Gas-Phase Kinetics

Introduction

Gas reactions are often monitored with pressure rather than solution concentration. For an ideal gas mixture, each species' molar concentration is cᵢ=pᵢ/(RT), where pᵢ is partial pressure. This conversion is simple only when temperature, volume and gas composition are handled carefully. Total pressure alone can hide species changes.

Core explanation

From pᵢV=nᵢRT, divide by VRT to obtain nᵢ/V=pᵢ/(RT). Thus at fixed T, concentration is proportional to partial pressure. If rate=k[A][B] in concentration units, substitute [A]=pA/(RT) and [B]=pB/(RT): rate=k pA pB/(RT)². A pressure-based rate constant can absorb the (RT) factors, but its units and temperature dependence differ from the original concentration-based k. State which form is used.

For gas A → 2B in a sealed rigid vessel at fixed T, total molecule count increases as reaction proceeds, so total pressure rises. Yet the A partial pressure falls. A total-pressure slope can be converted to reaction extent only with the stoichiometry and starting composition. If an inert gas is also present, total pressure includes its contribution but its partial pressure may remain constant in a rigid vessel.

Compression at fixed temperature increases reacting gas concentrations and often increases rate for positive-order laws. Adding an inert gas at constant volume and temperature raises total pressure but leaves reacting partial pressures unchanged, so an ideal-gas rate law based on their concentrations may be unaffected. Adding inert gas at constant total pressure can expand the volume, lower reacting partial pressures and alter rate. The phrase “pressure increases rate” is incomplete without saying how pressure changed.

Temperature changes both k and the conversion between pressure and concentration. At fixed rigid volume, heating raises gas pressure even if no reaction occurs. If a pressure sensor is used to infer reaction speed, thermal drift must be controlled. In a variable-volume reactor, concentration derivatives also include expansion effects, so extent or mole-flow methods may be more appropriate than a naive −dpA/dt conversion.

Gas-phase mechanisms can involve third bodies or falloff behavior. A nominally unimolecular process may need collisions to energize molecules at low pressure, causing apparent order to change with pressure. This advanced exception reinforces that a rate law is measured under a specified pressure regime rather than declared from the net equation.

Safety and engineering considerations matter at high pressure, but the conceptual calculation should stay clear: identify partial pressures, convert using R and T in matching units, and track stoichiometry. Units such as bar and Pa require compatible R values; mixing them silently creates large numerical errors.

Step-by-step reasoning

1. Identify each reacting species' partial pressure, not just total pressure. 2. Use cᵢ=pᵢ/(RT) with compatible units and absolute temperature. 3. Substitute into the measured concentration-based rate law if needed. 4. Account for stoichiometric changes in gas molecule count. 5. State whether volume, pressure or temperature is held constant.

Visual explanation

Draw a rigid box containing A and B dots with separate pA and pB labels. A second box shows inert gas added: total pressure rises but A and B dot densities remain the same. A third compressed box shows A and B densities rising, clarifying the distinct operations.

Real-world analogy

Total traffic on a road includes cars and buses, but the collision chances of two car types depend on each type's density. Raising the total by adding buses need not change car–car encounters in the same space.

Real-world example

In a sealed gas reactor, an A → 2B decomposition raises total pressure. Monitoring that rise can reveal progress if temperature is controlled and the stoichiometric relation is known.

Why?

Why can inert-gas addition at constant volume fail to change the reacting rate? The reacting gases' molecule counts and volume stay the same, so their concentrations and partial pressures remain unchanged in the ideal model.

Common misconception

“Any rise in total gas pressure increases reaction rate.” Heating or adding inert gas can raise total pressure without raising reacting species concentrations; the operation and rate law decide the effect.

Worked example

For a gas at pA=1.00 bar and T=300 K, use R=0.08314 L bar mol⁻¹ K⁻¹. Then [A]=pA/(RT)=1.00/(0.08314×300)=0.0401 mol L⁻¹. If rate=k[A] with k=0.20 s⁻¹, rate=0.00802 mol L⁻¹ s⁻¹. The bar units cancel only because R is expressed with bar.

Quick check

1. What pressure belongs in cᵢ=pᵢ/(RT) for species i? Answer: Its partial pressure pᵢ, not the total mixture pressure.

Exam focus

State gas-law assumptions and controlled variables, keep R units compatible with pressure, and distinguish inert-gas addition from compression. Normalize measured pressure changes through stoichiometry.

Advanced insight

In flow reactors, residence time, pressure drop and concentration gradients make local rates vary along the reactor. A single bulk pressure may not represent the conditions at every position.

Summary

Ideal-gas partial pressure converts to concentration by pᵢ/(RT). Gas rate effects depend on partial pressures, stoichiometry and whether volume or temperature changes. Total pressure alone is not a complete kinetic variable.

Practice questions

1. Does adding inert gas at fixed T and V change pA for an ideal mixture with fixed nA? Answer: No; pA=nART/V stays the same. 2. What happens to [A] under isothermal compression if nA remains fixed? Answer: It rises because V falls. 3. Why can heating mimic reaction progress on a total-pressure trace? Answer: Pressure rises with temperature at fixed volume even without chemical conversion.