Question
Question: The \( {E_{cell}} \) for \( Ag(s)|AgI(satd)||A{g^ + }(0.10M)|Ag(s) \) is \( + 0.413\;V \) . What is ...
The Ecell for Ag(s)∣AgI(satd)∣∣Ag+(0.10M)∣Ag(s) is +0.413V . What is the value of Ksp for AgI ?
A. 1.0×10−8
B. 1.0×10−7
C. 1.0×10−14
D. 1.0×10−16
Solution
The solubility product is the equilibrium constant for a substance which dissolves in an aqueous solution and breaks into its respective ions. It represents the level at which a solute can be dissolved in the solution. It is denoted by Ksp .
Complete answer:
As per question, the given cell is as follows:
Ag(s)∣AgI(satd)∣∣Ag+(0.10M)∣Ag(s)
We know that AgI dissociates to form silver and iodide ion, so the cell can alternatively be represented as follows:
Ag(s)∣Ag+(xM)∣∣Ag+(0.10M)∣Ag(s)
Here, we have considered the unknown concentration of Ag+ ion as x .
As the given cell is concentration cell, so the standard reduction potential of the cell will be zero, so according to Nernst equation:
Ecell=Ecello−n0.0592logc2c1
Where, c1 and c2 are the concentration of unknown and known Ag+ ions respectively and because Ecello=0 for concentration cells therefore, the equation can be represented as follows:
⇒Ecell=−n0.0592logc2c1
Substituting values of Ecell , n, c1 and c2 :
⇒+0.413=−10.0592log0.1x
⇒log0.1x=−6.97
Taking antilog on both sides of the expression:
⇒0.1x=10−6.97
⇒x=1.07×10−8M
Therefore, the concentration of saturated AgI=1.07×10−8M for the given concentration cell. Now, the dissociation of AgI takes place as follows:
AgI⇌Ag++I−
The ICE table for the above dissociation reaction is as follows:
| [AgI] | [Ag+] | [I−]
---|---|---|---
Initial concentration| 1.07×10−8M | 0 | 0
Change | −1.07×10−8M | +1.07×10−8M | +1.07×10−8M
Equilibrium concentration| 0 | 1.07×10−8M | 1.07×10−8M
The expression for solubility product can be written as follows:
Ksp=[Ag+][I−]
Substituting values as per given in ICE table:
⇒Ksp=1.07×10−8×1.07×10−8
⇒Ksp=1.0×10−16
Hence, the value of Ksp for AgI is 1.0×10−16 .
Thus, option (D) is the correct answer.
Note:
It is important to note that the value of Ksp for silver iodide in the given concentration cell can alternatively be calculated by directly substituting the value of c1 as Ksp in the Nernst equation. Also, remember that a concentration cell is an electrolytic cell that is composed of two half cells with the same electrodes but differ in concentrations.