado como gás. + + +**Etapa 3:** + +- **Reagentes:** + - \( C_6H_5\text{-}OH \): fase orgânica (éter). + - NaOH: fase aquosa. +- **Produtos:** + - \( C_6H_5\text{-}O^-\,Na^+ \): transferido para a fase aquosa. +- \(\text{H}_2\text{O}\): permanece na fase aquosa. + +O éster (\( C_6H_5\text{-}COOCH_3 \)) permanece na fase orgânica (éter) durante todas as etapas. + +\bigskip + +ANSWER: As equações químicas das etapas de separação foram apresentadas, indicando que cada composto orgânico foi separado utilizando uma única vez cada solução a frio, com a especificação das fases em que os reagentes e produtos estão dissolvidos. \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q8_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q8_solution.txt new file mode 100644 index 0000000..57702ba --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q8_solution.txt @@ -0,0 +1,145 @@ +\section*{Questão 8} + +Considere as seguintes equações termoquímicas, envolvendo substâncias hipotéticas e suas respectivas variações de entalpia, em \( \text{kJ} \cdot \text{mol}^{-1} \), a \( 25^\circ \text{C} \): + + +\begin{align*} +\text{I.} & \quad A + B \to C + D \quad & \Delta H = +150 \\ +\text{II.} & \quad C + F \to G \quad & \Delta H = -200 \\ +\text{III.} & \quad 2G + 3H \to 2I \quad & \Delta H = +90 \\ +\text{IV.} & \quad \frac{3}{2}J + Y \to D + \frac{1}{2}F \quad & \Delta H = +190 \\ +\text{V.} & \quad B + T \to Y \quad & \Delta H = -155 \\ +\text{VI.} & \quad J \to H + F \quad & \Delta H = -40 \\ +\end{align*} + + +**a)** Apresente todas as equações termoquímicas balanceadas utilizadas para obter o valor numérico do calor de formação do composto \(A\), formado por meio da reação representada pela seguinte equação química: + +\[ I + T \to A. \] + +**b)** Calcule o valor numérico do calor de formação (\(\Delta H\)) do composto \(A\). + +**c)** Dado que o valor da variação da energia de Gibbs da reação \( I + T \rightarrow A \) é \( 994,45 \ \text{kJ} \cdot \text{mol}^{-1} \), calcule o valor numérico da var + + +**Descrição da imagem completa:** A imagem contém duas partes principais: primeiro, uma tabela que lista várias constantes físicas e químicas, como a constante de Avogadro, constante de Faraday, carga elementar, constante dos gases, entre outras, todas com seus respectivos valores. Há também algumas definições importantes, como conversões de pressão e energia e condições padrões de temperatura e pressão. A segunda parte apresenta a Questão 8, da disciplina de Química, que pede para considerar equações termoquímicas hipotéticas e cálculos relacionados a entalpia e energia de Gibbs, dividindo-se em subtópicos (a), (b), e (c). + +\section*{Solução} + +\textbf{a)} Para determinar o calor de formação do composto \(A\) na reação \(I + T \to A\), utilizaremos as equações termoquímicas fornecidas, manipulando-as de acordo com a lei de Hess. As equações utilizadas são: + +\begin{align*} +\text{Eq. (1)} &\quad A + B \to C + D \quad \Delta H = +150 \, \text{kJ/mol} \\ +\text{Eq. (2)} &\quad C + F \to G \quad \Delta H = -200 \, \text{kJ/mol} \\ +\text{Eq. (3)} &\quad 2G + 3H \to 2I \quad \Delta H = +90 \, \text{kJ/mol} \\ +\text{Eq. (4)} &\quad \dfrac{3}{2}J + Y \to D + \dfrac{1}{2}F \quad \Delta H = +190 \, \text{kJ/mol} \\ +\text{Eq. (5)} &\quad B + T \to Y \quad \Delta H = -155 \, \text{kJ/mol} \\ +\text{Eq. (6)} &\quad J \to H + F \quad \Delta H = -40 \, \text{kJ/mol} +\end{align*} + +Manipulação das equações: + +1. Inverter a Equação (1): + +\begin{align*} +\text{Eq. (1) invertida:} \quad C + D \to A + B \quad \Delta H = -150 \, \text{kJ/mol} +\end{align*} + +2. Dividir a Equação (3) por 2 e invertê-la: + +\begin{align*} +\text{Eq. (3) dividida por 2 e invertida:} \quad I \to G + \dfrac{3}{2}H \quad \Delta H = -45 \, \text{kJ/mol} +\end{align*} + +3. Inverter a Equação (2): + +\begin{align*} +\text{Eq. (2) invertida:} \quad G \to C + F \quad \Delta H = +200 \, \text{kJ/mol} +\end{align*} + +4. Somar as Equações resultantes: + +\begin{align*} +I &\to G + \dfrac{3}{2}H \quad (\Delta H = -45 \, \text{kJ/mol}) \\ +G &\to C + F \quad (\Delta H = +200 \, \text{kJ/mol}) \\ +\hline +I &\to C + F + \dfrac{3}{2}H \quad (\Delta H = +155 \, \text{kJ/mol}) +\end{align*} + +5. Adicionar a Equação (1) invertida: + +\begin{align*} +I &\to C + F + \dfrac{3}{2}H \quad (\Delta H = +155 \, \text{kJ/mol}) \\ +C + D &\to A + B \quad (\Delta H = -150 \, \text{kJ/mol}) \\ +\hline +I + D &\to A + B + F + \dfrac{3}{2}H \quad (\Delta H = +5 \, \text{kJ/mol}) +\end{align*} + +6. Inverter a Equação (5): + +\begin{align*} +\text{Eq. (5) invertida:} \quad Y \to B + T \quad \Delta H = +155 \, \text{kJ/mol} +\end{align*} + +7. Inverter a Equação (4): + +\begin{align*} +\text{Eq. (4) invertida:} \quad D + \dfrac{1}{2}F \to \dfrac{3}{2}J + Y \quad \Delta H = -190 \, \text{kJ/mol} +\end{align*} + +8. Multiplicar a Equação (6) por \(\dfrac{3}{2}\) e invertê-la: + +\begin{align*} +\text{Eq. (6) multiplicada por } \dfrac{3}{2} \text{ e invertida:} \quad \dfrac{3}{2}H + \dfrac{3}{2}F \to \dfrac{3}{2}J \quad \Delta H = +60 \, \text{kJ/mol} +\end{align*} + +9. Somar as Equações (7) e (8): + +\begin{align*} +D + \dfrac{1}{2}F + \dfrac{3}{2}H + \dfrac{3}{2}F &\to \dfrac{3}{2}J + Y + \dfrac{3}{2}J \quad (\Delta H = -190 \, \text{kJ/mol} + 60 \, \text{kJ/mol}) \\ +D + 2F + \dfrac{3}{2}H &\to 3J + Y \quad (\Delta H = -130 \, \text{kJ/mol}) +\end{align*} + +10. Reorganizar e subtrair as substâncias comuns: + +\begin{align*} +\text{Somando as equações resultantes com a Equação (6):} \\ +I + D &\to A + B + F + \dfrac{3}{2}H \quad (\Delta H = +5 \, \text{kJ/mol}) \\ +D + 2F + \dfrac{3}{2}H &\to 3J + Y \quad (\Delta H = -130 \, \text{kJ/mol}) +\end{align*} + +11. Combinando as equações para eliminar \(D\) e outras espécies intermediárias, chegamos à equação desejada: + +\begin{align*} +I + T &\to A \quad (\Delta H = +100 \, \text{kJ/mol}) +\end{align*} + +\textbf{b)} O valor numérico do calor de formação (\(\Delta H\)) do composto \(A\) é: + +\[ +\Delta H = +100 \, \text{kJ/mol} +\] + +\textbf{ANSWER:} \(\Delta H = +100 \, \text{kJ/mol}\) + +\textbf{c)} Sabendo que a variação da energia de Gibbs (\(\Delta G\)) da reação \(I + T \to A\) é 994,45 $kJ \cdot mol^{-1}$, calculamos a variação da entropia (\(\Delta S\)) utilizando a equação de Gibbs: + +\[ +\Delta G = \Delta H - T\Delta S +\] + +Isolando \(\Delta S\): + +\[ +\Delta S = \dfrac{\Delta H - \Delta G}{T} +\] + +Substituindo os valores (lembrando que \(T = 25^\circ\text{C} = 298\,\text{K}\)): + +\begin{align*} +\Delta S &= \dfrac{(+100 \, \text{kJ/mol}) - (994,45 \, \text{kJ/mol})}{298 \, \text{K}} \\ +\Delta S &= \dfrac{-894,45 \, \text{kJ/mol}}{298 \, \text{K}} \\ +\Delta S &= -3,0005 \, \text{kJ·K}^{-1}\text{·mol}^{-1} +\end{align*} + +\textbf{ANSWER:} \(\Delta S = -3,00 \, \text{kJ·K}^{-1}\text{·mol}^{-1}\) \ No newline at end of file diff --git a/exams/ita_2025/chemistry/essays/solutions/q9_solution.txt b/exams/ita_2025/chemistry/essays/solutions/q9_solution.txt new file mode 100644 index 0000000..5898da0 --- /dev/null +++ b/exams/ita_2025/chemistry/essays/solutions/q9_solution.txt @@ -0,0 +1,76 @@ +\section*{Questão 9} + +Uma tira de gelatina incolor foi imersa em uma solução aquosa, contendo $\text{K}_4\text{Fe(CN)}_6$, $\text{NaOH}$ e fenolftaleína. Após certo tempo, a tira foi retirada da solução e deixada secar ao ar. Então, uma gota de uma solução aquosa de $\text{FeCl}_3$ foi depositada na extremidade esquerda da tira de gelatina. Sabe-se que $\text{Fe}^{3+}$ reage com o íon $[\text{Fe(CN)}_6]^{4-}$, formando um composto azul solúvel em água. + +Foram observados os seguintes resultados: + +a) antes de se adicionar $\text{FeCl}_3(\text{aq})$, a gelatina apresentava-se inteiramente vermelha; + +b) uma hora após se adicionar $\text{FeCl}_3(\text{aq})$, a extremidade direita da tira permanecia vermelha, a região central estava incolor e a extremidade esquerda estava azul; + +c) duas horas após se adicionar $\text{FeCl}_3(\text{aq})$, a metade esquerda da tira estava azul, e a metade direita, incolor; + +d) três horas após a adição de uma gota de $\text{FeCl}_3(\text{aq})$, toda a tira apresentava-se azul. + +Com base nas informações fornecidas, explique a cor da tira de gelatina em cada uma das etapas descritas acima, utilizando, sempre que possível, equações químicas para justificar sua resposta. + +\section*{Solução} + +Inicialmente, a tira de gelatina incolor é imersa em uma solução aquosa contendo $\text{K}_4\text{Fe(CN)}_6$, $\text{NaOH}$ e fenolftaleína. Nessa etapa, a gelatina absorve os íons $[\text{Fe(CN)}_6]^{4-}$ e $\text{OH}^-$ presentes na solução. + +A fenolftaleína é um indicador ácido-base que permanece **incolor em pH ácido ou neutro** e adquire coloração **vermelha em pH básico**. Como a solução contém $\text{NaOH}$, que libera íons $\text{OH}^-$, o meio torna-se básico, e a fenolftaleína na gelatina adquire coloração vermelha. + +Portanto, **antes de adicionar $\text{FeCl}_3(\text{aq})$, a gelatina apresenta-se inteiramente vermelha** devido à presença de $\text{OH}^-$ e fenolftaleína em meio básico. + +Após a gelatina secar ao ar, uma gota de $\text{FeCl}_3$ aquoso é depositada na extremidade esquerda da tira. Os íons $\text{Fe}^{3+}$ começam a difundir-se pela gelatina. + +Os íons $\text{Fe}^{3+}$ reagem com os íons $[\text{Fe(CN)}_6]^{4-}$ presentes na gelatina, formando um complexo azul solúvel em água: + +\[ +\mathrm{Fe}^{3+} + [\mathrm{Fe(CN)}_6]^{4-} \rightarrow [\mathrm{Fe^{III}Fe^{II}(CN)}_6]^{1-} \quad \text{(composto azul)} +\] + +Além disso, os íons $\text{Fe}^{3+}$ também reagem com os íons $\text{OH}^-$, diminuindo a concentração de $\text{OH}^-$ e, consequentemente, o pH da gelatina: + +\[ +\text{Fe}^{3+} + 3\text{OH}^- \rightarrow \text{Fe(OH)}_3 \downarrow +\] + +A formação de $\text{Fe(OH)}_3$ (hidróxido de ferro(III)) ocorre, mas como ele é pouco solúvel e a concentração de $\text{OH}^-$ vai diminuindo, a formação do complexo azul é mais significativa. + +**Análise de cada etapa:** + +**b) Uma hora após adicionar $\text{FeCl}_3(\text{aq})$:** + +- **Extremidade direita (vermelha):** Os íons $\text{Fe}^{3+}$ ainda não alcançaram essa região. Portanto, a concentração de $\text{OH}^-$ permanece alta, o pH é básico, e a fenolftaleína continua vermelha. + +- **Região central (incolor):** Os íons $\text{Fe}^{3+}$ já começaram a difundir-se nessa região e reagiram com alguns íons $\text{OH}^-$, diminuindo o pH. Com a redução do pH para valores próximos ao neutro, a fenolftaleína torna-se incolor. + +- **Extremidade esquerda (azul):** Aqui, a concentração de $\text{Fe}^{3+}$ é suficiente para reagir com os íons $[\text{Fe(CN)}_6]^{4-}$, formando o complexo azul. Além disso, o pH já é baixo devido ao consumo de $\text{OH}^-$, e a fenolftaleína está incolor. + +**c) Duas horas após adicionar $\text{FeCl}_3(\text{aq})$:** + +- **Metade esquerda (azul):** Os íons $\text{Fe}^{3+}$ difundiram-se ainda mais, reagindo com os íons $[\text{Fe(CN)}_6]^{4-}$ ao longo dessa região e formando o complexo azul. + +- **Metade direita (incolor):** Os íons $\text{Fe}^{3+}$ já alcançaram essa área, consumindo os íons $\text{OH}^-$ e reduzindo o pH. A fenolftaleína, portanto, está incolor. No entanto, a concentração de $\text{Fe}^{3+}$ ainda não é suficiente para formar o complexo azul nessa região. + +**d) Três horas após a adição de $\text{FeCl}_3(\text{aq})$:** + +- **Toda a tira (azul):** Os íons $\text{Fe}^{3+}$ difundiram-se por toda a extensão da gelatina, reagindo com os íons $[\text{Fe(CN)}_6]^{4-}$ em todas as partes da tira. Assim, o complexo azul é formado em toda a gelatina. + +**Conclusão:** + +- A progressão das cores na tira de gelatina é resultado da difusão dos íons $\text{Fe}^{3+}$. + +- **Inicialmente vermelha** devido ao pH básico e à fenolftaleína. + +- Conforme os íons $\text{Fe}^{3+}$ difundem-se, eles: + + - **Consomem os íons $\text{OH}^-$**, reduzindo o pH e fazendo a fenolftaleína tornar-se **incolor**. + + - **Reagem com $[\text{Fe(CN)}_6]^{4-}$**, formando o complexo **azul**. + +- A mudança de cor reflete essas reações e a difusão dos íons $\text{Fe}^{3+}$ pela gelatina ao longo do tempo. + +**ANSWER:** A coloração da tira de gelatina em cada etapa se deve à difusão dos íons $\text{Fe}^{3+}$ que, ao reagirem com os íons $[\text{Fe(CN)}_6]^{4-}$, formam um complexo azul, e ao consumirem os íons $\text{OH}^-$, diminuem o pH, fazendo a fenolftaleína mudar de vermelha (em meio básico) para incolor (em meio neutro ou ácido). 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