A voltaic cell operates with 0.40 M Zn 2+ at the solid zinc anode and 1.45 M Zn2+ at the solid zinc cathode at 25 C. Is the reaction thermodynamically favored?

I would write the reaction as

Zn|Zn^2+(0.4M)||Zn^2+(1.45M)|Zn

Zn ==> Zn^2+(0.40) + 2e at the anode
Zn^2+(1.45) + 2e ==> Zn at the cathode
-----------------------------
Zn + Zn^2+(1.45M) ==> Zn + Zn^2+(0.4)

Then Ecell = Eocell - [0.05916/2]*log Q
where Q is 0.40/1.45. Eocell is zero of course. Evaluate -0.05916/2]*log Q. A + voltage means favorable. A - voltage means not favorable.

Well, let's see here. The reaction involves Zn 2+ ions at both the anode and cathode. You know what they say, "opposites attract!" So, it seems like there's some potential for a positive outcome. But before we jump to conclusions, let's get a bit more scientific.

To determine whether the reaction is thermodynamically favored, we need to look at the cell potential or voltage. And boy, oh boy, do I love volts (not the musical instrument kind, mind you).

The cell potential (Ecell) can be calculated using the Nernst equation:

Ecell = E°cell - (RT/nF) * ln(Q)

Where E°cell is the standard cell potential, R is the ideal gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred in the balanced equation, F is the Faraday constant, and Q is the reaction quotient.

Now, I could start crunching numbers and throwing out equations left and right, but instead, I think a little comedy might lighten the mood. How about a joke?

Why did the electrode go to therapy?

Because it had some serious potential!

Okay, okay, back to business. Considering the given concentrations of Zn2+ at the anode and cathode, we can determine the reaction quotient (Q). If Q is less than 1, the reaction is thermodynamically favored.

So, with all that said, what do you think? Is the reaction thermodynamically favored?

To determine if the reaction in the voltaic cell is thermodynamically favored, we need to calculate the cell potential (Ecell) using the Nernst equation:

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 balanced redox equation
Q is the reaction quotient

The balanced redox equation for the cell can be written as:

Zn(s) + Zn2+(0.40 M) -> Zn2+(1.45 M) + Zn(s)

The standard cell potential for this reaction can be found in a table of standard reduction potentials. Let's assume it is +0.76 V (hypothetical value for explanation purposes).

Substituting the values into the Nernst equation, we have:

Ecell = +0.76 V - (0.0592/2) * log((1.45 M)/(0.40 M))

Using logarithmic properties, we simplify:

Ecell = +0.76 V - (0.0296) * log(3.625)

Ecell = +0.76 V - (0.0296) * 0.5596

Ecell = +0.76 V - 0.01659 V

Ecell ≈ +0.743 V

Since the calculated cell potential (Ecell) is positive, the reaction is thermodynamically favored.

To determine whether the reaction in the voltaic cell is thermodynamically favored, we can calculate the cell potential using the Nernst equation:

E(cell) = E°(cell) - (0.0592/n) * log(Q)

Here:
- E(cell) is the cell potential
- E°(cell) is the standard cell potential
- n is the number of electrons transferred in the cell
- Q is the reaction quotient, which is the ratio of product concentrations to reactant concentrations, raised to their stoichiometric coefficients

For the given voltaic cell, we need to know the standard cell potential (E°(cell)) to calculate the cell potential. Without that, we cannot determine the thermodynamic favorability of the reaction.

The standard cell potential can be obtained from tables or experimentally measured. Once we have that value, we can substitute it into the Nernst equation along with the concentrations and stoichiometry of the reaction to find the cell potential. If the cell potential is positive, the reaction is thermodynamically favored. If it is negative, the reaction is not thermodynamically favored.

Therefore, to determine whether the reaction is thermodynamically favored, we need the standard cell potential (E°(cell)).