Nernst equation forms for the MCAT
| Form | Equation | Use it for |
|---|---|---|
| General | E = E° − (RT / nF) ln Q | Any temperature |
| 25 °C shortcut | E = E° − (0.0592 V / n) log Q | Most MCAT electrochemistry questions |
| Equilibrium | E° = (0.0592 V / n) log K | Relating E° to K |
| Single ion at 37 °C | E = (61.5 mV / z) log([out] / [in]) | Neuron equilibrium potentials |
| Free energy | ΔG = −nFE | Checking whether the reaction is spontaneous |
How Q changes the cell potential
A larger n makes E less sensitive to Q. A higher temperature makes E more sensitive to Q.
| Condition | Cell potential | Meaning |
|---|---|---|
| Q < 1 | E > E° | Extra reactants give the cell more driving force |
| Q = 1 | E = E° | Standard conditions |
| Q > 1 | E < E° | Products have built up, so the driving force falls |
| Q = K | E = 0 | Equilibrium: the battery is dead |
Nernst equation in neuroscience
The Nernst equation gives the membrane potential at which one ion is at equilibrium. At 37 °C, E = (61.5 mV / z) log([ion]out / [ion]in).
The resting potential of a neuron, about −70 mV, lies close to the K+ value. The resting membrane is most permeable to K+.
The values below are typical for a mammalian neuron. They vary by cell type.
| Ion | Outside (mM) | Inside (mM) | Equilibrium potential |
|---|---|---|---|
| K+ | 5 | 140 | −89 mV |
| Na+ | 145 | 15 | +61 mV |
| Cl− | 110 | 10 | −64 mV |
| Ca2+ | 2 | 0.0001 | +132 mV |
Nernst equation MCAT practice questions
Question 1
A galvanic cell has E° = 1.10 V and n = 2. What is E at 25 °C when Q = 10?
- E = E° − (0.0592 / n) log Q.
- E = 1.10 − (0.0592 / 2) × 1 = 1.10 − 0.0296 = 1.07 V.
Answer: 1.07 V
Question 2
For the same cell, Q falls to 0.010. Does E rise or fall?
- log 0.010 = −2, so the correction is −(0.0296 × −2) = +0.0592 V.
- E = 1.10 + 0.0592 = 1.16 V.
Answer: E rises to 1.16 V because Q < 1.
Question 3
A copper concentration cell has 0.010 M Cu2+ at the anode and 1.0 M Cu2+ at the cathode. What is E at 25 °C?
- E° = 0 for a concentration cell, and n = 2.
- Q = [anode] / [cathode] = 0.010 / 1.0 = 0.010.
- E = 0 − (0.0592 / 2) × log 0.010 = +0.0592 V.
Answer: +0.059 V
Question 4
A neuron has 140 mM K+ inside and 5 mM K+ outside. What is the K+ equilibrium potential at 37 °C?
- E = (61.5 mV / 1) × log(5 / 140).
- log(0.0357) = −1.447, so E = 61.5 × −1.447 = −89 mV.
Answer: −89 mV
Question 5
A cell reaction has E° = 0.30 V and n = 1. What is K at 25 °C?
- log K = nE° ÷ 0.0592 = 0.30 ÷ 0.0592 = 5.07.
- K = 10^5.07 = 1.2 × 10^5.
Answer: About 1 × 10^5
How to use this calculator
- Enter the standard potential E° in volts.
- Enter n, the number of electrons transferred in the balanced reaction.
- Enter the reaction quotient Q and the temperature.
- For a cation, set E° to 0, n to its charge, and Q to [inside]/[outside].
Formula and variables
E = E0 - RT ln(Q)/(nF)
| Symbol | Meaning | Unit |
|---|---|---|
| E | cell potential | V |
| E0 | standard potential | V |
| Q | reaction quotient | dimensionless |
| n | electron count | mol e- |
Worked example
At 25 °C, a cell with E0 = 1.10 V, n = 2, and Q = 10 has E = 1.10 − (0.0592 / 2) × log 10 = 1.07 V.
Interpretation
The reaction quotient and balanced electron count determine the nonstandard-condition correction.
Common mistakes
- Q must be positive before taking its logarithm.
- Electron count is a positive integer from the balanced redox reaction.
Frequently asked questions
Is the Nernst equation on the MCAT?
Yes. It appears in electrochemistry and in neuron membrane potential questions. Know how Q, n, and temperature change E.
What is the Nernst equation at 25 °C?
E = E° − (0.0592 V / n) log Q. The 0.0592 V term is 2.303RT/F at 298 K.
When is the cell potential zero?
E is zero when Q equals K. The cell is at equilibrium and can do no more work.
How does the Nernst equation apply to neurons?
It gives the equilibrium potential of one ion: E = (61.5 mV / z) log([out]/[in]) at 37 °C.
What does a concentration cell show?
Both half-cells use the same reaction, so E° is 0. A potential exists only while the concentrations differ.
Can I use scientific notation?
Yes. Enter values such as 6.022e23 or 1.0e-6 in a numeric field.
How should I round the result?
Keep extra digits during the calculation. Round the final result to the precision required by your data.