Question

A first order reaction, A -> products, has a rate reaction of .00250 Ms-1 when [A] = . 484 M. (a) What is the rate constant, k, for this reaction? (b) Does t1/2 depend on the concentration

Answer 1

Answer: a) The rate constant, k, for this reaction is
`0.00516s^(-1)`

b) No
`t_{(1)/(2)}` does not depend on concentration.

Step-by-step explanation:

Rate law says that rate of a reaction is directly proportional to the concentration of the reactants each raised to a stoichiometric coefficient determined experimentally called as order.

`A\rightarrow products`

Given: Order with respect to
`A` = 1

Thus rate law is:

a)
`Rate=k[A]^1`

k= rate constant

`0.00250=k[0.484]^1`

`k=0.00516s^(-1)`

The rate constant, k, for this reaction is
`0.00516s^(-1)`

b) Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

`t_{(1)/(2)}=(2.303)/(k)\log(100)/(50)`

`t_{(1)/(2)}=(0.69)/(k)`

Thus
`t_{(1)/(2)}` does not depend on concentration.