Question

23. A voltaic cell is constructed with Cr3+/Cr and Zn2+/Zn half-cells at 25 °C.

a. If the concentration of Zn2+ is 0.10 M, what concentration of Cr3+ should be used so that the overall cell potential is 0 V?

b. What concentration of Cr3+ should you use to make the cell consume Zn (s)?

c. What concentration of Cr3+ should you use to make the cell deposit Zn (s)?

Answer 1

a) Here, Cr³⁺ undergoes reduction to Cr, whereas Zn undergoes oxidation to Zn²⁺. The balanced cell reaction can be written as follows.

2Cr³⁺(aq) + 3Zn(s) 2Cr(s) + 3Zn²⁺(aq) .................. Equation 1

According to Nernst equation: E = E^o - 0.06/n Log([Zn²⁺]³/[Cr³⁺]²)

Here, E = 0, E^o = 0.76-0.74 = 0.02 V, n = 6, [Zn²⁺] = 0.1 M

Now, 0 = 0.02 - 0.06/6 Log(0.1³/[Cr³⁺]²)

i.e. 0.01*Log(0.1³/[Cr³⁺]²) = 0.02

i.e. Log(0.1³/[Cr³⁺]²) = 2

i.e. 0.1³/[Cr³⁺]² = 10²

i.e. [Cr³⁺]² = 10^-5

i.e. [Cr³⁺] = (10^-5)^1/2 = 3.16*10^-3 M

b) According to the equation 1: [Cr³⁺] to make the cell consume Zn(s) = (2/3)*[Zn]

i.e. The required [Cr³⁺] = (2/3)*0.1 M = 0.0667 M

c) According to the given reaction, Cr³⁺ should be used to consume Zn(s), but not to deposit Zn(s).

If Zn(s) is deposited, then the reaction is nonspontaneous.