Q: For the reaction $$2\text{Fe}^{3+} + 2e^- \rightarrow 2\text{Fe}^{2+}$$, if $$E^ ext{cell} = 0.77\ \text{V}$$ and $$n = 2$$, what is $$\Delta G at 25$$°C? ($$F = 96485\ \text{C/mol})$$

$$-1.49 \times 10^5$\ \text{J}$$

Question 1

Which equation correctly relates the standard cell potential ($$E^	ext{cell}$$), the equilibrium constant ($$K$$), and the number of electrons transferred ($$n) at 25$$°C?

Accepted Answer

$$E^	ext{cell} = \frac{0.0592}{n} \log K$$

Question 2

If the equilibrium constant ($$K) $$for a redox reaction at 25°C is $$2.5 	imes 10$$^{18}$$ and 4 electrons are transferred, what is the standard cell potential (E^	$$ext{cell}$$)?

Accepted Answer

$$0.66\ 	ext{V}$$

Question 3

Which of the following statements best describes the relationship between Gibbs Free Energy ($$\Delta G) $$and the standard cell potential ($$E^	ext{cell}$$)?

Accepted Answer

$$\Delta G = -nFE^	ext{cell}$$

Question 4

Given the following reduction potentials at 25°C: $$	ext{Cu}^{2+} + 2e^- ightarrow 	ext{Cu}$$, $$E^	ext{red} = +0.34\ 	ext{V}$$; $$	ext{Zn}^{2+} + 2e^- ightarrow 	ext{Zn}$$, $$E^	ext{red} = -0.76\ 	ext{V}. $$What is the standard cell potential for the reaction $$	ext{Zn} + 	ext{Cu}^{2+} ightarrow 	ext{Zn}^{2+} + 	ext{Cu}$$?

Accepted Answer

$$1.10\ 	ext{V}$$

Question 5

A cell reaction has $$E^	ext{cell} = 0.00\ 	ext{V} at $$equilibrium. What is the value of the equilibrium constant $$K$$?

Accepted Answer

$$K = 1$$

Question 6

If $$\Delta G$$ for a reaction is negative, what can be inferred about the spontaneity and the cell potential ($$E^	ext{cell}$$)?

Accepted Answer

The reaction is spontaneous and $$E^	ext{cell} is $$positive.

Question 7

For the reaction $$2	ext{Fe}^{3+} + 2e^- ightarrow 2	ext{Fe}^{2+}$$, if $$E^	ext{cell} = 0.77\ 	ext{V}$$ and $$n = 2$$, what is $$\Delta G at 25$$°C? ($$F = 96485\ 	ext{C/mol})$$

Accepted Answer

$$-1.49 	imes 10^5$\ 	ext{J}$$

Question 8

Which of the following changes will increase the equilibrium constant $$K$$ for a redox reaction at 25°C?

Accepted Answer

Increasing the standard cell potential $$E^	ext{cell}$$

Question 9

A certain electrochemical reaction involves the transfer of 3 electrons and has a standard cell potential of $$0.45\ 	ext{V} at 25$$°C. What is the equilibrium constant $$K$$ for this reaction?

Accepted Answer

$$K = 1.2 	imes 10$$^{22}$$

Question 10

Which of the following is the correct simplified formula for calculating the standard cell potential ($$E^	ext{cell}) $$from the equilibrium constant ($$K) at 25$$°C?

Accepted Answer

$$E^	ext{cell} = \frac{0.0592}{n} \log K$$

Question 11

If a redox reaction at 25°C has $$K \u003c 1$$, what can be said about the sign of $$E^	ext{cell}$$?

Accepted Answer

$$E^	ext{cell} is $$negative

Question 12

A battery operates based on the following reaction: $$2	ext{Ag}^+ + 2e^- ightarrow 2	ext{Ag}$$ ($$E^	ext{red} = +0.80\ 	ext{V}) $$and $$	ext{Zn}^{2+} + 2e^- ightarrow 	ext{Zn}$$ ($$E^	ext{red} = -0.76\ 	ext{V}). $$What is the standard cell potential for the battery?

Accepted Answer

$$1.56\ 	ext{V}$$

Question 13

Which of the following best explains why a cell with $$E^	ext{cell} \u003e 0$$ will have $$K \u003e 1$$?

Accepted Answer

A positive cell potential means the reaction is spontaneous and favors product formation at equilibrium.

Question 14

If the standard cell potential for a reaction is $$-0.25\ 	ext{V}$$ and $$n = 2$$, what is the value of $$K at 25$$°C?

Accepted Answer

$$K = 1.2 	imes 10$$^{-9}$$

Question 15

Which of the following is NOT a correct use of the Faraday constant ($$F) in $$electrochemistry?

Accepted Answer

Calculating the mass of a substance produced: $$m = \frac{nF}{M}$$

Question 16

A medical device uses a redox reaction with $$n = 2$$ and $$E^	ext{cell} = 0.50\ 	ext{V}. $$What is the Gibbs Free Energy change ($$\Delta G) $$for this reaction? ($$F = 96485\ 	ext{C/mol})$$

Accepted Answer

$$-96,485\ 	ext{J}$$

Question 17

Which of the following is the correct formula for the equilibrium constant $$K in $$terms of $$E^	ext{cell}$$, $$n$$, and $$T$$?

Accepted Answer

$$K = e$$^{\frac{nFE^	ext{cell}$$}{RT}}$$

Cell Potentials, Gibbs Free Energy, and Equilibrium in Electrochemistry

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