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Following data are obtained for the reac...

Following data are obtained for the reaction :
`N_(2)O_(5)rarr2NO_(2)+(1)/(2)O_(2)`
`{:(t(s)," "0," "300," "600),([N_(2)O_(5)("mol.L"^(-1))],1.6xx10^(-2),0.8xx10^(-2),0.4xx10^(-2)):}`
Show that it follows first order reaction.

Text Solution

Verified by Experts

For first order reaction,
`k=(2.303)/(t)log.(([A]_(0))/([A])), "where "[A]_(0) and [A]` are the initial concentration and the concentration at time t of the reactant and k is the rate constant of the reaction.
`therefore "At "t = 300s`
`k=(2.303)/(300)log.((1.6xx10^(-2))/(0.8xx10^(-2)))=(2.303)/(300)log(2)`
`=(2.303xx0.3010)/(300)=0.00231s^(-1)`
At t = 600s
`k=(2.303)/(600)log.((1.6xx10^(-2))/(0.4xx10^(-2)))=(2.303)/(600)log(4)`
`=(2.303xx0.6021)/(600)=0.00231s^(-1)`
Therefore, the given reaction follows first order kinetics.
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