At 298 K the equilibrium constant for Cu(s) + 2Ag+(aq) Cu2+(aq) + 2Ag(s) is 2 x 10¹⁵. For the reaction (1/2) Cu2+(aq) + Ag(s) (1/2) Cu(s) + Ag+(aq) the equilibrium constant is x x 10⁻⁸. Find the value of x (nearest integer).

Question

At 298 K the equilibrium constant for Cu(s) + 2Ag+(aq) <-> Cu2+(aq) + 2Ag(s) is 2 x 10¹⁵. For the reaction (1/2) Cu2+(aq) + Ag(s) <-> (1/2) Cu(s) + Ag+(aq) the equilibrium constant is x x 10⁻⁸. Find the value of x (nearest integer).

Accepted Answer

2. Reversing the first reaction gives 1/K1 and halving all coefficients takes the square root, so K2 = (1/(2x10¹⁵))^(1/2) = sqrt(5x10⁻¹⁶) = 2.24x10⁻⁸, giving x approximately 2.

At 298 K the equilibrium constant for Cu(s) + 2Ag+(aq) <-> Cu2+(aq) + 2Ag(s) is 2 x 10¹⁵. For the reaction (1/2) Cu2+(aq) + Ag(s) <-> (1/2) Cu(s) + Ag+(aq) the equilibrium constant is x x 10⁻⁸. Find the value of x (nearest integer).

Solution

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