Question

The rate of reaction at 550 K is ten times faster than the rate of reaction at 440 K. Find the activation energy from the collision theory. a) 40075.14 J/mol b) 50078.5J/mol c) 44574.5 J/mol d) 43475.5 J/mol

Answer 1

Answer : a) 40075.14 J/mol

Explanation :

According to the Arrhenius equation,

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

or,

`\log ((K_2)/(K_1))=(Ea)/(2.303* R)[(1)/(T_1)-(1)/(T_2)]`

where,

`K_1` = rate constant at
`440K` = k

`K_2` = rate constant at
`550K` = 10 k

`Ea` = activation energy for the reaction = ?

R = gas constant = 8.314 J/mole.K

`T_1` = initial temperature = 440 K

`T_2` = final temperature = 550 K

Now put all the given values in this formula, we get :

`\log ((10k)/(k))=(Ea)/(2.303* 8.314J/mole.K)[(1)/(440K)-(1)/(550K)]`

`Ea=40075.14J/mol`

Therefore, the activation energy for the reaction is 40075.14J/mol.