A hydrogenation reaction is carried out at `500 K`. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is `400 K`. Calculate the activation energy of the reaction if the catalyst lowers the activation barrier by `20 kJ mol^(-1)`.

Options

A. 110 kJ/mol
B. 10 kJ/mol
C. 100 kJ/mol
D. 1000 kJ/mol

Answer

C

Explanation

`K_(500)=Ae^((-E_(1))/(RT_(1))),K_(400)=Ae^((-E_(2))/(RT_(2)))`
According to equation , `K_(500)=K_(400)`
`therefore" "(E_(1))/(RT_(1))=(E_(2))/(RT_(2))" "rArr" "(E_(2))/(E_(1))=(T_(2))/(T_(1))=(4)/(5)`
`"Also, "E_(1)=E_(2)+20000J`
`"So, "(E_(1)-20000)/(E_(2))=(4)/(5)," "E_(1)=100,000J`
So, `(E_(1)-20000)/(E_(2))=(4)/(5)," "E_(1)=100,000J=100kJ//mol`