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For the two gaseous reactions , followi...

For the two gaseous reactions , following data are given
`AtoB,k_(1)=10^(10)e^(-20,000//T)`
`CtoD,k_(2)=10^(12)e^(-24606//T)` the temperature at which `k_(1)` becomes equal to `k_(2)` is

A

a) 400 K

B

b) 1000 K

C

c) 800 K

D

d) 1500 K

Text Solution

Verified by Experts

The correct Answer is:
B
Given `k_(1)=10^(10)e^(-20,000//T)`
`k_(2)=10^(12)e^(-24,606//T)`
`10^(10)e^(-20,000//T)=10^(12)e^(-24,606//T)`
`e^((-20,000)/(T)+(24,606)/(T))=10^(2)`
`e^((4,606)/(T))=10^(2)`
On taking log both sides
`(4606)/(2.303T)=log10^(2)`
`2log10xxT=(4606)/(2.303)`
`T=(4606)/(2.303xx2)`
`=(4606)/(4.606)=1000K`
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