Determine [Zn2 ], [CN–], and [HCN] in a saturated solution of Zn(CN)2 with a fixed pH of 2.640. The Ksp for Zn(CN)2 is 3.0 × 10–16. The Ka for HCN is 6.2 × 10–10.

I need to know what equations to use to find the answer not just how to get it

Zn(CN)2 ==> Zn^2+ + 2CN^-

.....................+
.....................H^+
.....................v
.....................v
.....................HCN
Note that the added H^+ form HCN with the anion and that forces the solubility equilibrium t the right which increases the solubility of the salt.
Ksp = (Zn^+)(CN^-)^2
So let S = solubility Zn(CN)2 which makes Zn = S and CN^- = 2S*X where X is the fraction of HCN in the form of CN^-
X = Ka/(H^+ + Ka)
From pH you get X, 2S*X gives you CN, 100-X gives you fraction in HCN and you solve the Ksp equation to give you Zn^2+

To determine the concentrations of [Zn2+], [CN–], and [HCN] in a saturated solution of Zn(CN)2 with a fixed pH of 2.640, we can use the equations that relate to the dissociation of the compound and the acid-base equilibrium of HCN.

First, let's consider the dissociation of Zn(CN)2:
Zn(CN)2 ⇌ Zn2+ + 2CN–

Since Zn(CN)2 is a sparingly soluble salt, we can use the solubility product constant (Ksp) to relate the concentrations of the ions in the equilibrium expression.

Ksp = [Zn2+][CN–]^2

We can assume that the concentration of Zn2+ is equal to x, and then the concentration of CN– would be 2x since the stoichiometric coefficient is 2.

Next, let's look at the acid-base dissociation of HCN:
HCN ⇌ H+ + CN–

The equilibrium constant for this reaction is known as the acid dissociation constant (Ka).

Ka = [H+][CN–]/[HCN]

From this equation, we can assume that the concentration of HCN is equal to y, and the concentration of CN– is y as well since the stoichiometric coefficient is 1.

Now, we need to consider the relationship between pH and [H+]. The pH is defined as the negative logarithm of the concentration of H+ ions:

pH = -log[H+]

Given the value of pH as 2.640, we can convert it to [H+] using the following equation:

[H+] = 10^(-pH)

Now, we have all the information needed to find the concentrations.

To summarize, the equations we will use are:

Ksp = [Zn2+][CN–]^2
Ka = [H+][CN–]/[HCN]
pH = -log[H+]
[H+] = 10^(-pH)

Using these equations, you can solve for the concentrations of [Zn2+], [CN–], and [HCN] in the saturated solution of Zn(CN)2.