If a 2^nd order reaction has the rate equation R = k[A][B], and the rate constan
ID: 1056630 • Letter: I
Question
If a 2^nd order reaction has the rate equation R = k[A][B], and the rate constant, k, is 3.67M^-1 s^-1, [A] is 4.5M and [B] is 99M, a. what is the rate constant of its pseudo-1^st-order reaction? b. What is the half-life of a reaction with [A]_0 = 109M, [B]_0 = 1M, k' = 45M^-1 s^-1? c. If [A] = 55M at 39s, [A]_0 = 99M, and [B]_0 = 1000M, what is the 2^nd order reaction rate constant? d. What is the concentration of A at time 45s if [A]_0 1M, [B]_0 = 45M, and 2^nd order rate constant is 0.6M^-1 s^-1?Explanation / Answer
a)
The 2nd order reaction rate is
R = k [A] [B]
Now we can see that the B is in much excess as compared to A. So, we can consider the concentration B as constant.
Pseudo 1st order recation rate is written as
R = k' [A]
where k' = k [B] = rate constant for pseudo 1st order reaction
k' = 3.67 M-1s-1 * 99 M
k' = 363.33 s-1
b)
Given data: [A]0 = 109 M [B]0= 1 M k'= 45 M-1s-1
Here we can see that [A]0 >> [B]0
so, rate equation is this case is R= k' [B]
k= 45 M-1s-1
Half life of pseudo first order reaction is
t1/2 = ln 0.5 / (-k [A]0) = ln 0.5/ (-45*109)= 1.4131 *10 -4 s
c)
Given data: [A]= 55 M at 39 s, [A]0= 99 M, [B]0=1000 M,
k=?
For Pseudo first order reaction.
Expression for concentartion of A at any time t is
[A]= [A]0 exp (-k't)= [A]0 exp (-k[B]0t) ............... (Here B is in excess)
55 = 99 exp (-k * 1000 * 39)
ln 0.556= -k*1000*39
k = 1.505*10-5 M-1s-1 = rate constant of second order reaction
d)
Given: [A]0= 1 M, [B]0= 45 M, k= 0.6 M-1s-1
Here,
concentration of A at time t is given by
[A]= [A]0 exp (-kt) = 1 M * exp (-0.6 * 45) = 1.879 *10-12 M