15 Common Mistakes When Studying Physical Chemistry (And How to Fix Them) | LearnByTeaching.ai
Physical chemistry is where chemistry meets physics and mathematics head-on, and students who chose chemistry to avoid heavy math often hit a wall. These 15 mistakes span thermodynamics, quantum mechanics, and kinetics — the three pillars of p-chem — and reflect the most common conceptual and study-habit failures that lead to poor outcomes in this notoriously challenging course.
Confusing state functions with path functions
Students treat all thermodynamic quantities the same, not recognizing that internal energy and enthalpy depend only on initial and final states, while heat and work depend on the process path.
A student writes 'the heat of the system is 500 J' as if heat is a property the system possesses, rather than a quantity transferred along a specific path. They then incorrectly assume that heat is the same for reversible and irreversible paths between the same states.
How to fix it
Memorize which quantities are state functions (U, H, S, G) and which are path functions (q, w). State functions have exact differentials (dU); path functions have inexact differentials (dq). For state functions, only endpoints matter.
Using entropy as 'disorder' without quantitative understanding
The 'disorder' metaphor for entropy is misleading and breaks down in many situations. Students who rely on it can't calculate entropy changes or apply the second law rigorously.
A student claims that crystallization of a supersaturated solution violates the second law because 'the crystal is more ordered than the solution' — failing to account for the entropy increase of the surroundings from the exothermic process.
How to fix it
Define entropy quantitatively: dS = dq_rev / T for classical thermodynamics, or S = k_B ln W for statistical mechanics. Always calculate total entropy change (system + surroundings) to check the second law.
Treating the Schrodinger equation as a formula to plug into
Students try to use the Schrodinger equation like a physics formula (plug in values, get an answer) rather than understanding it as an eigenvalue problem that requires solving a differential equation.
A student asks 'what values do I plug into the Schrodinger equation to get the energy of a hydrogen atom?' rather than understanding that you must solve the differential equation with appropriate boundary conditions to find the allowed energies.
How to fix it
Understand that solving the Schrodinger equation means finding wavefunctions (eigenfunctions) and energies (eigenvalues) that satisfy H psi = E psi with boundary conditions. Work through the particle-in-a-box solution step by step to build this understanding.
Skipping math derivations and just memorizing results
Students jump to the final equations (ideal gas law, Clausius-Clapeyron, partition function) without working through the derivations, losing the understanding of when and why each equation applies.
A student memorizes the Clausius-Clapeyron equation but can't derive it from dG = VdP - SdT at phase equilibrium, so they don't recognize when its assumptions (ideal gas vapor, negligible liquid volume) break down.
How to fix it
Work through every major derivation by hand at least once. The derivation tells you the assumptions and therefore the limitations of the final equation. If you can derive it, you understand when to use it.
Misapplying the Gibbs free energy criterion
Students memorize 'delta G < 0 means spontaneous' without understanding that this criterion only applies at constant temperature and pressure. At other conditions, different potentials apply.
A student applies the Gibbs free energy criterion to a constant-volume process (like a bomb calorimeter), where Helmholtz free energy (A) is the appropriate thermodynamic potential.
How to fix it
Learn the conditions for each thermodynamic potential: Gibbs (constant T, P), Helmholtz (constant T, V), enthalpy (constant S, P), internal energy (constant S, V). Use the natural variables to match potential to process.
Confusing the rate law with the rate equation from a mechanism
Students conflate the empirical rate law (determined experimentally) with the rate equation derived from a proposed mechanism. These must agree, but they come from different sources.
A student writes the rate law directly from the balanced equation coefficients (e.g., 2A + B -> products, so rate = k[A]^2[B]) without realizing that the rate law depends on the mechanism, not the stoichiometry.
How to fix it
Always distinguish between empirical rate laws (from experimental data) and mechanistic rate equations (from elementary steps). The rate law can only be determined from the rate-determining step or the full mechanism, never from the overall equation.
Not defining the system and surroundings before solving problems
Students jump into thermodynamic calculations without clearly defining what is the system, what is the surroundings, and whether the process is open, closed, or isolated.
A student calculates the entropy change for an ice cube melting in a warm room but only calculates the entropy change of the ice, forgetting to account for the entropy decrease of the warm room.
How to fix it
Start every thermodynamics problem by writing: System = ___. Surroundings = ___. Type = open/closed/isolated. Process = isothermal/adiabatic/isobaric/isochoric. This prevents most errors.
Misunderstanding what the wavefunction physically represents
Students think the wavefunction psi gives the probability of finding a particle at a point, when it's actually psi-squared (|psi|^2) that gives the probability density.
A student says 'the wavefunction is zero at the node, so the particle can never be there' — which is correct — but then says 'the wavefunction is large here, so the particle is probably here,' confusing psi with |psi|^2.
How to fix it
Remember: psi is the probability amplitude, |psi|^2 is the probability density, and |psi|^2 dx is the probability of finding the particle in the interval dx. The wavefunction itself can be negative or complex; only |psi|^2 has direct physical meaning.
Neglecting units and dimensional analysis
Physical chemistry involves multiple systems of units (SI, cgs, atomic units) and students frequently make errors by mixing units or forgetting unit conversions.
A student calculates a Gibbs free energy change and gets an answer in kJ but the gas constant R was used in J/(mol K), producing a result off by a factor of 1000.
How to fix it
Write units on every number in every step of every calculation. Check that units cancel correctly before computing the numerical answer. Keep R in consistent units (8.314 J/mol K) and convert everything else to match.
Confusing reversible and irreversible processes
Students don't understand that reversible processes are idealized limits that maximize work and minimize entropy production, and that real processes are always irreversible.
A student calculates the work done by an ideal gas expanding against a vacuum using W = -nRT ln(V2/V1), which is the reversible work formula. Free expansion against a vacuum does zero work.
How to fix it
For irreversible processes, you can't use the reversible work formula. Calculate work from the actual external pressure: w = -P_ext * delta V. Use reversible paths only to calculate state function changes (delta S, delta G) between the same endpoints.
Not connecting quantum mechanics to spectroscopy
Students solve quantum mechanical problems (particle in a box, harmonic oscillator, rigid rotor) without understanding that these models directly explain spectroscopic observations.
A student solves the rigid rotor problem and gets quantized energy levels but doesn't connect this to the pattern of lines in a rotational absorption spectrum or how bond lengths are determined from microwave spectra.
How to fix it
For every quantum mechanical model, learn the corresponding spectroscopic technique: rigid rotor -> microwave spectroscopy, harmonic oscillator -> IR spectroscopy, electronic transitions -> UV-Vis. This makes the quantum mechanics concrete and practically relevant.
Struggling with the steady-state approximation in kinetics
Students apply the steady-state approximation mechanically without understanding when it's valid or what it physically means.
A student sets d[intermediate]/dt = 0 for the steady-state approximation but can't explain why — the intermediate is produced and consumed at nearly equal rates, so its concentration stays approximately constant after an initial transient.
How to fix it
Understand the physical basis: the steady-state approximation works when an intermediate is reactive (consumed quickly after formation). Practice deriving rate laws using SSA for common mechanisms (Lindemann, Michaelis-Menten).
Studying p-chem without reviewing prerequisite math
Physical chemistry assumes comfort with multivariable calculus, differential equations, and linear algebra. Students who haven't reviewed these struggle with the mathematical formalism.
A student can't follow a derivation involving partial derivatives and the chain rule, falling behind in thermodynamics because the math is a barrier rather than a tool.
How to fix it
Before p-chem starts, review: partial derivatives, exact vs inexact differentials, separation of variables for ODEs, eigenvalue problems, and basic linear algebra. Even a one-week refresher can make a huge difference.
Not using computational tools to build intuition
Students work through equations on paper without visualizing wavefunctions, molecular orbitals, or potential energy surfaces, missing the physical intuition that visual tools provide.
A student solves the hydrogen atom wavefunctions algebraically but has no intuition for what the 2p orbital looks like in 3D or why it has a nodal plane.
How to fix it
Use computational chemistry software (ORCA, Gaussian, or free tools like WebMO) to visualize orbitals and molecular properties. Plot wavefunctions and probability densities in Mathematica, Python, or even Desmos.
Misapplying the Arrhenius equation to non-elementary reactions
Students assume the Arrhenius equation (k = A exp(-Ea/RT)) gives a simple activation energy for all reactions, not realizing that for complex mechanisms, the 'activation energy' is an apparent quantity that may not correspond to a single barrier.
A student plots ln(k) vs 1/T for an enzyme-catalyzed reaction and interprets the slope as a single activation barrier, when the observed rate constant is a composite of multiple elementary steps with different activation energies.
How to fix it
Distinguish between elementary reactions (where Ea is a true barrier height) and overall reactions (where Ea is apparent). For complex mechanisms, understand which elementary steps contribute to the observed activation energy.
Quick Self-Check
- Can you identify whether a given thermodynamic quantity is a state function or path function?
- Can you set up and solve the Schrodinger equation for a particle in a one-dimensional box from scratch?
- Can you derive the Clausius-Clapeyron equation starting from the condition for phase equilibrium?
- Can you use the steady-state approximation to derive a rate law from a two-step mechanism?
- Can you calculate the total entropy change (system + surroundings) for an irreversible process?
Pro Tips
- ✓Start every thermodynamics problem by defining system, surroundings, type (open/closed/isolated), and process (isothermal/adiabatic/isobaric/isochoric) before writing any equations.
- ✓For quantum mechanics, solve the three canonical problems (particle-in-a-box, harmonic oscillator, rigid rotor) from scratch repeatedly — they are the building blocks for everything else.
- ✓When stuck on a derivation, check whether you're confusing a state function with a path function — this is the source of most thermodynamic errors.
- ✓Use dimensional analysis as a final check on every calculation — if the units don't work out, the answer is wrong regardless of the arithmetic.
- ✓Connect every quantum mechanics result to an observable: energy levels to spectra, wavefunctions to electron density, selection rules to which transitions are allowed.