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The rate of reaction ((dx)/(dt)) varies ...

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.
The temperature coefficient of reaction `I` is `2` and reaction `II` is `3`. Both have same speed at `25^(@)C` and show `I` order kinetics. The rati of rates of reaction of these two at `75^(@)C` is:

A

(a) `7.6`

B

(b) `5.6`

C

(c ) `6.6`

D

(d) `8.6`

Text Solution

Verified by Experts

The correct Answer is:
a
For `I` order reaction, `r_(1)=K[]^(1)`
`:. R_(1)/r_(2)=K_(1)/K_(2)`=temperature coefficient
Let the rate of reaction for `I` at `25^(@)C` be `R_(1)` and the rate of reaction for `II` at `25^(@)C` be `R_(2)`
`{:(,"Also"",",,,,R_(1)=R_(2)),(,,,,,"Rate of reaction"),( :.,At 25^(@)C,,R_(1),,R_(2)),(,35^(@)C,,2R_(1),,3R_(2)),(,45^(@)C,,(2)^(2)R_(1),,(3)^(2)R_(2)),(,55^(@)C,,(2)^(3) R_(1),,(3)^(2)R_(2)),(,65^(@)C,,(2)^(4)R_(1),,(3)^(4)R_(2)),(,75^(@)C,,(2)^(5)R_(1),,(3)^(5)R_(2)):}`
:. Temperature coefficient for `I` reaction
`=K_(35)/K_(25)=R_(35)/R_(25)=2`
i.e., for each `10^(@)C` rise in temperature, rate becomes `2` times. Similarly for `II` reaction it becomes `3` times.
`therefore 75^(@)C`,
`("rate of reaction for II")/("rate of reaction for I")=((3)^(5)R^(2))/((2)^(5)R^(1))` `(because R_(1)=R_(2))`
=7.5937
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