How Does Partial Pressure Affect Rate?

Increased partial pressure of a gaseous reactant generally leads to a faster reaction rate, while decreased partial pressure slows it down.

Here's a more in-depth explanation:

The Connection Between Partial Pressure and Reaction Rate

Partial pressure is the pressure exerted by an individual gas in a mixture of gases. In the context of chemical reactions involving gases, the partial pressure of a reactant directly relates to its concentration. A higher partial pressure means a higher concentration of that gas is present.

• Increased Concentration, Increased Collisions: According to collision theory, for a reaction to occur, reactant molecules must collide with sufficient energy and proper orientation. A higher concentration of reactants (achieved through higher partial pressure for gases) increases the frequency of these collisions.

• Rate Law and Partial Pressure: The rate law mathematically expresses the relationship between reactant concentrations (and thus, partial pressures for gases) and the reaction rate. For example, consider a simple reaction:

  A (g) + B (g) → Products

  The rate law might look like this:

  Rate = k[A]^m[B]ⁿ

  Where:

  • k is the rate constant (temperature-dependent)
  • [A] and [B] are the concentrations of reactants A and B
  • m and n are the reaction orders with respect to A and B (determined experimentally)

  Since the concentration of a gas is directly proportional to its partial pressure (from the ideal gas law, PV = nRT, so P ∝ n/V ∝ concentration), we can rewrite the rate law in terms of partial pressures:

  Rate = k(P_A)^m(P_B)ⁿ

  This demonstrates that if the partial pressure of A or B increases, the reaction rate will also increase (assuming m and n are positive).

Examples

• Combustion: The rate of combustion (burning) is heavily dependent on the partial pressure of oxygen. Increasing the oxygen partial pressure (e.g., using pure oxygen instead of air, which is only about 21% oxygen) dramatically increases the rate of burning.

• Haber-Bosch Process: This industrial process for synthesizing ammonia (N₂ + 3H₂ → 2NH₃) uses high pressures of nitrogen and hydrogen to increase the reaction rate and yield of ammonia.

Factors Affecting the Impact of Partial Pressure

The exact impact of partial pressure on the reaction rate depends on:

• Reaction Order: The exponents m and n in the rate law determine the magnitude of the effect. A reaction that is first order with respect to a particular reactant (exponent = 1) will have a linear relationship between its partial pressure and the rate. A reaction that is second order (exponent = 2) will have a squared relationship, meaning a change in partial pressure will have a more significant effect.

• Other Reactants: The partial pressures of all gaseous reactants are important. If one reactant is present in excess, changing its partial pressure may have a less noticeable effect than changing the partial pressure of a reactant present in a lower concentration.

• Temperature: Temperature also influences reaction rate. Increasing the temperature generally increases the rate constant k, making the reaction proceed faster regardless of the partial pressures.

Summary

In essence, the partial pressure of a gaseous reactant affects the reaction rate by influencing the reactant concentration, which, in turn, affects the frequency of collisions between reactant molecules. Higher partial pressure typically means a higher reaction rate.