The rate constant of a reaction at temperature 200 K is 10 times less than the rate constant at 400 K. What is the activation energy Ea of the reaction? (R = Gas constant)

Question

The rate constant of a reaction at temperature 200 K is 10 times less than the rate constant at 400 K. What is the activation energy Ea of the reaction? (R = Gas constant) (A) 1842.4 R (B) 921.2 R (C) 460.6 R (D) 230.3 R

Tardigrade Admin · Accepted Answer

Activation energy can be calculated with Arrhenius equation
log

\frac{k _{2}}{k _{1}} = \frac{E _{a}}{2.303 R} [\frac{T _{2} = T _{1}}{T _{1} T _{2}}]

where,

k_{1}

= rate constant at

T_{1}

temperature

k_{2}

= rate constant at

T_{2}

temperature

E_{a}

= activation energy
R = gas constant

T_{1}, T_{2}

= temperatures in keivin
log

\frac{10}{I} = \frac{E _{a}}{2.303 R} [\frac{400 - 200}{400 \times 200}]

i =

\frac{E _{a}}{2.303 R} [\frac{200}{400 \times 200}]

E_{a} = 2.303 \times T \times 400

E_{a} = 921.2 R

Q. The rate constant of a reaction at temperature 200 K is 10 times less than the rate constant at 400 K. What is the activation energy Ea​ of the reaction? (R = Gas constant)

1842.4 R

921.2 R

460.6 R

230.3 R

Q. The rate constant of a reaction at temperature 200 K is 10 times less than the rate constant at 400 K. What is the activation energy $E_{a}$ of the reaction? (R = Gas constant)