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Chapter 19: Problem 60

Using data from Appendix \(\mathrm{C}\) , calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous at 298 \(\mathrm{K}\) under standard conditions. $$ \begin{array}{l}{\text { (a) } 2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)} \\ {\text { (b) } \mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (c) } \mathrm{CH}_{4}(g)+4 \mathrm{F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)} \\ {\text { (d) } 2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)}\end{array} $$

Short Answer

Expert verified
For each reaction, we calculate \(\Delta G^{\circ}\) using the formula \[\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\]. (a) \(\Delta G^{\circ}\)=-109.8 kJ/mol; spontaneous at 298 K (b) \(\Delta G^{\circ}\)=91.0 kJ/mol; nonspontaneous at 298 K (c) \(\Delta G^{\circ}\)=-216.2 kJ/mol; spontaneous at 298 K (d) \(\Delta G^{\circ}\)=46.9 kJ/mol; nonspontaneous at 298 K

Step by step solution

01

Find \(\Delta H^{\circ}\) for the reaction

Use the values for standard enthalpy of formation (\(\Delta H_f^{\circ}\)) for each compound from Appendix C. Subtract the sum of \(\Delta H_f^{\circ}\) of the reactants from the sum of \(\Delta H_f^{\circ}\) of the products.
02

Find \(\Delta S^{\circ}\) for the reaction

Use the values for standard entropy (\(S^{\circ}\)) for each compound from Appendix C. Subtract the sum of \(S^{\circ}\) of the reactants from the sum of \(S^{\circ}\) of the products.
03

Calculate \(\Delta G^{\circ}\) for the reaction

Use the formula \[\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\] to calculate \(\Delta G^{\circ}\) for the reaction at 298 K.
04

Determine the spontaneity of the reaction

If \(\Delta G^{\circ}\) is negative, the reaction is spontaneous at 298 K under standard conditions. If \(\Delta G^{\circ}\) is positive, the reaction is nonspontaneous at that temperature. Repeat these steps for each reaction (a), (b), (c), and (d).

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Most popular questions from this chapter

(a) Is the standard free-energy change, \(\Delta G^{\circ},\) always larger than \(\Delta G ?(\mathbf{b})\) For any process that occurs at constant temperature and pressure, what is the significance of \(\Delta G=0\) ? (c) For a certain process, \(\Delta G\) is large and negative. Does this mean that the process, necessarily has a low activation barrier?

Does the entropy of the system increase, decrease, or stay the same when (a) a solid melts, (b) a gas liquefies, (c) a solid sublimes?

For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0,\) and \(w=0 .\) (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. (c) What is the "driving force" for the expansion of the gas: enthalpy or entropy?

For each of the following pairs, predict which substance has the higher entropy per mole at a given temperature: (a) \(\operatorname{Ar}(l)\) or \(\operatorname{Ar}(g),(\mathbf{b}) \operatorname{He}(g)\) at 3 atm pressure or \(\operatorname{He}(g)\) at 1.5 atm pressure, (c) 1 mol of \(\mathrm{Ne}(g)\) in 15.0 \(\mathrm{L}\) or 1 \(\mathrm{mol}\) of \(\mathrm{Ne}(g)\) in \(1.50 \mathrm{L},(\mathbf{d}) \mathrm{CO}_{2}(g)\) or \(\mathrm{CO}_{2}(s) .\)

Consider the decomposition of barium carbonate: $$ \mathrm{BaCO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{CO}_{2}(g) $$ Using data from Appendix \(\mathrm{C}\) , calculate the equilibrium pressure of \(\mathrm{CO}_{2}\) at (a) 298 \(\mathrm{K}\) and \((\mathbf{b}) 1100 \mathrm{K} .\)
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