Derive the integrated rate equation for a first order reaction
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Answer:
Consider a general first order reaction
R → P
The differential rate equation for given reaction can be written as
Rate=−
dt
d[R]
=K[R]
1
Rearrange above equation.
[R]
d[R]
=−K×dt
Integrating on both sides of the given equation
∫
[R]
d[R]
=−k∫dt
ln[R]=−Kt+I ..(1)
Where I is Integration constant
At t=0 the concentration of reactant [R]=[R]
0
where [R]
0
is initial concentration of reactant
Substituting in equation (1) we get
ln [R]
0
=(−K×0)+I
ln [R]
0
=I (2)
Substitute I value in equation (1)
ln [R]=−Kt+ln[R]
0
Kt=ln[R]
0
−lnR
Kt=ln
[R]
[R]
o
or K=
t
1
ln
[R]
[R]
0
.
or K=
t
2.303
log
[R]
[R]
0
.
solution
Explanation:
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