PLEASE HELP *Which of the following pairs of conditions are needed to construct a similar cell that generates the highest cell potential?

Question

Fe²⁺(aq)+Zn(s)→Fe(s)+Zn²⁺(aq)E°cell=+0.32V

A galvanic cell generates a cell potential of +0.32V when operated under standard conditions according to the reaction above. Which of the following pairs of conditions are needed to construct a similar cell that generates the highest cell potential?

Fe²⁺(aq)+Zn(s)→Fe(s)+Zn²⁺(aq)E°cell=+0.32V

A galvanic cell generates a cell potential of +0.32V when operated under standard conditions according to the reaction above. Which of the following pairs of conditions are needed to construct a similar cell that generates the highest cell potential?

1.   [Zn²⁺]=2M and [Fe²⁺]=1M because Q<1.

.

1.   [Zn²⁺]=0.25M and [Fe²⁺]=1M because Q<1.

1.   [Zn²⁺]=1M and [Fe²⁺]=2M because Q>1.
2.   [Zn²⁺]=2M and [Fe²⁺]=0.5M because Q>1.

Answer 1

So the equation that we use to calculate cell potential at nonstandard conditions is the Nernst equation.

E = E^o - (RT/nF) ln(Q)

Where E^o is the cell potential under standard conditions (Q=1), R is the ideal gas constant, T is temperature in K, n is the number of moles of electrons involved in this redox reaction, F is the Faraday constant, Q is the reaction quotient, and in case you have seen it before, ln() is the natural logarithm, logarithm base e.

The only thing we have control over is Q. We calculate Q the same way as the equilibrium constant K, but using non equilibrium concentrations. So Q = [products]^{their coefficients}/[reactants]^{their coefficients}. In this case,

Q = [Zn⁺²]/[Fe⁺²]

Now how does Q effect our cell potential? Well since we are taking the natural log of Q we need to talk about when the sign of natural log changes. If we are taking the natural log of a number less than one, it will be negative, while if we take the natural log of something greater than one it will be positive. Taking the natural log of one gives us zero.

Q < 1 --> ln(Q) < 0

Q > 1 --> ln(Q) > 0

Q = 1 --> ln(Q) = 0 (Which would result in E = E^o. This makes sense because Q = 1 is standard conditions!)

So this determines the sign of the term we are subtracting from E^o.

Q < 1 --> ln(Q) < 0 --> E > E^o (E goes up because we subtract a negative number)

Q > 1 --> ln(Q) > 0 --> E < E^o (E goes down because we subtract a positive number)

Q = 1 --> ln(Q) = 0 --> E = E^o (because we subtract 0)

So now that that's established let's consider each answer choice.

"[Zn²⁺]=2M and [Fe²⁺]=1M because Q<1"

Q = [Zn⁺²]/[Fe⁺²] = 2/1 --> Q > 1. This answer choice claims Q < 1 so it is false.

"[Zn²⁺]=0.25M and [Fe²⁺]=1M because Q<1"

Q = [Zn⁺²]/[Fe⁺²] = 0.25/1 --> Q < 1 --> ln(Q) < 0, E goes up, this answer makes sense.

" [Zn²⁺]=1M and [Fe²⁺]=2M because Q>1"

Q = [Zn⁺²]/[Fe⁺²] = 1/2 --> Q < 1. But answer claims Q>1, which is false.

"[Zn²⁺]=2M and [Fe²⁺]=0.5M because Q>1"

Q = [Zn⁺²]/[Fe⁺²] = 2/0.5 = 4 --> Q > 1 --> ln(Q) > 0, E goes down, this answer does not make sense.

So only the second choice makes sense.