Arrhenius Equation & Temperature Dependence | Chemical Kinetics Class 12

Arrhenius Equation

Temperature Dependence of Reaction Rate | Chemical Kinetics Class 12

1. Temperature Dependence

For most chemical reactions, the rate of reaction increases significantly with an increase in temperature. A general rule of thumb is that for every 10°C rise in temperature, the rate constant is nearly doubled.

                    Temperature Coefficient:
                    $$ \frac{k_{(T+10)}}{k_T} \approx 2 \text{ to } 3 $$
                

2. The Arrhenius Equation

Svante Arrhenius proposed a quantitative relationship between rate constant ($k$) and temperature ($T$):

$$ k = A e^{-E_a/RT} $$

Where:

$A$ = Arrhenius Factor / Frequency Factor / Pre-exponential Factor.
$E_a$ = Activation Energy ($J \cdot mol^{-1}$).
$R$ = Gas Constant ($8.314 \, J \cdot K^{-1} \cdot mol^{-1}$).
$T$ = Temperature in Kelvin.
$e^{-E_a/RT}$ = Boltzmann factor (Fraction of molecules with energy $\ge E_a$).

3. Logarithmic Forms & Graphs

Taking natural logarithm ($\ln$) on both sides:

$$ \ln k = \ln A - \frac{E_a}{RT} $$

Converting to base 10 log ($\log$):

$$ \log k = \log A - \frac{E_a}{2.303RT} $$

                    Graph of $\log k$ vs $1/T$:
                    This is a straight line equation ($y = mx + c$).
Slope: $m = -\frac{E_a}{2.303R}$
Intercept: $c = \log A$

                

4. Calculation for Two Temperatures

If rate constants $k_1$ and $k_2$ are measured at temperatures $T_1$ and $T_2$ respectively:

$$ \log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left[ \frac{1}{T_1} - \frac{1}{T_2} \right] $$
$$ \log \frac{k_2}{k_1} = \frac{E_a}{2.303R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right] $$

5. Effect of Catalyst

A catalyst increases the rate of reaction by providing an alternate pathway with a lower Activation Energy ($E_a$). It does not alter Gibbs Energy ($\Delta G$) or Equilibrium Constant ($K$).

Practice Quiz

Test your knowledge on Arrhenius Theory.

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