Physical Chemistry Tutoring

Physical chemistry is where chemistry meets math and physics. The ideas are not always harder than in organic chemistry, but the tools are different: partial derivatives in thermodynamics, differential equations in kinetics and quantum mechanics, and probability in statistical mechanics. Students who earned strong grades in earlier chemistry courses can find the first exam a shock. STEM Tutor 360's one-on-one physical chemistry tutoring pairs the chemistry with the math it needs, so equations become tools you can derive and use instead of strings you copy.

Courses split in different ways, so sessions follow yours. The thermodynamics and kinetics half covers the laws of thermodynamics, chemical potential, phase equilibria, an introduction to statistical thermodynamics, and rate laws. The quantum half covers the particle in a box, the harmonic oscillator, the hydrogen atom, and molecular spectroscopy. We also help with physical chemistry lab data and reports.

A typical physical chemistry problem, worked

An electron is confined to a one-dimensional box 0.500 nm long. Find the ground-state energy. Then find the wavelength of light absorbed in the $n = 1$ to $n = 2$ transition.

The allowed energies are $E_n = \dfrac{n^{2} h^{2}}{8 m L^{2}}$. For $n = 1$, with $h = 6.626 \times 10^{-34}\ \text{J s}$, $m = 9.109 \times 10^{-31}\ \text{kg}$, and $L = 5.00 \times 10^{-10}\ \text{m}$: $$E_1 = \dfrac{(6.626 \times 10^{-34})^{2}}{8 \times (9.109 \times 10^{-31}) \times (5.00 \times 10^{-10})^{2}} = 2.41 \times 10^{-19}\ \text{J, or } 1.50\ \text{eV}$$

Energy grows as $n^{2}$, so $E_2 = 4E_1$ and the gap is $3E_1 = 7.23 \times 10^{-19}\ \text{J}$. The wavelength is $$\lambda = \dfrac{hc}{\Delta E} = \dfrac{(6.626 \times 10^{-34}\ \text{J s})(2.998 \times 10^{8}\ \text{m/s})}{7.23 \times 10^{-19}\ \text{J}} = 2.75 \times 10^{-7}\ \text{m, or } 275\ \text{nm}$$ That is ultraviolet light.

A useful check: energy scales as $1/L^{2}$, so halving the box to 0.250 nm would multiply every energy by 4.

The math behind the chemistry

Most P-Chem trouble is a math gap that shows up in a chemistry setting. Sessions teach each tool when a problem calls for it.

• Partial derivatives and exact differentials, including reading $\partial U / \partial T$ with $V$ held constant
• Integration and separable differential equations for rate laws
• Operators, eigenvalue equations, and normalization in quantum mechanics
• Exponentials, logarithms, and series for the Boltzmann distribution and partition functions

Where students usually get stuck

• Work and heat signs. Chemistry texts usually write $\Delta U = q + w$, while many engineering texts use the opposite sign for work.
• Forgetting which variable is held constant in a partial derivative.
• Using $\Delta G^{\circ}$ where $\Delta G$ is needed, or mixing up standard states.
• Units for $R$: $8.314\ \text{J/(mol K)}$ in energy problems and $0.08206\ \text{L atm/(mol K)}$ in gas problems.
• Treating a wavefunction as a picture instead of a solution to an equation with boundary conditions.