Question: The solubility of a salt in water increases if either ion of the salt undergoes hydrolysis. Comput the molar solubility of AgCN in water assuming no hydrolysis. B) compute the molar solubility of AnCN in water assuming hydrolysis occurs.
The equation would be AgCN goes to Ag + CN. You would get S^2= Ksp value. Is this right? I'm not sure i'm setting this up right. How do you solve when hydrolysis occurs in the system?
Right, S = sqrt Ksp for no hydrolysis.
With hydrolysis, here is what you have.
AgCN ==> Ag+ + CN^-
and CN^- + HOH ==> HCN + OH^-
Let S = solubility AgCN, then (Ag^+) = S and total (Ag^+) = (CN^-) + (HCN)
so S = (CN^-) + (HCN).
For HCN we can write a Ka,
Ka = (H^+)(CN^-)/(HCN)
Since the problem doesn't list a H^+ (which would make it even more soluble), I would use 1 x 10^-7 for (H^+) in the Ka expression and solve for
(HCN). Check my work but I believe
(HCN) = 1 x 10^-7*(CN^-)/Ka.
Look up Ka and (HCN) = some number*(CN^-). Then
S = (CN^-) + (HCN from above) and solve for (CN^-) in terms of S.
Then use Ksp expression to solve for S.
Using 7.2 x 10^-11 for Ka for HCN, I obtain 8.5 x 10^-6 for solubility with no hydrolysis and 5.9 x 10^-5 for solubility with hydrolysis (or its about 10x more soluble with hydrolysis).
I couldn't find a ksp value for the AgCn. How do you know to use a Ka value
I made a typo.
Ka for HCN = 2.1 x 10^-9
and Ksp for AgCN = 7.2 x 10^-11 according to my quant book (about 15 years old). However, the final values i quoted still are ok; i.e., I used the correct values in my calculations but I didn't copy them correctly when I posted my response. Are you asking how I know to use a Ka for HCN. Because HCN is a weak acid. That's why CN^- hydrolyzes.
To accurately compute the molar solubility of AgCN in water, we need to consider the effect of hydrolysis.
First, in the absence of hydrolysis, the dissolution equation for AgCN in water can be written as:
AgCN(s) ⇌ Ag+(aq) + CN-(aq)
To solve this, we need to set up an equilibrium expression using the solubility product constant (Ksp). The Ksp expression for AgCN is:
Ksp = [Ag+][CN-]
Since AgCN dissociates into one Ag+ ion and one CN- ion, we have:
Ksp = [Ag+][CN-] = S × S = S^2
Here, S represents the molar solubility of AgCN in mol/L.
To solve for the molar solubility (S) of AgCN, we need to know the Ksp value of AgCN, which is not provided in the question. Therefore, we cannot directly compute the molar solubility without this information.
However, if we assume hydrolysis occurs, the hydrolysis reactions for the Ag+ and CN- ions can be represented as follows:
Ag+ + H2O ⇌ AgOH + H+
CN- + H2O ⇌ HCN + OH-
Now, we need to consider the hydrolysis of Ag+ and CN- ions and its impact on solubility. If hydrolysis occurs, the solubility of AgCN will decrease because some of the Ag+ and CN- ions will no longer be available to form AgCN.
To compute the molar solubility of AgCN in water assuming hydrolysis occurs, you need additional information related to the hydrolysis equilibrium constants for Ag+ and CN-. Without these values, we cannot proceed with the calculation.
If you have the hydrolysis equilibrium constants, you can set up the equilibrium expressions for hydrolysis, solve the system of equations including the dissolution reaction, and calculate the molar solubility accounting for hydrolysis.