A concentration cell consists of two Sn/Sn2+ half-cells. The cell has a potential of 0.12V at 25 ∘C.

What is the ratio of the Sn2+ concentrations in the two half-cells?

To find the ratio of the Sn2+ concentrations in the two half-cells, we can use the Nernst equation.

The Nernst equation in this case is given by:

E = E° - (RT / nF) * ln(Q)

Where:
E = cell potential
E° = standard cell potential
R = gas constant (8.314 J/(mol·K))
T = temperature in Kelvin
n = number of electrons transferred in the balanced equation
F = Faraday's constant (96,485 C/mol)
ln = natural logarithm
Q = reaction quotient

In this case, the half-cell reaction is:

Sn2+ + 2e- → Sn

The balanced equation shows that the number of electrons transferred (n) is 2.

Given that the cell potential is 0.12V, and assuming the reaction is at 25 °C (298 K), we can substitute these values into the Nernst equation:

0.12V = E° - [(8.314 J/(mol·K) * 298 K) / (2 * 96485 C/mol)] * ln(Q)

Simplifying the equation:

0.12V = E° - (0.008617 V) * ln(Q)

Now, since the half-cells are identical except for the Sn2+ concentrations, the standard cell potential (E°) is 0V.

0.12V = - (0.008617 V) * ln(Q)

Dividing both sides by -0.008617 V:

-13.91 = ln(Q)

Taking the natural exponent of both sides:

Q = e^(-13.91)

Calculating Q:

Q ≈ 1.6659 × 10^-7

Now, the reaction quotient (Q) is equal to the ratio of the Sn2+ concentrations in the two half-cells. Therefore, the ratio of the Sn2+ concentrations is approximately 1.6659 × 10^-7.

To find the ratio of the Sn2+ concentrations in the two half-cells of the concentration cell, we can use the Nernst equation. The Nernst equation relates the cell potential to the concentrations of the reactants in the half-cells.

The Nernst equation is given as:

Ecell = E°cell - (0.0592/n) * log(Q)

Where:
- Ecell is the cell potential
- E°cell is the standard cell potential
- n is the number of electrons transferred in the cell reaction
- Q is the reaction quotient, which is the ratio of product concentrations to reactant concentrations

In the given problem, the cell potential (Ecell) is 0.12 V. However, we need the value of the standard cell potential (E°cell) to use the Nernst equation. The standard cell potential can be found by referring to tables or literature.

Once you have the standard cell potential, you can substitute the values into the Nernst equation. Then, you can rearrange the equation to solve for the ratio of Sn2+ concentrations.

Let's assume the concentrations of Sn2+ in the two half-cells are [Sn2+]1 and [Sn2+]2. The ratio of the concentrations can be represented as [Sn2+]1:[Sn2+]2.

Using the Nernst equation, we have:

Ecell = E°cell - (0.0592/n) * log(Q)
0.12 = E°cell - (0.0592/n) * log ([Sn2+]1/[Sn2+]2)

Now, rearrange the equation to solve for [Sn2+]1:[Sn2+]2:

log ([Sn2+]1/[Sn2+]2) = (E°cell - 0.12) * (n/0.0592)

Once you obtain this equation, you can solve for [Sn2+]1:[Sn2+]2 by taking the antilog of both sides to eliminate the logarithm.

Ecell = Eocell = 0.0592/2*log (ratio)

Eocell = 0 and Ecell = 0.12
Solve for ratio.

0.11