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Chapter 17: Problem 100

Consider the dissociation of a weak acid HA \(\left(K_{\mathrm{a}}=4.5 \times 10^{-3}\right)\) in water: $$ \mathrm{HA}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{A}^{-}(a q) $$ Calculate \(\Delta G^{\circ}\) for this reaction at \(25^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The standard Gibbs free energy change for the dissociation of the weak acid HA in water at 25°C is ΔG° = 13.39 kJ/mol.

Step by step solution

01

Convert temperature to Kelvin

First, we need to convert the given temperature from Celsius to Kelvin. The temperature is given as 25°C. To convert it to Kelvin, we add 273.15: $$ T = 25 + 273.15 = 298.15 \ \mathrm{K} $$
02

Calculate Gibbs free energy change

Now we can use the formula to find ΔG°, which relates the equilibrium constant, Ka, and the standard Gibbs free energy change, ΔG°: $$ \Delta G^{\circ} = -RT\ln K $$ Plugging in the known values, R = 8.314 J/mol·K, T = 298.15 K, and Ka = 4.5 x 10⁻³: $$ \Delta G^{\circ} = -(8.314 \ \mathrm{J/mol \cdot K})(298.15 \ \mathrm{K})\ln(4.5 \times 10^{-3}) $$
03

Solve for ΔG°

Now, we compute the standard Gibbs free energy change: $$ \Delta G^{\circ} = -(8.314)(298.15) \cdot (-5.41) $$ $$ \Delta G^{\circ} = 13389 \ \mathrm{J/mol} = 13.39 \ \mathrm{kJ/mol} $$ So, the standard Gibbs free energy change for the dissociation of the weak acid HA in water at 25°C is 13.39 kJ/mol.

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Most popular questions from this chapter

You have a \(1.00\) - \(L\) sample of hot water \(\left(90.0^{\circ} \mathrm{C}\right)\) sitting open in a \(25.0^{\circ} \mathrm{C}\) room. Eventually the water cools to \(25.0^{\circ} \mathrm{C}\) while the temperature of the room remains unchanged. Calculate \(\Delta S_{\text {surr }}\) for this process. Assume the density of water is \(1.00 \mathrm{~g} / \mathrm{cm}^{3}\) over this temperature range, and the heat capacity of water is constant over this temperature range and equal to \(75.4 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\).

Which of the following reactions (or processes) are expected to have a negative value for \(\Delta S^{\circ}\) ? a. \(\mathrm{SiF}_{6}(a q)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)+\mathrm{SiF}_{4}(g)\) b. \(4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\) c. \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{COCl}_{2}(g)\) d. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) e. \(\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\)

Hydrogen cyanide is produced industrially by the following exothermic reaction: Is the high temperature needed for thermodynamic or kinetic reasons?

Carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\) and benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) form ideal solutions. Consider an equimolar solution of \(\mathrm{CCl}_{4}\) and \(\mathrm{C}_{6} \mathrm{H}_{6}\) at \(25^{\circ} \mathrm{C}\). The vapor above the solution is collected and condensed. Using the following data, determine the composition in mole fraction of the condensed vapor.

What types of experiments can be carried out to determine whether a reaction is spontaneous? Does spontaneity have any relationship to the final equilibrium position of a reaction? Explain.
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