Calculate the solubility of AgI in 0.10 M NaI solution at 25 ° C. K _sp for AgI is 8.5×10^{- 17} at 25 ° C.

Question

Quizplus · Accepted Answer

First, we need to write out the equilibrium expression for the dissolution of AgI in water:

AgI(s) ⇌ Ag⁺(aq) + I⁻(aq)

Next, we need to add in the effect of the NaI solution:

AgI(s) ⇌ Ag⁺(aq) + I⁻(aq)

I⁻(aq) + Na⁺(aq) ⇌ NaI(aq)

The Ksp expression now becomes:

Ksp = [Ag⁺][I⁻]

However, we also need to consider the effect of the presence of Na⁺ ions on the solubility of AgI. This is done using the common ion effect, where the solubility of a salt decreases when a common ion is added to the solution.

Using an ICE table, we can calculate the concentration of I⁻ ions:

I⁻(aq) + Na⁺(aq) ⇌ NaI(aq)

I⁻(aq)      0.10  + x          x

Na⁺(aq)     0.10           x

The equilibrium concentration of I⁻ ions is equal to the initial concentration plus the concentration added from the NaI solution (x). The equilibrium concentration of Na⁺ ions is also equal to x.

Substituting these values into the Ksp expression:

Ksp = [Ag⁺][I⁻]

Ksp = (x)(8.5×10⁻¹⁷)

Substituting x = [I⁻] into the above expression, we get:

Ksp = (0.10 + [I⁻])(8.5×10⁻¹⁷)

Since the solubility of AgI is equal to the concentration of I⁻ ions at equilibrium, we can rearrange the equation to solve for the solubility:

Solubility = [I⁻] = (Ksp / (0.10 + [I⁻]))

There is no simple algebraic way to solve for the concentration of I⁻ ions, so we must use an iterative method or a calculator. Using an iterative method, we can make an initial guess that [I⁻] is equal to the initial concentration added by the NaI solution, which is 0.10 M. This gives:

Solubility = [I⁻] = (8.5×10⁻¹⁷ / (0.10 + 0.10)) = 4.25×10⁻⁹ M

This value is not exact, but it is close enough to the actual value that we can assume it is correct to the appropriate number of significant figures. The correct answer is option D: 8.5×10⁻¹⁶ M.

Calculate the Solubility of AgI in 0