1.

Derive the integrated rate law for afirst order reaction ?

Answer»

Solution :A reaction rate depends on the reactant concentration raise to the power is called a first ORDER reaction.
First order reaction.
`A rarr` product
Rate law can be expressedas Rate `=k[A]^1`
Where, k is the first order rate constant
`(-d[A])/(dt)=k[A]^1`
`=(-d[A])/([A])=k dt""...(1)`
Integrate the above equation (1) between the limits of time t = - time equal to t , while the concentration varies from initial concentration `[A_0]" to" [A]` at the later times.
`int_(A_0)^(A) (-d[A])/([A])=kint_0^t dt`
`-LN[A]_A_0^A=k(t)_0^t`
`-ln[A]-[In[A_0])=k(t=0)`
`ln[A]+In [A_0]=kt `
`ln(([A_0])/([A]))=kt""...(2)`
This equation (2) is in natural logarithm . to convert it into usual logarithm the with base 10 , we have to MULTIPLY the term by 2.303
`2.303log(([A_0])/([A]))=kt`
`k=2.303/tlog(([A_0])/([A]))"".....(3)`


Discussion

No Comment Found