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Chapter 18: Problem 62

In the Mond process for the purification of nickel, carbon monoxide is reacted with heated nickel to produce \(\mathrm{Ni}(\mathrm{CO})_{4},\) which is a gas and can therefore be separated from solid impurities: $$ \mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g) $$ Given that the standard free energies of formation of \(\mathrm{CO}(g)\) and \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) are \(-137.3 \mathrm{~kJ} / \mathrm{mol}\) and \(-587.4 \mathrm{~kJ} / \mathrm{mol}\), respectively, calculate the equilibrium constant of the reaction at \(80^{\circ} \mathrm{C}\). Assume that \(\Delta G_{f}^{\circ}\) is temperature independent.

Short Answer

Expert verified
The equilibrium constant \(K\) for the reaction at \(80^{\circ}C\) is approximately \(57224.29\).

Step by step solution

01

Calculate the Free Energy Change for the Reaction

To calculate the free energy change \(\Delta G\) for the reaction, use the formula \(\Delta G = \sum G_f(\text{products}) - \(\sum G_f(\text{reactants})\). The free energy of formation (\(G_f\)) of \(Ni(CO)_4\) is given as -587.4 kJ/mol, the \(G_f\) of \(CO\) is given as -137.3 kJ/mol. The \(G_f\) of \(Ni\) is 0 because \(Ni\) is in its elemental form. Thus, \(\Delta G = (-587.4) - 4\times(-137.3) = -38.2 \,kJ/mol\).
02

Convert the Temperature to Kelvin

The temperature is given in Celsius, but we need it in Kelvin for the formula. To convert it, use the formula \(T(K) = T(C) + 273.15\), which gives \(80 + 273.15 = 353.15\,K\).
03

Calculate the Equilibrium Constant

Now we can use the formula \(\Delta G = -RT \cdot lnK\) to calculate the equilibrium constant \(K\). Rearranging the formula gives \(K = e^{(-\Delta G / RT)} = e^{((-(-38.2\times10^3) \, J/mol) / (8.314 \, J/mol·K \cdot 353.15\,K))}\). After evaluating the expression inside the exponential, the answer turns out to be \(K = 57224.29\).

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Most popular questions from this chapter

Explain the difference between \(\Delta G\) and \(\Delta G^{\circ}\).

Large quantities of hydrogen are needed for the synthesis of ammonia. One preparation of hydrogen involves the reaction between carbon monoxide and steam at \(300^{\circ} \mathrm{C}\) in the presence of a copper-zinc catalyst: $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) $$.

State the second law of thermodynamics in words and express it mathematically.

Which of the following processes are spontaneous and which are nonspontaneous at a given temperature? (a) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q)\) saturated soln (b) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q) \quad\) unsaturated soln (c) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q)\) supersaturated soln

The equilibrium constant \(\left(K_{P}\right)\) for the reaction $$ \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) $$ is 4.40 at \(2000 \mathrm{~K}\). (a) Calculate \(\Delta G^{\circ}\) for the reaction. (b) Calculate \(\Delta G\) for the reaction when the partial pressures are \(P_{\mathrm{H}_{2}}=0.25 \mathrm{~atm}, P_{\mathrm{CO}_{2}}=0.78 \mathrm{~atm}\) \(P_{\mathrm{H}_{2} \mathrm{O}}=0.66 \mathrm{~atm},\) and \(P_{\mathrm{CO}}=1.20 \mathrm{~atm}\)
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