Electrochemisry. Candy Chemist wishes to determine the concentration of CrO4^2- by electrochemical means in solution, and subsequently the Ksp of Ag2CrO4. She sets up one half-cell comprised of the Ag+|Ag couple (E=+0.799V) and a second half-cell in which a silver elctrode is coated with Ag2CrO4 (E=+0.446V). This cell may be written as Ag2CrO4+2e- --->2Ag+CrO4^2-

a. Calculate the Ecell for the Ag2CrO4 half-reaction at 25 c when the CrO4^2- = 1.0x10^-5

b. Write the overall spontaneous cell reaction and determine Ecell.

c.When the electrochemical cell is at equilibrium what is Ecell?

d.Calculate the K for the electrochemical cell

e. Write the chemical equilibrium equation associated with Ksp of Ag2CrO4

f. Note that the reaction in b and e are related but not identical therefore determine the Ksp of Ag2CrO4

a. To calculate the Ecell for the Ag2CrO4 half-reaction, we can use the Nernst equation:

Ecell = Ecathode - Eanode

Given that Eanode = +0.799V (from the Ag+|Ag couple) and Ecathode = +0.446V (from the coated silver electrode), we can substitute these values into the equation:

Ecell = 0.446V - 0.799V = -0.353V

b. The overall spontaneous cell reaction can be obtained by combining the two half-reactions:

Ag2CrO4 + 2e- ---> 2Ag + CrO4^2-

By multiplying the Ag2CrO4 half-reaction by 2 and adding it to the Ag+|Ag half-reaction, we get the overall cell reaction:

2Ag2CrO4 + 2e- ---> 4Ag + 2CrO4^2-

The Ecell for this overall reaction remains the same as the Ecell for the Ag2CrO4 half-reaction (-0.353V).

c. At equilibrium, the Ecell is zero (Ecell = 0) because no net reaction is occurring.

d. The equilibrium constant (K) for the electrochemical cell can be calculated using the Nernst equation:

Ecell = (0.0592V/n) * log(K)

where n is the number of electrons transferred in the cell reaction. In this case, n = 2.

At equilibrium (Ecell = 0), we can rearrange the equation to solve for K:

0 = (0.0592V/2) * log(K)

0 = 0.0296V * log(K)

log(K) = 0

Therefore, K = 10^0 = 1

e. The chemical equilibrium equation associated with the Ksp of Ag2CrO4 is:

Ag2CrO4 (s) ⇌ 2Ag+ (aq) + CrO4^2- (aq)

This equation represents the dissolution of solid Ag2CrO4 into its constituent ions in an aqueous solution.

f. The Ksp of Ag2CrO4 is the equilibrium constant for the dissolution of Ag2CrO4, which can be represented by the equation:

Ksp = [Ag+]^2 * [CrO4^2-]

Since the stoichiometric coefficients in the equilibrium equation are 2:2:1 (Ag2CrO4:Ag+:CrO4^2-), the concentration of Ag+ in the equilibrium equation is twice the concentration of Ag2CrO4:

Ksp = (2[Ag2CrO4])^2 * [CrO4^2-]

By substituting the given concentration of CrO4^2- (1.0x10^-5) and knowing that Ksp = 1 (as calculated in part d), we can solve for [Ag2CrO4]:

1 = (2[Ag2CrO4])^2 * (1.0x10^-5)

[Ag2CrO4] = √(1/(2 * 1.0x10^-5))

[Ag2CrO4] = 1.41x10^-3