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Two first order reactions proceed at the...

Two first order reactions proceed at the same rate at `25^(@)C` when started with same initial concentration. The temperature coefficient of the first reaction is 2 while that of the second reaction is 3. What will be the ratio of the rates reactions at `55^(@)C` ?

Text Solution

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If `R_(1)` is the rate of first reaction at `25^(@)C`, then as its temperature coefficient is 2, its rate at `35^(@)C` will be
`=2" R"_(1),"at "45^(@)C=2xx2" R"_(1)=4" R"_(1)" and at "55^(@)C=2xx4" R"_(1)=8" R"_(1)`
If `R_(2)` is the rate of the second reaction at `25^(@)C`, then as its temperature coefficient is 3, its rate at `35^(@)C` will
be `=3" R"_(2)," at "45^(@)C=3xx3" R"_(2)=9" R"_(2)" and at "55^(@)C=3xx9" R"_(2)=27" R"_(2)`
Also, we are given `R_(1)=R_(2)`, i.e., at `25^(@)C`, the rates are equal.
`:." At "55^(@)C," "("Rate of 2nd reaction")/("Rate of 1st reaction")=(27" R"_(2))/(8" R"_(1))=(27)/(8)`
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