Chemical equilibrium and routes to K
After midterm · Session 5 of 6 · 180 minutes
30 September 2026
The question for today
Why can composition change while the equilibrium constant stays the same?
Before class: 3-page reading · 15–20 minutes
Bring the three preparation answers. Revisit your prediction after one controlled comparison and an independent check.
The 180-minute class
| Activity | Minutes |
|---|---|
| Opening question and essential concepts | 30 |
| One hand calculation | 20 |
| One lab demonstration | 20 |
| Break | 10 |
| Student pair investigation | 70 |
| Discussion and exit question | 30 |
The 70-minute investigation is student work with instructor support.
Start with extent and driving force
n_i=n_{i,0}+\nu_i\xi,\qquad n_i\geq0 \left(\frac{dG}{d\xi}\right)_{T,P}=\Delta_rG=\Delta_rG^\circ+RT\ln Q
Write the feasible extent interval first. A negative derivative favors increasing extent; a positive derivative favors decreasing extent.
An interior equilibrium has zero derivative. Boundary minima need one-sided checks.
The equilibrium condition gives K
\Delta_rG=0\ \Rightarrow\ Q=K,\qquad\ln K=-\frac{\Delta_rG^\circ}{RT}
Obtain standard Gibbs energy from direct data, formation properties, or H−TS at the evaluation temperature.
K depends on T and the reaction/standard-state convention. Q describes the current composition and pressure.
Additional K(T) routes are in the appendix and lab.
A reference-state check
Lab 12 synthetic A₂ ⇌ 2A at 350 K uses ΔrG°=−4.000 kJ/mol.
\ln K=\frac{4000}{R(350)}=1.37454,\qquad K\approx3.95326
With ΔrH°=50.000 kJ/mol and ΔrS°=54000/350 J mol⁻¹ K⁻¹, the H−TS route gives the same value.
Check the minimum and the reaction quotient
At ξ≈0.70503 mol, Q≈3.95326=K. Check the atom balance.
One demonstration · 20 minutes
Use the synthetic Lab 12 case. Write nA₂=1−ξ, nA=2ξ and 0≤ξ≤1 mol first. Compare the supplied Gibbs-energy and H−TS routes, then change only pressure and inspect K and extent.
Keep one saved baseline for the pair investigation.
Pair investigation · 70 minutes
- 10 min: predict and record the baseline.
- 25 min: change one input and calculate.
- 20 min: exchange roles and check the result by hand.
- 15 min: prepare one plot or table and a short explanation.
In Lab 12, compare the supplied Gibbs-energy and H−TS routes at the reference temperature. Change pressure at fixed T and compare K with equilibrium extent. Check one balance.
Discussion and exit question · 30 minutes
Use 20 minutes to compare results and discuss unexpected behavior.
Why can composition change while the equilibrium constant stays the same?
Use the final 10 minutes to explain your answer individually and name one assumption that limits it.
Follow-up practice · 30–40 minutes
In Lab 12, compare the supplied Gibbs-energy and H−TS routes at the reference temperature. Change pressure at fixed T and compare K with equilibrium extent. Check one balance.
Assessment 5 and independent checkpoint
Retain one study JSON, one comparison and a short explanation. Continue from your classroom case. The hand checkpoint is included. With pre-class reading, independent work totals 45–60 minutes.
Optional study
Choose one extension: vary temperature with and without a heat-capacity correction, reverse the reaction, or scale its coefficients consistently.
Session appendix · Module reference
Learning path · Offline package
Optional work is additional. Complete the required investigation first.