derive integrate rate of eqution for first order reaction
Answers
Answer:
Rate R = K [A] where [A] is the concentration of the reactant A and k is the velocity constant or specific rate of the reaction. This is the integranted rate equation for the first order reaction . This is also called integrated rate law.
a) 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
.