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Chapter 19: Problem 95

Consider the following three reactions: $$ \begin{array}{l}{\text { (i) } \operatorname{Ti}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \operatorname{TiCl}_{4}(g)} \\ {\text { (ii) } \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{CCl}_{4}(g)+6 \mathrm{HCl}(g)} \\ {\text { (iii) } \mathrm{BaO}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{BaCO}_{3}(s)}\end{array} $$ (a) For each of the reactions, use data in Appendix \(C\) to calculate \(\Delta H^{\circ}, \Delta G^{\circ}, K,\) and \(\Delta S^{\circ}\) at \(25^{\circ} \mathrm{C}\) . (b) Which of these reactions are spontaneous under standard conditions at \(25^{\circ} \mathrm{C} ?(\mathbf{c})\) For each of the reactions, predict the manner in which the change in free energy varies with an increase in temperature.

Short Answer

Expert verified
To find the thermodynamic parameters for each of the given reactions at 25°C, use the following steps: 1. Calculate ∆H° using standard enthalpies of formation values from the appendix and the equation ∆H° = ∑n∆H°(products) - ∑m∆H°(reactants). 2. Calculate ∆S° using standard molar entropy values from the appendix and the equation ∆S° = ∑n∆S°(products) - ∑m∆S°(reactants). 3. Calculate ∆G° using the equation ∆G° = ∆H° - T∆S°, where T = 298 K. 4. Calculate K using the equation K = exp(−∆G°/RT), where R = 8.314 J/(mol K) and T = 298 K. Determine if each reaction is spontaneous at 25°C by checking if ∆G° is negative. Predict how ∆G changes with temperature by analyzing the signs of ∆H° and ∆S° according to the given rules.

Step by step solution

01

Calculate ∆H° for each reaction

To calculate the enthalpy change (∆H°) for each reaction, use the following equation: ∆H° = ∑n∆H°(products) - ∑m∆H°(reactants), where n and m are coefficients in the balanced chemical equation, and ∆H° represents the standard enthalpy of formation. You need to find the enthalpy of formation values for each species from the appendix.
02

Calculate ∆S° for each reaction

To calculate the entropy change (∆S°) for each reaction, use the following equation: ∆S° = ∑n∆S°(products) - ∑m∆S°(reactants), where n and m are coefficients in the balanced chemical equation, and ∆S° represents the standard molar entropy. You need to find the molar entropy values for each species from the appendix.
03

Calculate ∆G° for each reaction

Once you have the values for ∆H° and ∆S°, you can calculate the free energy change (∆G°) for each reaction using the following equation: ∆G° = ∆H° - T∆S°, where T is the temperature in Kelvin (298 K in this case)
04

Calculate K for each reaction

To calculate the equilibrium constant (K) for each reaction, use the following equation: K=exp(−∆G°/RT), where R is the gas constant 8.314 J/(mol K), and T is the temperature in Kelvin (298 K in this case)
05

Determine which reactions are spontaneous under standard conditions at 25°C

If ∆G° is negative, the reaction is spontaneous under standard conditions at 25°C; if it is positive, the reaction is non-spontaneous.
06

Predict the behavior of ∆G with an increase in temperature

Use the equation ∆G° = ∆H° - T∆S° to analyze the behavior of ∆G with increasing temperature: - If ∆H° > 0 and ∆S° > 0, the reaction will be spontaneous at high temperatures. - If ∆H° < 0 and ∆S° < 0, the reaction will be spontaneous at low temperatures. - If ∆H° > 0 and ∆S° < 0, the reaction will be non-spontaneous at any temperature. - If ∆H° < 0 and ∆S° > 0, the reaction will be spontaneous at any temperature. Perform these steps for each of the given reactions and analyze the results accordingly.

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Most popular questions from this chapter

The conversion of natural gas, which is mostly methane into products that contain two or more carbon atoms, such as ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right),\) is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) $$ In practice, this reaction is carried out in the presence of oxygen: $$ 2 \mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ (a) Using the data in Appendix C, calculate \(K\) for these reactions at \(25^{\circ} \mathrm{C}\) and \(500^{\circ} \mathrm{C}\) . (b) Is the difference in \(\Delta G^{\circ}\) for the two reactions due primarily to the enthalpy term \((\Delta H)\) or the entropy term \((-T \Delta S) ?\) (c) Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the "Chemistry and Life" box in Section 19.7 . (d) The reaction of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) to form \(\mathrm{C}_{2} \mathrm{H}_{6}\) and \(\mathrm{H}_{2} \mathrm{O}\) must be carried out carefully to avoid a competing reaction. What is the most likely competing reaction?

Use data in Appendix C to calculate \(\Delta H^{\circ}, \Delta S^{\circ},\) and \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) for each of the following reactions. $$ \begin{array}{l}{\text { (a) } 4 \mathrm{Cr}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s)} \\ {\text { (b) } \mathrm{BaCO}_{3}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)} \\\ {\text { (c) } 2 \mathrm{P}(s)+10 \mathrm{HF}(g) \longrightarrow 2 \mathrm{PF}_{5}(g)+5 \mathrm{H}_{2}(g)} \\ {\text { (d) } \mathrm{K}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{KO}_{2}(s)}\end{array} $$

Indicate whether each statement is true or false. (a) The third law of thermodynamics says the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) "Translational motion" of molecules refers to their change in spatial location as a func-tion of time. ( c ) "Rotational" and "vibrational" motions contribute to the entropy in atomic gases like He and Xe.(d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.

(a) For each of the following reactions, predict the sign of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) without doing any calculations. (b) Based on your general chemical knowledge, predict which of these reactions will have \(K>1 .\) (c) In each case, indicate whether \(K\) should increase or decrease with increasing temperature. $$ \begin{array}{l}{\text { (i) } 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{MgO}(s)} \\ {\text { (ii) } 2 \mathrm{KI}(s) \rightleftharpoons 2 \mathrm{K}(g)+\mathrm{I}_{2}(g)} \\ {\text { (iii) } \mathrm{Na}_{2}(g) \rightleftharpoons 2 \mathrm{Na}(g)} \\ {\text { (iv) } 2 \mathrm{V}_{2} \mathrm{O}_{5}(s) \rightleftharpoons 4 \mathrm{V}(s)+5 \mathrm{O}_{2}(g)}\end{array} $$

The normal freezing point of \(n\) -octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) is \(-57^{\circ} \mathrm{C}\) . (a) Is the freezing of \(n\) -octane an endothermic or exothermic process? (b) In what temperature range is the freezing of \(n\) -octane a spontaneous process? (c) In what temperature range is it a nonspontaneous process? (d) Is there any temperature at which liquid \(n\) -octane and solid \(n\) -octane are in equilibrium? Explain.
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