Question

Activation energy of a chemical reaction can be determined by ______________

• A. determining the rate constant at standard temperature.
• B. determining the rate constants at two temperatures.
• C. using catalyst.
• D. determining probability of collision.

Answer 1

The correct option is B determining the rate constants at two temperatures.

Activation energy is calculated by using rate constants known at two different temperatures. Let us consider the following equation,

$ln\left(k\right)=\left(ln\right(A)-\frac{E_a}{RT})$

Using above equation at two different temperatures and subtracting we have,

$ln\left(k_2\right)-ln\left(k_1\right)$

$=\left(ln\right(A)-\frac{E_a}{R{T}_2})-\left(ln\right(A)-\frac{E_a}{R{T}_1})$

$ln\left(\frac{k_2}{k_1}\right)=\frac{E_a}{R}(\frac{1}{T_1}-\frac{1}{T_2})$

$log\left(\frac{k_2}{k_1}\right)=\frac{E_a}{2.303R}\left(\frac{1}{T_2}\frac{1}{T_2}\right)$



Where, $E_a$=Activation energy

$T_1$=lower temperature

$T_2$=Higher temperature

$K_1$=rate constant at temperature$T_1$

$K_2$=rate constant at temperature $T_2$

Hence, option (B) is correct.