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The rate constant of decomposition of me...

The rate constant of decomposition of methyl nitrite `(K_(1))` and ethyl nitrite `(K_(2))` follow the equations.
`K_(1)(s^(-1))=10^(13)e^([(-152.3xx10^(3))/(RT)Jmol^(-1)])`
and `K_(2)(s^(-1))=10^(14)e^([(-152.3xx10^(3))/(RT)Jmol^(-1)])`
Calculate the temperature at which both have same rate of decomposition if `0.1M` of each is taken and both show `I` order kinetics.

Text Solution

Verified by Experts

Rate= `K "[Reactant"]^(1)`
Since [Reactant]=`0.1 M` and rates are same, thus at same temperature
`K_(1)=K_(2)`
`10^(13)e^((-152.3xx10^(3))/(RT))=10^(14) e^((-157.7xx10^(3))/(RT)`
`e^(((+5.4xx10^(3))/(RT)))=10`
`(5.4xx10^(3))/(RT)=2.303`
`:. T=(5.4xx10^(3))/(8.314xx2.303)=282 K`
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