题目 1 · long_free_response
10 分Answer the following questions related to cobalt and its compounds.
(a) Cobalt is a transition metal that exhibits multiple oxidation states.
(i) Write the complete ground-state electron configuration for a neutral \(\text{Co}\) atom.
(ii) When cobalt forms the \(\text{Co}^{2+}\) cation, electrons are removed from which subshell first? State both the principal quantum number and the letter corresponding to the subshell.
A student designs an experiment to determine the empirical formula of an unknown cobalt iodide compound, \(\text{Co}_x\text{I}_y(s)\). The student places a sample of pure cobalt metal into a crucible and heats it in the presence of excess iodine vapor inside a fume hood according to the reaction below:
\[ x\,\text{Co}(s) + \frac{y}{2}\,\text{I}_2(g) \rightarrow \text{Co}_x\text{I}_y(s) \]
The student heats the crucible until the reaction is complete and all excess unreacted \(\text{I}_2\) has sublimed away. The recorded data are shown in the table.
| Measurement | Mass (g) |
| :--- | :--- |
| Mass of empty crucible | \(28.450\text{ g}\) |
| Mass of crucible and \(\text{Co}(s)\) before reaction | \(29.628\text{ g}\) |
| Mass of crucible and \(\text{Co}_x\text{I}_y(s)\) after reaction | \(34.704\text{ g}\) |
(b) Calculate the mass, in grams, of iodine that reacted with the cobalt to form \(\text{Co}_x\text{I}_y(s)\).
(c) Calculate the number of moles of iodine atoms present in the sample of \(\text{Co}_x\text{I}_y(s)\).
(d) The student used \(0.0200\text{ mol}\) of \(\text{Co}(s)\) in the reaction. Determine the empirical formula of the cobalt iodide produced.
(e) If a small amount of the solid product splattered out of the crucible during heating, would the calculated number of moles of iodine in the empirical formula be greater than, less than, or equal to the actual value? Justify your answer.
(f) Cobalt is also utilized in rechargeable electrochemical cells. Relevant standard reduction potentials are provided in the table below.
| Reduction Half-Reaction | \(E^\circ\text{ (V)}\) |
| :--- | :--- |
| \(\text{Co}^{2+}(aq) + 2e^- \rightarrow \text{Co}(s)\) | \(-0.28\) |
| \(\text{Ag}^+(aq) + e^- \rightarrow \text{Ag}(s)\) | \(+0.80\) |
| \(\text{CoO}_2(s) + \text{H}_2\text{O}(l) + e^- \rightarrow \text{CoO(OH)}(s) + \text{OH}^-(aq)\) | \(+0.60\) |
(i) Write the balanced net ionic equation for the thermodynamically favorable reaction that occurs spontaneously between a \(\text{Co}^{2+}/\text{Co}\) half-cell and an \(\text{Ag}^+/\text{Ag}\) half-cell under standard conditions.
(ii) Calculate the standard cell potential, \(E^\circ_{\text{cell}}\), for the reaction in part (f)(i).
(iii) Calculate the value of the standard Gibbs free energy change, \(\Delta G^\circ\), in \(\text{kJ/mol}_{\text{rxn}}\), for the overall reaction in part (f)(i).
(iv) A student operates a sealed, rigid voltaic cell utilizing the reaction from part (f)(i). The student claims that the overall mass of the sealed cell decreases during discharge because the cobalt anode is oxidized and loses mass. Do you agree or disagree with the student's claim? Justify your answer.
(a) Cobalt is a transition metal that exhibits multiple oxidation states.
(i) Write the complete ground-state electron configuration for a neutral \(\text{Co}\) atom.
(ii) When cobalt forms the \(\text{Co}^{2+}\) cation, electrons are removed from which subshell first? State both the principal quantum number and the letter corresponding to the subshell.
A student designs an experiment to determine the empirical formula of an unknown cobalt iodide compound, \(\text{Co}_x\text{I}_y(s)\). The student places a sample of pure cobalt metal into a crucible and heats it in the presence of excess iodine vapor inside a fume hood according to the reaction below:
\[ x\,\text{Co}(s) + \frac{y}{2}\,\text{I}_2(g) \rightarrow \text{Co}_x\text{I}_y(s) \]
The student heats the crucible until the reaction is complete and all excess unreacted \(\text{I}_2\) has sublimed away. The recorded data are shown in the table.
| Measurement | Mass (g) |
| :--- | :--- |
| Mass of empty crucible | \(28.450\text{ g}\) |
| Mass of crucible and \(\text{Co}(s)\) before reaction | \(29.628\text{ g}\) |
| Mass of crucible and \(\text{Co}_x\text{I}_y(s)\) after reaction | \(34.704\text{ g}\) |
(b) Calculate the mass, in grams, of iodine that reacted with the cobalt to form \(\text{Co}_x\text{I}_y(s)\).
(c) Calculate the number of moles of iodine atoms present in the sample of \(\text{Co}_x\text{I}_y(s)\).
(d) The student used \(0.0200\text{ mol}\) of \(\text{Co}(s)\) in the reaction. Determine the empirical formula of the cobalt iodide produced.
(e) If a small amount of the solid product splattered out of the crucible during heating, would the calculated number of moles of iodine in the empirical formula be greater than, less than, or equal to the actual value? Justify your answer.
(f) Cobalt is also utilized in rechargeable electrochemical cells. Relevant standard reduction potentials are provided in the table below.
| Reduction Half-Reaction | \(E^\circ\text{ (V)}\) |
| :--- | :--- |
| \(\text{Co}^{2+}(aq) + 2e^- \rightarrow \text{Co}(s)\) | \(-0.28\) |
| \(\text{Ag}^+(aq) + e^- \rightarrow \text{Ag}(s)\) | \(+0.80\) |
| \(\text{CoO}_2(s) + \text{H}_2\text{O}(l) + e^- \rightarrow \text{CoO(OH)}(s) + \text{OH}^-(aq)\) | \(+0.60\) |
(i) Write the balanced net ionic equation for the thermodynamically favorable reaction that occurs spontaneously between a \(\text{Co}^{2+}/\text{Co}\) half-cell and an \(\text{Ag}^+/\text{Ag}\) half-cell under standard conditions.
(ii) Calculate the standard cell potential, \(E^\circ_{\text{cell}}\), for the reaction in part (f)(i).
(iii) Calculate the value of the standard Gibbs free energy change, \(\Delta G^\circ\), in \(\text{kJ/mol}_{\text{rxn}}\), for the overall reaction in part (f)(i).
(iv) A student operates a sealed, rigid voltaic cell utilizing the reaction from part (f)(i). The student claims that the overall mass of the sealed cell decreases during discharge because the cobalt anode is oxidized and loses mass. Do you agree or disagree with the student's claim? Justify your answer.
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解题
(a)(i) Ground-state electron configuration of neutral cobalt (\(Z = 27\)):
\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7\) or \([\text{Ar}]\,4s^2 3d^7\) (or \([\text{Ar}]\,3d^7 4s^2\)).
(a)(ii) Transition metals lose their outermost valence electrons first upon ionization. Therefore, electrons are removed from the \(4s\) subshell first.
(b) Mass of \(\text{I}\) in product = (Mass of crucible and product) \(-\) (Mass of crucible and \(\text{Co}\))
\[ \text{Mass of I} = 34.704\text{ g} - 29.628\text{ g} = 5.076\text{ g I} \]
(c) Moles of \(\text{I}\) atoms:
\[ n_{\text{I}} = 5.076\text{ g I} \times \frac{1\text{ mol I}}{126.90\text{ g I}} = 0.04000\text{ mol I} \]
(d) Mole ratio of \(\text{I}\) to \(\text{Co}\):
\[ \frac{0.04000\text{ mol I}}{0.0200\text{ mol Co}} = \frac{2.00\text{ mol I}}{1.00\text{ mol Co}} \]
Empirical formula: \(\text{CoI}_2\).
(e) Less than. If solid product splatters out of the crucible, the final recorded mass of crucible and product will be too low. Since the mass of iodine is calculated by subtracting the initial mass of cobalt and crucible from the final mass, the calculated mass (and therefore calculated moles) of iodine will be less than the actual value.
(f)(i) The spontaneous reaction pairs the oxidation of \(\text{Co}\) with the reduction of \(\text{Ag}^+\):
Anode (oxidation): \(\text{Co}(s) \rightarrow \text{Co}^{2+}(aq) + 2e^-\)
Cathode (reduction): \(2\,\text{Ag}^+(aq) + 2e^- \rightarrow 2\,\text{Ag}(s)\)
Net ionic equation: \(\text{Co}(s) + 2\,\text{Ag}^+(aq) \rightarrow \text{Co}^{2+}(aq) + 2\,\text{Ag}(s)\)
(f)(ii) Standard cell potential:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = +0.80\text{ V} - (-0.28\text{ V}) = +1.08\text{ V} \]
(f)(iii) Gibbs free energy calculation:
\[ \Delta G^\circ = -nFE^\circ = -(2\text{ mol } e^-)\left(96{,}485\text{ C/mol } e^-\right)(1.08\text{ J/C}) = -208{,}408\text{ J/mol}_{\text{rxn}} = -208\text{ kJ/mol}_{\text{rxn}} \]
(f)(iv) Disagree. The battery is a closed system. Although the cobalt anode dissolves into solution as \(\text{Co}^{2+}\), silver ions in solution are simultaneously reduced and deposited onto the cathode as solid \(\text{Ag}\). No matter enters or leaves the system, so the total mass of the sealed battery remains constant according to the law of conservation of mass.
\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7\) or \([\text{Ar}]\,4s^2 3d^7\) (or \([\text{Ar}]\,3d^7 4s^2\)).
(a)(ii) Transition metals lose their outermost valence electrons first upon ionization. Therefore, electrons are removed from the \(4s\) subshell first.
(b) Mass of \(\text{I}\) in product = (Mass of crucible and product) \(-\) (Mass of crucible and \(\text{Co}\))
\[ \text{Mass of I} = 34.704\text{ g} - 29.628\text{ g} = 5.076\text{ g I} \]
(c) Moles of \(\text{I}\) atoms:
\[ n_{\text{I}} = 5.076\text{ g I} \times \frac{1\text{ mol I}}{126.90\text{ g I}} = 0.04000\text{ mol I} \]
(d) Mole ratio of \(\text{I}\) to \(\text{Co}\):
\[ \frac{0.04000\text{ mol I}}{0.0200\text{ mol Co}} = \frac{2.00\text{ mol I}}{1.00\text{ mol Co}} \]
Empirical formula: \(\text{CoI}_2\).
(e) Less than. If solid product splatters out of the crucible, the final recorded mass of crucible and product will be too low. Since the mass of iodine is calculated by subtracting the initial mass of cobalt and crucible from the final mass, the calculated mass (and therefore calculated moles) of iodine will be less than the actual value.
(f)(i) The spontaneous reaction pairs the oxidation of \(\text{Co}\) with the reduction of \(\text{Ag}^+\):
Anode (oxidation): \(\text{Co}(s) \rightarrow \text{Co}^{2+}(aq) + 2e^-\)
Cathode (reduction): \(2\,\text{Ag}^+(aq) + 2e^- \rightarrow 2\,\text{Ag}(s)\)
Net ionic equation: \(\text{Co}(s) + 2\,\text{Ag}^+(aq) \rightarrow \text{Co}^{2+}(aq) + 2\,\text{Ag}(s)\)
(f)(ii) Standard cell potential:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = +0.80\text{ V} - (-0.28\text{ V}) = +1.08\text{ V} \]
(f)(iii) Gibbs free energy calculation:
\[ \Delta G^\circ = -nFE^\circ = -(2\text{ mol } e^-)\left(96{,}485\text{ C/mol } e^-\right)(1.08\text{ J/C}) = -208{,}408\text{ J/mol}_{\text{rxn}} = -208\text{ kJ/mol}_{\text{rxn}} \]
(f)(iv) Disagree. The battery is a closed system. Although the cobalt anode dissolves into solution as \(\text{Co}^{2+}\), silver ions in solution are simultaneously reduced and deposited onto the cathode as solid \(\text{Ag}\). No matter enters or leaves the system, so the total mass of the sealed battery remains constant according to the law of conservation of mass.
评分标准
(a)(i) [1 point] For the correct ground-state electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7\) or \([\text{Ar}]\,4s^2 3d^7\).
(a)(ii) [1 point] For identifying the \(4s\) subshell (must include both principal quantum number 4 and letter s).
(b) [1 point] For the correct calculated mass of iodine with appropriate units: \(34.704\text{ g} - 29.628\text{ g} = 5.076\text{ g}\).
(c) [1 point] For the correct calculated moles of iodine atoms: \(0.04000\text{ mol I}\) (accept \(0.0400\text{ mol}\)).
(d) [1 point] For the correct empirical formula consistent with part (c): \(\text{CoI}_2\) with supporting whole-number mole ratio calculation shown.
(e) [1 point] For choosing 'less than' AND providing a valid justification connecting the loss of mass from splattering to a decreased calculated mass/moles of iodine.
(f)(i) [1 point] For the correct balanced net ionic equation: \(\text{Co}(s) + 2\,\text{Ag}^+(aq) \rightarrow \text{Co}^{2+}(aq) + 2\,\text{Ag}(s)\) (states of matter not required).
(f)(ii) [1 point] For the correct calculated value: \(E^\circ_{\text{cell}} = +1.08\text{ V}\) (or consistent with half-reactions chosen in (f)(i)).
(f)(iii) [1 point] For the correct calculated value of \(\Delta G^\circ\) in \(\text{kJ/mol}_{\text{rxn}}\) including correct algebraic negative sign: \(-208\text{ kJ/mol}_{\text{rxn}}\) (using \(n = 2\)).
(f)(iv) [1 point] For disagreeing and providing a valid justification (e.g., stating that the battery is a closed/sealed system so total mass is conserved, or noting that mass lost at the anode is offset by mass gained at the cathode).
(a)(ii) [1 point] For identifying the \(4s\) subshell (must include both principal quantum number 4 and letter s).
(b) [1 point] For the correct calculated mass of iodine with appropriate units: \(34.704\text{ g} - 29.628\text{ g} = 5.076\text{ g}\).
(c) [1 point] For the correct calculated moles of iodine atoms: \(0.04000\text{ mol I}\) (accept \(0.0400\text{ mol}\)).
(d) [1 point] For the correct empirical formula consistent with part (c): \(\text{CoI}_2\) with supporting whole-number mole ratio calculation shown.
(e) [1 point] For choosing 'less than' AND providing a valid justification connecting the loss of mass from splattering to a decreased calculated mass/moles of iodine.
(f)(i) [1 point] For the correct balanced net ionic equation: \(\text{Co}(s) + 2\,\text{Ag}^+(aq) \rightarrow \text{Co}^{2+}(aq) + 2\,\text{Ag}(s)\) (states of matter not required).
(f)(ii) [1 point] For the correct calculated value: \(E^\circ_{\text{cell}} = +1.08\text{ V}\) (or consistent with half-reactions chosen in (f)(i)).
(f)(iii) [1 point] For the correct calculated value of \(\Delta G^\circ\) in \(\text{kJ/mol}_{\text{rxn}}\) including correct algebraic negative sign: \(-208\text{ kJ/mol}_{\text{rxn}}\) (using \(n = 2\)).
(f)(iv) [1 point] For disagreeing and providing a valid justification (e.g., stating that the battery is a closed/sealed system so total mass is conserved, or noting that mass lost at the anode is offset by mass gained at the cathode).