Question

The rate consnt for a reaction is measured as a function of temperature. A plot of ln k versus 1/T is linear and has s slope of -1.01 x 1-^4K. Calculate the activation energy for the reaction

Answer 1

Answer : The activation energy for the reaction is,
`8.39* 10^4J`

Explanation :

According to the Arrhenius equation,

`K=A* e^{(-Ea)/(RT)}`

Taking logarithm on both side, we get:

`\ln K=(-Ea)/(RT)+\ln A`

where,

`Ea` = activation energy for the reaction

R = gas constant = 8.314 J/mole.K

T = temperature

K = rate constant

A = pre-exponential factor

The linear equation expression is:

y = mx + c

Plot of ln (K) versus (1/T) gives a straight line with a slope is equal to,
`(-Ea)/(R)`

As we are given that:

Slope =
`-1.01* 10^4K`

So,

`Slope=(-Ea)/(R)=-1.01* 10^4K`

`-Ea=-1.01* 10^4K* R`

`Ea=1.01* 10^4K* 8.314J/mol.K`

`Ea=83971.4J=8.39* 10^4J`

Thus, the activation energy for the reaction is,
`8.39* 10^4J`