Hard MCAT Electrochemistry Practice Questions

Mastering Hard MCAT Electrochemistry Practice Questions requires a deep understanding of the relationship between chemical reactions and electrical energy, specifically how electrons move through redox processes. This guide provides the high-level analysis needed to tackle complex problems involving the Nernst equation, Gibbs free energy, and electrolytic cell stoichiometry.

Concept Explanation

Electrochemistry is the study of the movement of electrons in oxidation-reduction reactions and how this movement can be harnessed to perform work or be driven by an external power source. At the core of this subject is the distinction between galvanic (voltaic) cells, which use spontaneous reactions to generate electricity, and electrolytic cells, which use electricity to drive non-spontaneous reactions. For the MCAT, you must be comfortable manipulating the relationship between the standard cell potential $E^{\circ}_{ \text{cell}}$, the equilibrium constant $K$, and the Gibbs free energy change $\Delta G^{\circ}$. These are linked by the fundamental equation: $$\Delta G^{\circ} = -nFE^{\circ}_{ \text{cell}}$$ where $n$ is the number of moles of electrons transferred and $F$ is Faraday’s constant (approximately $96,485 \text{ C/mol } e^{-}$).

When conditions are not standard—meaning concentrations are not $1 \text{ M}$ or pressures are not $1 \text{ atm}$—the Nernst equation becomes the primary tool for calculation: $$E_{ \text{cell}} = E^{\circ}_{ \text{cell}} - \frac{0.0592}{n} \log Q$$ This equation allows you to predict how changes in concentration shift the cell potential, a concept frequently tested in the context of concentration cells and biological gradients. Furthermore, understanding the Faraday laws of electrolysis is essential for calculating the mass of a substance deposited at an electrode during electrolytic processes. Effective preparation often involves retrieval practice for medical education, ensuring these complex formulas are accessible under the pressure of the exam.

Solved Examples

Below are three worked examples that demonstrate the level of mathematical and conceptual integration required for hard MCAT electrochemistry problems.

Example 1: Calculating Non-Standard Cell Potential
A galvanic cell is constructed using the following half-reactions at $298 \text{ K}$:
$\text{Ag}^{+} + e^{-} \rightarrow \text{Ag}(s) \quad E^{\circ} = +0.80 \text{ V}$
$\text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu}(s) \quad E^{\circ} = +0.34 \text{ V}$
If the concentration of $[ \text{Ag}^{+}] = 0.01 \text{ M}$ and $[ \text{Cu}^{2+}] = 1.0 \text{ M}$, what is the cell potential?

1. Identify the cathode and anode. Silver has a higher reduction potential, so it is the cathode. Copper is the anode.
2. Calculate the standard cell potential: $E^{\circ}_{ \text{cell}} = E^{\circ}_{ \text{red, cathode}} - E^{\circ}_{ \text{red, anode}} = 0.80 - 0.34 = 0.46 \text{ V}$.
3. Write the balanced net equation: $2 \text{Ag}^{+} + \text{Cu}(s) \rightarrow 2 \text{Ag}(s) + \text{Cu}^{2+}$. Note that $n = 2$.
4. Set up the reaction quotient $Q$: $Q = \frac{[ \text{Cu}^{2+}]}{[ \text{Ag}^{+}]^{2}} = \frac{1.0}{(0.01)^{2}} = 10,000 = 10^{4}$.
5. Apply the Nernst equation: $E = 0.46 - \frac{0.0592}{2} \log(10^{4}) = 0.46 - 0.0296(4) = 0.46 - 0.1184 = 0.3416 \text{ V}$.

Example 2: Electrolytic Deposition
How many grams of Aluminum ($\text{atomic mass} = 27 \text{ g/mol}$) can be produced by the electrolysis of molten $\text{AlCl}_{3}$ if a current of $10 \text{ A}$ is applied for $9650 \text{ seconds}$?

1. Determine total charge passed: $Q = I \times t = 10 \text{ A} \times 9650 \text{ s} = 96,500 \text{ C}$.
2. Convert charge to moles of electrons: Since $F \approx 96,500 \text{ C/mol } e^{-}$, we have $1 \text{ mole of electrons}$.
3. Write the reduction half-reaction: $\text{Al}^{3+} + 3e^{-} \rightarrow \text{Al}(s)$.
4. Calculate moles of Aluminum: $1 \text{ mol } e^{-} \times \frac{1 \text{ mol Al}}{3 \text{ mol } e^{-}} = 0.333 \text{ mol Al}$.
5. Convert to mass: $0.333 \text{ mol} \times 27 \text{ g/mol} = 9 \text{ grams}$.

Example 3: Relating K and E°
A redox reaction has a standard cell potential of $-0.0592 \text{ V}$ at $298 \text{ K}$. If $n = 1$, what is the equilibrium constant $K$?

1. Recall the relation: $E^{\circ}_{ \text{cell}} = \frac{0.0592}{n} \log K$.
2. Substitute the values: $-0.0592 = \frac{0.0592}{1} \log K$.
3. Divide both sides by $0.0592$: $-1 = \log K$.
4. Solve for $K$: $K = 10^{-1} = 0.1$.

Practice Questions

1. A concentration cell is constructed with two silver electrodes. One half-cell contains $1.0 \text{ M AgNO}_{3}$ and the other contains $0.001 \text{ M AgNO}_{3}$. Calculate the cell potential at $25^{\circ} \text{C}$.
2. If the reduction of $\text{Fe}^{2+}$ to $\text{Fe}(s)$ has an $E^{\circ} = -0.44 \text{ V}$ and the reduction of $\text{Fe}^{3+}$ to $\text{Fe}^{2+}$ has an $E^{\circ} = +0.77 \text{ V}$, calculate the standard reduction potential for $\text{Fe}^{3+} + 3e^{-} \rightarrow \text{Fe}(s)$.
3. In an electrolytic cell, a current of $5 \text{ A}$ is passed through a solution of $\text{Cr}_{2}( \text{SO}_{4})_{3}$ for $1 \text{ hour}$. How many moles of Chromium metal are deposited?

4. A galvanic cell has a $\Delta G^{\circ}$ of $-100 \text{ kJ}$. If $2 \text{ moles}$ of electrons are transferred per mole of reaction, what is the approximate standard cell potential?
5. Compare a galvanic cell and an electrolytic cell. Which electrode is positive in each, and where does oxidation occur?
6. Consider the reaction: $\text{Sn}^{2+}(aq) + \text{Pb}(s) \rightarrow \text{Sn}(s) + \text{Pb}^{2+}(aq)$. If $E^{\circ}( \text{Sn}^{2+}/ \text{Sn}) = -0.14 \text{ V}$ and $E^{\circ}( \text{Pb}^{2+}/ \text{Pb}) = -0.13 \text{ V}$, is this reaction spontaneous under standard conditions?
7. Using the retrieval practice for STEM subjects method, explain how a lead-acid battery acts as both a galvanic and electrolytic cell.
8. A certain redox reaction has $K = 10^{6}$. What can you conclude about the sign of $\Delta G^{\circ}$ and $E^{\circ}_{ \text{cell}}$?
9. If the pH of a hydrogen electrode half-cell is increased from $0$ to $7$ at $25^{\circ} \text{C}$ (at $P_{ \text{H}_{2}} = 1 \text{ atm}$), what is the new reduction potential for $2 \text{H}^{+} + 2e^{-} \rightarrow \text{H}_{2}$?
10. An unknown metal $M$ is plated from a solution of $M( \text{NO}_{3})_{2}$. If $1.2 \text{ g}$ of metal is deposited by $0.04 \text{ moles}$ of electrons, what is the molar mass of the metal?

Answers & Explanations

1. Answer: 0.1776 V. In a concentration cell, $E^{\circ}_{ \text{cell}} = 0$. The reaction is $\text{Ag}^{+}( \text{conc}) \rightarrow \text{Ag}^{+}( \text{dilute})$. Here, $n = 1$. $Q = \frac{0.001}{1.0} = 10^{-3}$. $E = 0 - (0.0592/1) \log(10^{-3}) = -0.0592(-3) = 0.1776 \text{ V}$.
2. Answer: -0.037 V. You cannot simply add $E^{\circ}$ values; you must add $\Delta G^{\circ}$ values.
   $\Delta G^{\circ}_{1} ( \text{Fe}^{2+} \rightarrow \text{Fe}) = -(2)F(-0.44) = 0.88F$
   $\Delta G^{\circ}_{2} ( \text{Fe}^{3+} \rightarrow \text{Fe}^{2+}) = -(1)F(0.77) = -0.77F$
   Total $\Delta G^{\circ}_{3} = 0.88F - 0.77F = 0.11F$.
   Since $\Delta G^{\circ}_{3} = -nFE^{\circ}_{3}$, then $0.11F = -(3)FE^{\circ}_{3}$.
   $E^{\circ}_{3} = -0.11 / 3 \approx -0.037 \text{ V}$.
3. Answer: 0.062 mol. Total charge $Q = 5 \text{ A} \times 3600 \text{ s} = 18,000 \text{ C}$. Moles of electrons $= 18,000 / 96,500 \approx 0.1865 \text{ mol } e^{-}$. Chromium in $\text{Cr}_{2}( \text{SO}_{4})_{3}$ is $\text{Cr}^{3+}$, so it needs $3e^{-}$ per atom. Moles $\text{Cr} = 0.1865 / 3 = 0.062 \text{ mol}$.
4. Answer: ~0.52 V. Use $\Delta G^{\circ} = -nFE^{\circ}$. $-100,000 \text{ J} = -(2)(96,500)E^{\circ}$. $E^{\circ} = 100,000 / 193,000 \approx 0.518 \text{ V}$.
5. Answer: Galvanic: Anode (-), Cathode (+). Electrolytic: Anode (+), Cathode (-). In both cells, oxidation ALWAYS occurs at the anode and reduction ALWAYS occurs at the cathode. The signs differ because the galvanic cell is a source of voltage, while the electrolytic cell is driven by an external source.
6. Answer: No. $E^{\circ}_{ \text{cell}} = E^{\circ}_{ \text{red, cathode}} - E^{\circ}_{ \text{red, anode}}$. Here, Tin is reduced and Lead is oxidized. $E^{\circ} = -0.14 - (-0.13) = -0.01 \text{ V}$. Since $E^{\circ} < 0$, the reaction is non-spontaneous.
7. Answer: Discharge = Galvanic; Charging = Electrolytic. When starting a car, the battery provides energy (spontaneous redox). When the alternator runs, it forces the reaction to reverse, acting as an electrolytic cell to restore the lead and lead dioxide plates. Mastering such conceptual links is a key part of retrieval practice vs practice tests strategies.
8. Answer: $\Delta G^{\circ}$ is negative; $E^{\circ}_{ \text{cell}}$ is positive. A large $K$ ($> 1$) indicates a spontaneous reaction at standard conditions. Spontaneity corresponds to a negative Gibbs free energy and a positive cell potential.
9. Answer: -0.414 V. The half-reaction is $2 \text{H}^{+} + 2e^{-} \rightarrow \text{H}_{2}$. $E^{\circ} = 0$. At $\text{pH } 7$, $[ \text{H}^{+}] = 10^{-7}$. $E = 0 - (0.0592/2) \log(1 / (10^{-7})^{2}) = -0.0296 \log(10^{14}) = -0.0296(14) \approx -0.414 \text{ V}$.
10. Answer: 60 g/mol. The ion is $M^{2+}$, so $2 \text{ moles}$ of electrons deposit $1 \text{ mole}$ of metal. If $0.04 \text{ moles}$ of electrons were used, then $0.02 \text{ moles}$ of metal were deposited. $\text{Molar mass} = \text{mass} / \text{moles} = 1.2 \text{ g} / 0.02 \text{ mol} = 60 \text{ g/mol}$.

Frequently Asked Questions

What is the difference between E and E°?

$E^{\circ}$ represents the cell potential under standard conditions (1 M concentrations, 1 atm pressure, 298 K), while $E$ is the actual potential under any given set of conditions. You calculate $E$ using the Nernst equation to account for deviations from standard states.

Why is the anode negative in a galvanic cell but positive in an electrolytic cell?

In a galvanic cell, the anode is the source of electrons released by spontaneous oxidation, making it the negative terminal. In an electrolytic cell, the external power source pulls electrons away from the anode, effectively "forcing" it to be positive.

How do I calculate n in the Nernst equation?

$n$ is the total number of moles of electrons transferred in the balanced redox equation. You find this by ensuring the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction.

What does a cell potential of zero indicate?

A cell potential of zero ($E = 0$) indicates that the chemical system has reached equilibrium. At this point, the reaction quotient $Q$ equals the equilibrium constant $K$, and the cell can no longer perform work.

Can I use the Nernst equation for electrolytic cells?

Yes, the Nernst equation applies to any electrochemical cell to determine the voltage required or produced. For electrolytic cells, it helps determine the minimum external voltage necessary to drive a non-spontaneous reaction at specific concentrations.

What is a Faraday?

A Faraday ($F$) is a unit of electric charge equivalent to the charge of one mole of electrons, approximately $96,485 \text{ Coulombs}$. It is a vital constant for converting between chemical moles and electrical charge in electrolysis problems.