Question

Show by calculation whether the reaction $$ \mathrm{HF}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q) \quad \Delta G^{\circ}=18.0 \mathrm{~kJ} $$ is spontaneous at \(25^{\circ} \mathrm{C}\) when (a) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=0.78 \mathrm{M}\) and \([\mathrm{HF}]=0.24 \mathrm{M}\) (b) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=0.0030 \mathrm{M}\) and \([\mathrm{HF}]=1.85 \mathrm{M}\)

Short answer

a) [H+] = [F-] = 0.78 M and [HF] = 0.24 M b) [H+] = [F-] = 0.0030 M and [HF] = 1.85 M Answer: - The reaction is spontaneous for case (a) with concentrations: [H+] = [F-] = 0.78 M and [HF] = 0.24 M - The reaction is not spontaneous for case (b) with concentrations: [H+] = [F-] = 0.0030 M and [HF] = 1.85 M.

Step-by-step solution

Calculate the temperature in Kelvin and identify the given concentrations

Temperature in Celsius is given as 25°C. To convert it to Kelvin, we can use the following formula: $$ T (K) = T (°C) + 273.15 $$ So, T = 25 + 273.15 = 298 K. Now, let's identify the given concentrations for each case: (a) [H+] = [F-] = 0.78 M and [HF] = 0.24 M (b) [H+] = [F-] = 0.0030 M and [HF] = 1.85 M

Calculate the reaction quotient Q for each case

Q is the ratio of the product concentrations to the reactant concentrations. In this case, it can be expressed as: $$ Q = \frac{[\mathrm{H}^{+}][\mathrm{F}^{-}]}{[\mathrm{HF}]} $$ For case (a): $$ Q_a = \frac{(0.78)(0.78)}{0.24} = 2.53 $$ For case (b): $$ Q_b = \frac{(0.0030)(0.0030)}{1.85} = 4.86 \times 10^{-6} $$

Calculate ΔG for each case

We can now calculate ΔG for both cases using the formula: $$ \Delta G = \Delta G^{\circ} + RT\ln Q $$ For case (a): $$ \Delta G_a = 18000 + (8.314)(298)\ln 2.53 = 18000 + 5.474.85 = -672.85 \thinspace J $$ For case (b): $$ \Delta G_b = 18000 + (8.314)(298)\ln (4.86 \times 10^{-6}) = 18000 - 12456.56 = 5543.44 \thinspace J $$

Determine if the reaction is spontaneous

For a reaction to be spontaneous, ΔG should be negative. For case (a), ΔG is negative, so the reaction is spontaneous. But for case (b), ΔG is positive, so the reaction is not spontaneous. So in conclusion, - The reaction is spontaneous for case (a) which has the following concentrations: [H+] = [F-] = 0.78 M and [HF] = 0.24 M - The reaction is not spontaneous for case (b) which has the following concentrations: [H+] = [F-] = 0.0030 M and [HF] = 1.85 M.