The rate of reaction `((dx)/(dt))` varies with nature, physical state and concentration of reactants, temperature, exposure to light and catalyst, whereas rate constant `(K)` varies with temperature and catalyst only. The rate constant `K` is given as `K=Ae^(-E_(a)//RT)` where `A` is Arrhenius parameter or pre-exponential factor and `E_(a)` is energy of activation. The minimum energy required for a reaction is called threshold energy and the additional energy required by reactant molecules to attain threshold energy level is called energy of activation.
How much faster would a reaction proceed at `25^(@)C` than at `0^(@)C` if the activation energy is `2` cal?

Options

A. (a) `2` times
B. (b) `16` times
C. (c ) `11` times
D. (d) Almost at same speed

Answer

d

Explanation

`K_(1)=Ae^(-2/(RxxT_(1)))=Ae^(-2/(2xx273))`
`K_(2)=Ae^(-2/(RxxT_(2)))=Ae^(-2/(2xx298))`
`:. K_(1)/K_(2)=e^([-1/298+1/273])=1.0003`
`:. r_(1)/r_(2)=1.0003`