Free MCAT study guide — Chemical and Physical Foundations of Biological Systems
Electrochemistry connects redox chemistry to electrical energy and is a high-yield MCAT topic. You must understand how galvanic (voltaic) cells convert chemical energy into electrical energy spontaneously, and how electrolytic cells use electrical energy to drive non-spontaneous reactions. Key concepts include standard reduction potentials, cell potential calculations (E cell = E cathode - E anode), the relationship between E cell, delta G, and the equilibrium constant K (delta G = -nFE, and at standard conditions, delta G degrees = -nFE degrees = -RTlnK), the Nernst equation for non-standard conditions, and Faraday's law relating charge passed to the amount of substance oxidized or reduced. You should also understand concentration cells, the effect of changing conditions on cell potential, and practical applications like batteries and corrosion. Electrolysis calculations (determining the mass of substance deposited given current and time) are common quantitative problems. The MCAT bridges electrochemistry to biology through topics like the electron transport chain, nerve impulse propagation, and the electrochemical gradient that drives ATP synthesis.
A galvanic cell generates electrical energy from a spontaneous redox reaction. It consists of two half-cells connected by a salt bridge and an external wire. Oxidation occurs at the anode (negative terminal in galvanic cells, mnemonic: AN OX = anode oxidation), and reduction occurs at the cathode (positive terminal, mnemonic: RED CAT = reduction cathode). Electrons flow from anode to cathode through the external wire (from more negative to more positive electrode). The salt bridge contains an inert electrolyte (e.g., KNO3) that allows ion migration to maintain electrical neutrality: anions migrate toward the anode compartment (where positive charge accumulates from metal dissolution), and cations migrate toward the cathode compartment (where positive charge is depleted by metal deposition). The standard cell potential is calculated as E degrees cell = E degrees cathode - E degrees anode, using standard reduction potentials from a table. A positive E degrees cell means the reaction is spontaneous under standard conditions.
Standard reduction potentials (E degrees) are measured relative to the standard hydrogen electrode (SHE, defined as 0.00 V). A more positive E degrees means a greater tendency to be reduced (stronger oxidizing agent). A more negative E degrees means a greater tendency to be oxidized (stronger reducing agent). When calculating cell potential, always subtract: E degrees cell = E degrees cathode - E degrees anode. Importantly, standard reduction potentials are intensive properties -- they do NOT change when the half-reaction is multiplied by a coefficient to balance electrons. The half-reaction with the more positive E degrees will be the reduction (cathode), and the one with the more negative E degrees will be reversed to become the oxidation (anode). For example, if E degrees(Cu2+/Cu) = +0.34 V and E degrees(Zn2+/Zn) = -0.76 V, then Cu2+ is reduced, Zn is oxidized, and E degrees cell = 0.34 - (-0.76) = 1.10 V. The spontaneous direction is always the one that gives a positive cell potential.
The relationship between cell potential and free energy is delta G = -nFE, where n is the number of moles of electrons transferred, F is Faraday's constant (96,485 C/mol, approximately 96,500 C/mol), and E is the cell potential. A positive E means negative delta G (spontaneous), consistent with galvanic cells. At standard conditions: delta G degrees = -nFE degrees. The equilibrium constant K is related by delta G degrees = -RTlnK, which combines to give E degrees = (RT/nF)lnK = (0.0592/n)logK at 25 degrees Celsius. If E degrees > 0, K > 1, products are favored at equilibrium. If E degrees < 0, K < 1, reactants are favored. The Nernst equation adjusts cell potential for non-standard conditions: E = E degrees - (RT/nF)ln(Q) = E degrees - (0.0592/n)log(Q) at 25 degrees Celsius. When Q increases (more products relative to reactants), E decreases. At equilibrium, Q = K and E = 0 (the cell is dead). These three equations (delta G, K, and E) are all interconnected and the MCAT may ask you to move between them.
Electrolytic cells use an external power source to drive a non-spontaneous reaction. The anode is now the positive terminal (connected to the positive terminal of the battery) and the cathode is the negative terminal. Oxidation still occurs at the anode and reduction at the cathode. In electrolysis of molten salts, the cation is reduced at the cathode and the anion is oxidized at the anode (e.g., electrolysis of molten NaCl produces Na metal and Cl2 gas). In aqueous electrolysis, water may be preferentially oxidized or reduced instead of the dissolved ions, depending on the reduction potentials and overpotentials. Water is oxidized at the anode (2H2O -> O2 + 4H+ + 4e-) when the dissolved anion has a more negative oxidation potential. Water is reduced at the cathode (2H2O + 2e- -> H2 + 2OH-) when the dissolved cation has a more negative reduction potential than water. Electroplating uses electrolysis to deposit a thin layer of metal onto an object (the object serves as the cathode).
Faraday's law relates the amount of substance transformed during electrolysis to the charge passed: moles of substance = (It)/(nF), where I is current in amperes, t is time in seconds, n is the number of electrons transferred per formula unit, and F is Faraday's constant. To find mass deposited, multiply moles by molar mass. For example, to deposit copper from Cu2+ solution: Cu2+ + 2e- -> Cu, so n = 2. If 10 A flows for 965 seconds, charge = 10 x 965 = 9,650 C. Moles of Cu = 9,650 / (2 x 96,500) = 0.05 mol. Mass = 0.05 x 63.5 g/mol = 3.175 g. The MCAT often asks you to calculate the mass deposited, the time required to deposit a given mass, or to compare the amounts of different metals deposited by the same charge. Remember that 1 ampere = 1 coulomb/second, and 1 faraday = 96,500 coulombs = 1 mole of electrons.
A concentration cell is a special galvanic cell where both electrodes are the same metal but immersed in solutions of different concentrations. The cell potential arises solely from the concentration difference. The more dilute solution is the anode (metal dissolves to increase ion concentration), and the more concentrated solution is the cathode (ions deposit to decrease concentration). E degrees = 0 for a concentration cell (same half-reactions), but E > 0 due to the concentration difference (Nernst equation). The cell runs until concentrations equalize. Practical applications of electrochemistry include: lead-acid batteries (rechargeable, E approximately 2 V per cell, 6 cells = 12 V car battery), dry cell batteries (Zn anode, MnO2 cathode), lithium-ion batteries (rechargeable, high energy density), fuel cells (H2/O2 reaction generates electricity), and corrosion (iron oxidation accelerated by water and electrolytes, prevented by galvanization with zinc, which acts as a sacrificial anode). The nerve impulse (action potential) involves electrochemical gradients maintained by the Na+/K+ ATPase.
Galvanic cell: spontaneous, E > 0, delta G < 0. Electrolytic cell: non-spontaneous, requires external power.
AN OX, RED CAT: Anode = Oxidation, Cathode = Reduction (true for BOTH cell types).
In galvanic cells: anode is negative, cathode is positive. In electrolytic cells: anode is positive, cathode is negative.
E degrees cell = E degrees cathode - E degrees anode. Positive value = spontaneous.
delta G = -nFE. Positive E means negative delta G (spontaneous).
Nernst equation: E = E degrees - (0.0592/n)log(Q) at 25 degrees Celsius.
At equilibrium, E = 0 and Q = K.
Standard reduction potentials are intensive -- do NOT multiply by stoichiometric coefficients.
Faraday's constant F = 96,485 C/mol of electrons.
Faraday's law: moles = (It)/(nF). Mass = moles x molar mass.
Salt bridge maintains electrical neutrality; without it, the cell stops immediately.
Zinc is used as a sacrificial anode in galvanization because it has a more negative reduction potential than iron.
Electrolysis of water: cathode produces H2, anode produces O2.
Multiplying E degrees by a coefficient when balancing half-reactions -- E degrees is intensive and does NOT change.
Confusing the sign of the anode in galvanic vs. electrolytic cells -- oxidation is ALWAYS at the anode regardless of cell type.
Forgetting that at equilibrium, E = 0 (not E degrees = 0).
Using the wrong sign convention: always use E degrees cathode - E degrees anode, not the reverse.
Confusing the direction of electron flow (anode to cathode through the wire) with ion flow (through the salt bridge/solution).
Forgetting to convert minutes or hours to seconds when using Faraday's law.
Assuming the Nernst equation uses concentrations of solids or pure liquids -- only aqueous species and gases appear in Q.
Practice calculating cell potentials from standard reduction potential tables. Given two half-reactions, identify which is the cathode and which is the anode, calculate E degrees, and determine delta G and K. Then use the Nernst equation to adjust for non-standard concentrations. The MCAT typically provides a table of reduction potentials in the passage and asks you to predict the spontaneous direction, calculate cell potential, or determine the effect of changing concentrations.
Work through Faraday's law problems until the calculations are routine: given current and time, calculate mass deposited, or given desired mass, calculate required time. Be comfortable converting between coulombs, moles of electrons, and moles of substance. Also practice predicting products of aqueous electrolysis by comparing the reduction potentials of water with those of the dissolved ions. Understanding these quantitative relationships is essential for the physical sciences sections.
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