Final answer:
To determine the pH of a 0.050 M HCN solution, we can use the given Ka value and the equilibrium expression for the acid dissociation reaction. By assuming that the concentration of H+ ions and CN- ions will be equal, we can solve for the concentration of H+ ions and calculate the pH.
Step-by-step explanation:
To determine the pH of a 0.050 M HCN solution, we need to use the given Ka value and the equilibrium expression for the acid dissociation reaction:
HCN(aq) ↔ H+(aq) + CN-(aq)
The equilibrium constant expression is Ka = [H+][CN-]/[HCN]. Since the initial concentration of HCN is given as 0.050 M, we can assume that the change in concentration of HCN will be small when it dissociates. Therefore, we can neglect x in the denominator and write the equilibrium expression as Ka = [H+][CN-].
Given that Ka = 4.9 x 10-10, we can assume that the concentration of H+ ions and CN- ions will be equal since HCN is a weak acid and does not dissociate completely. Therefore, [H+] = [CN-].
Let x be the concentration of H+ and CN- ions. Then, according to the equilibrium expression, [H+] = x and [CN-] = x.
Substituting these values into the equilibrium expression, we have:
4.9 x 10-10 = (x)(x)
Solving for x gives x = 7.0 x 10-6 M. Since [H+] = x, the pH of the solution is equal to the negative logarithm of x:
pH = -log(7.0 x 10-6) ≈ 5.16