Question 19.7: An electrochemical cell is constructed for the purpose of de...
An electrochemical cell is constructed for the purpose of determining the K_{sp} of silver cyanide (\text{AgCN}) at 25°\text{C}. One half-cell consists of a silver electrode in a 1.00-M solution of silver nitrate. The other half-cell consists of a silver electrode in a saturated solution of silver cyanide. The cell potential is measured and found to be 0.470 \text{V}. Determine the concentration of silver ion in the saturated silver cyanide solution and the value of K_{sp} for \text{AgCN}.
Strategy Use Equation 19.7 to solve for the unknown concentration of silver ion. The half-cell with the higher \text{Ag}^+ (1.0 M \text{AgNO}_3) concentration will be the cathode; the half-cell with the lower, unknown \text{Ag}^+ concentration (saturated \text{AgCN} solution) will be the anode. The overall reaction is \text{Ag}^+(1.0 M) → \text{Ag}^+(x M).
Setup Because this is a concentration cell, E^\circ_\text{cell} = 0 \text{V}. The reaction quotient, Q, is (x M)/(1.00 M); and the value of n is 1.
E = E^\circ − \frac{0.0592 \text{V}}{n} \text{log} Q Equation 19.7
E = E^\circ − \frac{0.0592 \text{V}}{n} \text{log} Q
0.470 \text{V} = 0 − \frac{0.0592 \text{V}}{1 } \text{log} \frac{x}{1.00}
–7.939 = \text{log} \frac{x}{1.00}
10^{–7.939} = 1.15 × 10^{–8} = \text{log} \frac{x}{1.00}
x = 1.15 × 10^{–8}
Therefore,[\text{Ag}^+] = 1.15 × 10^{–8} M and K_{sp} for \text{AgCN} = x^2 = 1.3 × 10^{–16}