Excess silver powder is shaken at $298\ \text{K}$ with a solution of iron(III) perchlorate, $[\text{Fe}^{3+}] = 0.100\ \text{mol L}^{-1}$, in dilute perchloric acid. The acid stops the iron(III) ions from hydrolysing, and perchlorate does not react. The reaction is $\text{Ag}(s) + \text{Fe}^{3+}(aq) \rightleftharpoons \text{Ag}^+(aq) + \text{Fe}^{2+}(aq)$. At the start there are no $\text{Ag}^+$ or $\text{Fe}^{2+}$ ions. Take $E^\circ(\text{Fe}^{3+}/\text{Fe}^{2+}) = 0.77\ \text{V}$, $E^\circ(\text{Ag}^+/\text{Ag}) = 0.80\ \text{V}$ and $\dfrac{2.303RT}{F} = 0.059\ \text{V}$. Treat the solution as ideal, and take its volume as fixed. The mixture is left until it reaches equilibrium. What is $[\text{Ag}^+]$ at equilibrium? Give the answer in $\text{mmol L}^{-1}$, to two decimal places.