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what will be the effect of temperature on rate constant

Increasing temperature increases the rate constant kkk of a reaction, usually quite sharply; decreasing temperature lowers kkk. This temperature effect is described quantitatively by the Arrhenius equation.

Core idea

  • The rate constant kkk depends on temperature ; it is not actually “constant” if temperature changes.
  • As temperature TTT increases, more reacting molecules have energy greater than or equal to the activation energy EaE_aEa​, so successful collisions become more frequent and kkk becomes larger.

In many ordinary reactions, a rise of about 10 °C roughly doubles the value of the rate constant, though this is an approximate rule of thumb.

Arrhenius equation

The temperature dependence of the rate constant is given by the Arrhenius equation :

k=Ae−Ea/RTk=Ae^{-E_a/RT}k=Ae−Ea​/RT

  • kkk: rate constant
  • AAA: pre‑exponential (frequency) factor
  • EaE_aEa​: activation energy
  • RRR: gas constant
  • TTT: absolute temperature (in kelvin)

From this expression: as TTT increases, −Ea/RT-E_a/RT−Ea​/RT becomes less negative , so e−Ea/RTe^{-E_a/RT}e−Ea​/RT increases, and hence kkk increases.

Taking natural logs gives a straight‑line form:

ln⁡k=−EaR1T+ln⁡A\ln k=-\frac{E_a}{R}\frac{1}{T}+\ln Alnk=−REa​​T1​+lnA

  • A plot of ln⁡k\ln klnk versus 1/T1/T1/T is linear, with slope −Ea/R-E_a/R−Ea​/R and intercept ln⁡A\ln AlnA.
  • This allows experimental determination of activation energy and the factor AAA from rate data at different temperatures.

Physical explanation (qualitative)

  • At higher temperature, particles move faster, so:
    • Collision frequency increases slightly.
    • More importantly, the fraction of molecules with energy ≥ EaE_aEa​ increases markedly (as seen from the Maxwell–Boltzmann distribution).
  • Because only those higher‑energy collisions are effective, a small rise in temperature causes a disproportionately large increase in kkk and the reaction rate.

In short, raising temperature increases the rate constant (often roughly doubling it per 10 °C for many reactions), and this effect is captured mathematically by the Arrhenius equation.

TL;DR:

  • Higher TTT → higher kkk (reaction faster).
  • Lower TTT → lower kkk (reaction slower).
  • Quantitative relation: Arrhenius equation k=Ae−Ea/RTk=Ae^{-E_a/RT}k=Ae−Ea​/RT.

Information gathered from public forums or data available on the internet and portrayed here.