Question

consider the unimolecular elementary irreversible reaction: A--> B

1. The rate constant is 2.0 s-1, the concentrations of A and B at time zero are 0.16 M and 0 M, respectively.

Compute (a) the half-life of A and the time constant for the process, and (b) compute the concentrations of A and

B at times t = 0.30, and 1.40 s.

2. The concentration of A at time zero is 0.160 M. At time t=3.0 s and t=6.0 s the concentrations of A are

measured to be 0.111 M and 0.077 M, respectively. Compute (a) the rate constant and (b) the half-life of A and

the time constant for the process.

Answer 1

1.) Rate constant, K = 2.0 s^-1

At t = 0, [Ao] = 0.16 M

a)

time constant = 1/k = 1/2=0.5 s

b)

At time, t = 0.30 s

Formula

This the concentration of A remained in the reaction at t = 0.30 s

[B] = 0.16 - 0.0878 = 0.0722 M

At time, t = 1.40 s

Formula

This the concentration of A remained in the reaction at t = 1.40 s

[B] = 0.16 - 0.00973 = 0.150 M

----------------------------

2)

[A_o] = 0.16 M

t = 3.0 s

[A] = 0.111 M

Formula

K = 0.122 s^-1

similarly we have to check for other [A]

If we get same "K" then it is first order reaction

K = 0.122 s^-1

Thus it is a first order reaction and k = 0.122 s^-1

Half life =

Half life = 5.68 s

Time constant = 1/k = 1/0.122 = 8.2 s