The Sealed Vessel and the Shifting Equilibrium
A 2.0 L rigid steel vessel at 700 K is charged with 0.40 mol H2, 0.40 mol I2, and 1.20 mol HI. The reaction H2(g) + I2(g) ⇌ 2 HI(g) has Kc = 54.3 at 700 K. A technician argues that because there are equal moles of gas on each side, adding more HI can never change the equilibrium position, and therefore the vessel is already at equilibrium. A second technician measures the pressure and notes it is higher than expected for 2.0 mol of gas and suspects a leak of H2 through a valve seal. The vessel is then compressed to 1.0 L with a piston while temperature is held at 700 K.
1. Determine whether the initial mixture is at equilibrium and, if not, the direction in which it must shift.
Read the worked answer
Compute the reaction quotient with concentrations.
- [H2] = [I2] = 0.40/2.0 = 0.200 M
- [HI] = 1.20/2.0 = 0.600 M
- Qc = [HI]²/([H2][I2]) = (0.600)²/(0.200 × 0.200) = 0.360/0.0400 = 9.0
Qc = 9.0 < Kc = 54.3, so the system is not at equilibrium; it must shift toward products (right) to raise Qc to 54.3.
The technician's claim is wrong: equal moles of gas on each side means pressure/volume changes do not shift this equilibrium, but adding or removing a species still changes Qc, so composition changes do shift it.
2. Predict the effect of compressing to 1.0 L at constant temperature, and explain whether the leak hypothesis is consistent with the equal-moles argument.
Read the worked answer
Compression: Δn_gas = 2 − 2 = 0, so Kc is unchanged and the equilibrium position is unaffected by volume change. All concentrations double, but Qc = (2[HI])²/((2[H2])(2[I2])) = Qc, so no shift occurs. Only the rate of both forward and reverse reactions increases.
Leak hypothesis: If H2 leaks, [H2] falls, Qc = [HI]²/([H2][I2]) rises, and the system shifts left, consuming HI and producing more H2 and I2. This is fully consistent - the equal-moles rule only protects against pressure/volume changes, not against removal of a component. The technician conflated the two effects. A pressure lower than expected for the stated moles supports a leak, but the composition shift would partly offset the mole loss.