Concept of Chemical Equilibrium
Chemical equilibrium is the state of a reversible reaction in which the rate of the forward reaction equals the rate of the reverse reaction. At the beginning of the process, the reactant concentration is at its maximum and products are absent, so the forward reaction rate is high, while the reverse rate is zero. As products accumulate, the forward reaction rate decreases and the reverse rate increases. At the point where they equalize, dynamic equilibrium is established: the reaction continues in both directions, but no visible changes in concentrations occur.
It is important to understand that the equilibrium concentration of a substance is not the amount formed in the forward reaction, but what remains after the partial return of products to reactants via the reverse reaction.
Task Condition
Methane and oxygen were placed in a constant-volume reactor. The reaction proceeds:
CH₄ + 2O₂ ⇌ 2CO + 4H₂ + ... (simplified scheme for illustrating the calculation using 1 : 2 : 2 : 4 coefficients).
- Initial concentration of O₂: 0.5 mol/L
- Initial concentration of CH₄: x (target)
- Equilibrium concentration of CO: 0.4 mol/L
- Equilibrium concentration of H₂: 0.8 mol/L
- Equilibrium concentration of CH₄: 0.2 mol/L
- Equilibrium concentration of O₂: y (target)
Typical Error: Calculation Based on Oxygen
It is tempting to calculate using the known oxygen concentration (0.5 mol/L). According to stoichiometry, 0.5 mol/L of O₂ yields 0.5 mol/L of CO and 1.0 mol/L of H₂. Then the reverse reaction "consumes" 0.6 mol/L of CO and 1.2 mol/L of H₂, forming 0.6 mol/L of CH₄. However, this contradicts the condition: the equilibrium methane concentration must be 0.2 mol/L.
The reason for the discrepancy is excess and limiting reactant. The condition does not state which reactant is in excess. If the calculation is performed using the excess substance, stoichiometry distorts the result. Therefore, calculations must be based on the limiting reactant — in this case, methane.
Correct Solution Steps
- Analysis of the reverse reaction via methane. The equilibrium concentration of CH₄ is 0.2 mol/L — this is the amount regenerated by the reverse reaction.
- Stoichiometric recalculation. 0.2 mol/L of CH₄ were formed from 0.2 mol/L of CO and 0.4 mol/L of H₂ (coefficients 1 : 2 : 4 → for methane 1, carbon monoxide 2, hydrogen 4; the reverse pathway yields a proportion of 0.2 : 0.2 (per coefficients in the initial reaction 2:2... — accounted for by the ratio from the lecture)).
- Products actually formed in the forward reaction: CO — 0.4 + 0.2 = 0.6 mol/L; H₂ — 0.8 + 0.4 = 1.2 mol/L.
- Initial methane concentration: according to stoichiometry, CH₄ → 2CO, meaning 0.6 mol/L of methane reacted. Adding the equilibrium residue of 0.2: x = 0.6 + 0.2 = 0.8 mol/L (or another option depending on the reaction notation; in the lecture, x = 0.6 was used as the amount that reacted in the forward reaction).
Calculation of Equilibrium Oxygen Concentration
Checking the excess: for 0.6 mol/L of reacted methane, only 0.3 mol/L of O₂ is required (coefficient 2 balanced by the task ratio). Given 0.5 mol/L — oxygen is indeed in excess, confirming the hypothesis.
The reverse reaction returns oxygen: 0.2 mol/L of CO in the reverse reaction yield 0.1 mol/L of O₂. The regenerated oxygen is added to the excess remainder (0.2 mol/L):
y = 0.2 + 0.1 = 0.3 mol/L.
Methodological Conclusions
- In problems with a single given reactant, the calculation is always based on it — the issue of excess does not arise.
- In problems with two given reactants, it is required to determine which of them is limiting and perform the calculation based on it — otherwise, stoichiometry will yield a false result.
- Equilibrium concentration of a product = (formed in forward reaction) − (returned in reverse).
- Equilibrium concentration of a reactant = (initial) − (reacted) + (regenerated in reverse reaction).
- The problem requires not only theoretical knowledge, but also the skill of identifying excess and limiting reactants, practiced through problem-solving.
Key points
- Chemical equilibrium is a state with equal rates of forward and reverse reactions.
- Equilibrium concentration is the result of two opposing processes, not the outcome of the forward reaction alone.
- In a system with two known reactants, the calculation is performed via the limiting substance.
- Stoichiometric coefficients are used to test the excess hypothesis.
- The reverse reaction returns part of the reactants: their equilibrium concentration is higher than that calculated from the "complete" forward reaction.
- Stoichiometric coefficients are applied in both forward and reverse directions.
- Unified State Exam Task 26/32 on equilibrium is one of the most difficult and requires systematic practice.