Answer to Question #121858 in General Chemistry for Tiffany

Question

The following reaction was monitored as a function of time:
AB→A+B
A plot of 1/[AB] versus time yields a straight line with slope 5.5×10−2 (M⋅s)−1 .

If the initial concentration of AB is 0.230 M , and the reaction mixture initially contains no products, what are the concentrations of A and B after 75 s ?
Express your answers numerically using two significant figures, separated by a comma.
[A],[B] = ?M
(There are 2 answers to this, separated by a comma)

Answer 1

Answer

The plot of 1/[AB] vs time is a straight line plot, so, the reaction is second order in nature with respect to AB. And the value of slope of the straighline is equal to the rate constant of the reaction

Considering the reaction to be second order

AB---->A+B

When t->0, [AB] = a, [B] = 0, [A] = 0

And when t -> t, [AB] = a-x, [B] = x, [A] = x

So, the rate equation of the reaction is

-d[AB]/dt = k[AB]² where k is the rate constant

integrating the above equation between t = o, and [AB] = a to t = t and [AB] = a-x we get,

1/(a-x) -1/a = kt

Here, according to the question, t = 75s, k = 5.5x10^-2 MS^-1 and a = 0.230 M

So (a-x) = 0.227 M

x = 0. 003 M

So, concentration of A and B after 75s are 0.003 and 0.003 M respectively.