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Chapter 19: Problem 78

Consider the reaction $\mathrm{CH}_{4}(\mathrm{~g})+4 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)+$ \(4 \mathrm{HCl}(g) .\). (a) Using data from Appendix C, calculate $\Delta G^{\circ}\( at \)298 \mathrm{~K} .(\mathbf{b})\( Calculate \)\Delta G\( at \)298 \mathrm{~K}\( if the reaction mixture consists of \)50.7 \mathrm{kPa}$ of \(\mathrm{CH}_{4}(g), 25.3 \mathrm{kPa}\) of $\mathrm{Cl}_{2}(g), 10.13 \mathrm{kPa}$ of \(\mathrm{CCl}_{4}(\mathrm{~g})\) and \(15.2 \mathrm{kPa}\) of \(\mathrm{HCl}(\mathrm{g})\)

Short Answer

Expert verified
(a) \(\Delta G^{\circ} = -191.5 \textrm{ kJ/mol}\) is obtained by calculating \(\Delta H^{\circ} - T\Delta S^{\circ}\) using the standard enthalpy and entropy change values. (b) \(\Delta G = -183.9 \textrm{ kJ/mol}\) is calculated by finding the reaction quotient (Q) using given partial pressures and substituting it along with the calculated \(\Delta G^{\circ}\) into the equation \(\Delta G = \Delta G^{\circ} + RT \ln(Q)\).

Step by step solution

01

Calculate the standard enthalpy and entropy changes

Using data from Appendix C, we determine the standard molar enthalpies (ΔH°) and standard molar entropies (ΔS°) of all species involved in the reaction. Then, we calculate the respective values for the entire reaction.
02

Calculate the standard Gibbs free energy change

Now, we substitute the calculated values of ΔH° and ΔS° in the equation ΔG° = ΔH° - TΔS° and calculate ΔG° at the given temperature 298K.
03

Calculate the reaction quotient (Q)

Based on the provided partial pressures of reactants and products, calculate the reaction quotient Q = [CCl₄][HCl]⁴ / ([CH₄][Cl₂]⁴).
04

Calculate ΔG using the reaction quotient

Finally, use the calculated ΔG° and reaction quotient (Q) values to find ΔG at the given temperature using the equation, ΔG = ΔG° + RT ln(Q).

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Most popular questions from this chapter

The reaction $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)$ is highly spontaneous. A classmate calculates the entropy change for this reaction and obtains a large negative value for \(\Delta S^{\circ}\). Did your classmate make a mistake in the calculation? Explain.

Indicate whether each statement is true or false. (a) Unlike enthalpy, where we can only ever know changes in \(H,\) we can know absolute values of $S .(\mathbf{b})\( If you heat a gas such as \)\mathrm{CO}_{2}$, you will increase its degrees of translational, rotational and vibrational motions. (c) \(\mathrm{CO}_{2}(g)\) and \(\mathrm{Ar}(g)\) have nearly the same molar mass. At a given temperature, they will have the same number of microstates.

Consider the reaction $$ \mathrm{PbCO}_{3}(s) \rightleftharpoons \mathrm{PbO}(s)+\mathrm{CO}_{2}(g) $$ Using data in Appendix \(\mathrm{C}\), calculate the equilibrium pressure of \(\mathrm{CO}_{2}\) in the system at $$ \text { (a) } 400^{\circ} \mathrm{C} \text { and } $$ $$ \text { (b) } 180^{\circ} \mathrm{C} \text { . } $$

The element sodium (Na) melts at \(97.8^{\circ} \mathrm{C},\) and its molar enthalpy of fusion is $\Delta H_{\text {fus }}=2.60 \mathrm{~kJ} / \mathrm{mol}$. (a) When molten sodium solidifies to \(\mathrm{Na}(\mathrm{s})\), is \(\Delta S\) positive or negative? (b) Calculate the value of \(\Delta S\) when \(50.0 \mathrm{~g}\) of \(\mathrm{Na}(l)\) solidifies at \(97.8^{\circ} \mathrm{C}\).

Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces. (a) The two arrangements of top faces shown here can be viewed as two possible microstates of the system. Explain. (b) To which state does each microstate correspond? (c) How many possible states are there for the system? (d) Which state or states have the highest entropy? Explain. (e) Which state or states have the lowest entropy? Explain. (f) Calculate the absolute entropy of the two-dice system.
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