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Chapter 17: Problem 19

Use Table \(17.1\) to calculate \(\Delta S^{\circ}\) for each of the following reactions. (a) \(2 \mathrm{Cl}^{-}(a q)+\mathrm{I}_{2}(s) \longrightarrow \mathrm{Cl}_{2}(g)+2 \mathrm{I}^{-}(a q)\) (b) \(\mathrm{SO}_{4}{ }^{2-}(a q)+4 \mathrm{H}^{+}(a q)+\mathrm{Cd}(s) \longrightarrow\) \(\mathrm{Cd}^{2+}(a q)+\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (c) \(2 \mathrm{Br}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Br}_{2}(l)+\mathrm{H}_{2}(g)+2 \mathrm{OH}^{-}(a q)\)

Short Answer

Expert verified
Question: Calculate the standard entropy change for the following reactions using the data provided in Table 17.1: (a) 2Cl⁻(aq) + I₂(s) → Cl₂(g) + 2I⁻(aq) (b) SO₄²⁻(aq) + 4H⁺(aq) + Cd(s) → Cd²⁺(aq) + SO₂(g) + 2H₂O(l) (c) 2Br⁻(aq) + 2H₂O(l) → Br₂(l) + H₂(g) + 2OH⁻(aq)

Step by step solution

01

(a) Calculate the entropy for the reactants and products

First, we will find the entropy for the reactants and products using the values from Table \(17.1\). For the reactants: \(2\mathrm{Cl}^{-}(a q)\) and \(\mathrm{I}_{2}(s)\), For the products: \(\mathrm{Cl}_{2}(g)\) and \(2\mathrm{I}^{-}(a q)\). Note: Remember to multiply the individual entropy values by the stoichiometric coefficients before calculating the entropy change.
02

(a) Calculate the standard entropy change, \(\Delta S^{\circ}\)

Now that we have the entropies for the reactants and products, we can calculate the standard entropy change for the reaction using the following formula: \(\Delta S^{\circ} = S_{\text{products}} - S_{\text{reactants}}\)
03

(b) Calculate the entropy for the reactants and products

For the reactants: \(\mathrm{SO}_{4}^{2-}(a q)\), \(4\mathrm{H}^{+}(a q)\), and \(\mathrm{Cd}(s)\), For the products: \(\mathrm{Cd}^{2+}(a q)\), \(\mathrm{SO}_{2}(g)\), and \(2\mathrm{H}_{2}\mathrm{O}(l)\). Proceed similarly as in part (a).
04

(b) Calculate the standard entropy change, \(\Delta S^{\circ}\)

Use the same formula as in part (a) to calculate the standard entropy change for the second reaction.
05

(c) Calculate the entropy for the reactants and products

For the reactants: \(2\mathrm{Br}^{-}(a q)\) and \(2\mathrm{H}_{2}\mathrm{O}(l)\), For the products: \(\mathrm{Br}_{2}(l)\), \(\mathrm{H}_{2}(g)\), and \(2\mathrm{OH}^{-}(a q)\). Proceed similarly as in part (a).
06

(c) Calculate the standard entropy change, \(\Delta S^{\circ}\)

Use the same formula as in part (a) to calculate the standard entropy change for the third reaction.

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Most popular questions from this chapter

Consider the reaction $$ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{NO}(g) \quad K=4.4 \times 10^{-19} $$ (a) Calculate \(\Delta G^{\circ}\) for the reaction at \(25^{\circ} \mathrm{C}\). (b) Calculate \(\Delta G_{i}^{\circ}\) for \(\mathrm{N}_{2} \mathrm{O}\) at \(25^{\circ} \mathrm{C}\).

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)\) (b) \(\mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(g)\) (c) \(\mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s)\)

The overall reaction that occurs when sugar is metabolized is $$ \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)+12 \mathrm{O}_{2}(g) \longrightarrow 12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) $$ For this reaction, \(\Delta H^{\circ}\) is \(-5650 \mathrm{~kJ}\) and \(\Delta G^{\circ}\) is \(-5790 \mathrm{~kJ}\) at \(25^{\circ} \mathrm{C}\). (a) If \(25 \%\) of the free energy change is actually converted to useful work, how many kilojoules of work are obtained when one gram of sugar is metabolized at body temperature, \(37^{\circ} \mathrm{C}\) ? (b) How many grams of sugar would a 120 -lb woman have to eat to get the energy to climb the Jungfrau in the Alps, which is \(4158 \mathrm{~m}\) high? \(\left(w=9.79 \times 10^{-3} \mathrm{mh}\right.\), where \(w=\) work in kilojoules, \(m\) is body mass in kilograms, and \(h\) is height in meters.)

Given the following standard free energies at \(25^{\circ} \mathrm{C}\), $$ \begin{array}{ll} \mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow 2 \mathrm{NO}(g)+\frac{3}{2} \mathrm{O}_{2}(g) & \Delta G^{\circ}=-59.2 \mathrm{~kJ} \\ \mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) & \Delta G^{\circ}=-35.6 \mathrm{~kJ} \end{array} $$ calculate \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) for the reaction $$ 2 \mathrm{NO}_{2}(g)+{ }_{2}^{1} \mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g) $$

At \(25^{\circ} \mathrm{C}\), a \(0.13 \mathrm{M}\) solution of a weak acid, \(\mathrm{HB}\), has a \(\mathrm{pH}\) of \(3.71\). What is \(\Delta G^{\circ}\) for $$ \mathrm{H}^{+}(a q)+\mathrm{B}^{-}(a q) \rightleftharpoons \mathrm{HB}(a q) $$
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