A solution of K2CrO4 was titrated with AgNO3, using a silver indicator electrode (E=0.799V) and a S.C.E. electrode (E=0.241V). The product, Ag2CrO4, has a Ksp = 1.1x10^-12. What is the potential at the equivalence point?
To determine the potential at the equivalence point in this titration, we need to consider the reaction that takes place between K2CrO4 and AgNO3.
The balanced chemical equation is:
2 AgNO3 + K2CrO4 → Ag2CrO4 + 2 KNO3
At the equivalence point, the moles of AgNO3 added is equal to the moles of K2CrO4 initially present in the solution. This means that the concentrations of Ag+ and CrO4^-2 ions are equal. Since AgNO3 is a strong electrolyte that dissociates completely in water, we can assume that the concentration of Ag+ is equal to the concentration of K2CrO4.
Now, let's consider the Nernst equation, which gives the potential (Ecell) of an electrochemical cell:
Ecell = E°cell - (0.0592/n) * log(Q)
Where:
- Ecell is the cell potential
- E°cell is the standard cell potential (theoretical value when concentrations are 1M and pressures are 1 atm)
- n is the number of moles of electrons transferred in the balanced equation
- Q is the reaction quotient (ratio of the product concentrations to reactant concentrations)
For the half-reaction, Ag+ + e- → Ag, the standard reduction potential (E°) is 0.799V. Since two moles of electrons are transferred in the balanced equation, n = 2.
Considering the reaction quotient at the equivalence point, Q = [Ag+]^2, as the concentration of Ag+ equals the concentration of CrO4^-2.
Since Ksp = [Ag+]^2[CrO4^-2], we can substitute Ksp into the equation:
Ecell = E°cell - (0.0592/2) * log([Ag+]^2)
Given that Ksp = 1.1x10^-12, perform the following steps to find [Ag+]:
1. Express Ksp using the concentration of Ag+:
1.1x10^-12 = [Ag+]^2[CrO4^-2]
At the equivalence point, [Ag+] = [CrO4^-2]. Thus, substitute [Ag+] = [CrO4^-2] into the equation:
1.1x10^-12 = [Ag+]^2 * [Ag+]
2. Simplify the equation:
[Ag+]^3 = 1.1x10^-12
3. Take the cube root of both sides:
[Ag+] = (1.1x10^-12)^(1/3)
Now, substitute this value of [Ag+] into the Nernst equation:
Ecell = 0.799V - (0.0592/2) * log((1.1x10^-12)^(1/3))^2)
Simplify the equation and evaluate to find the potential at the equivalence point.