Question

3) A certain reaction has the following general form: A + B à AB At a particular temperature the concentration versus time were collected for this reaction, and a plot of ln[A]t versus time resulted in a straight line with a slope of −3.7 x 10−3 s−1. Show your math! (5 points) a. What is the order of the reaction? b. What is the rate constant (including units)? c. Calculate the half-life for the reaction. d. If the initial concentration of A is 0.250 M, what is the concentration after 220 seconds?

Answer 1

a. First order.

b.
`k=3.7x10^(-3)s ^(-1)`

c.
`t_(1/2)=187.3s`

d.
`[A]=0.111M`

Step-by-step explanation:

Hello.

a. In this case since the slope is in s⁻¹ we can infer that the lineal form of the rate law is:

`ln[A]=-kt+ln[A]_0`

Which is also:

`y=mx+b`

It means that the reaction is first-order as slope equals the negative of the rate constant which also has units of first-oder reaction.

b. Since the slope is −3.7 x 10−3 s−1 the rate constant is:

`k=-m\\\\k=-(-3.7x10^(-3)s ^(-1))\\\\k=3.7x10^(-3)s ^(-1)`

c. For first-order reactions, the half-life is:

`t_(1/2)=(ln(2))/(k)\\ \\t_(1/2)=(ln(2))/(3.7x10^(-3)s^(-1))\\\\t_(1/2)=187.3s`

d. In this case, since the integrated first-order rate law is:

`[A]=[A]_0exp(-kt)`

The concentration once 220 seconds have passed is:

`[A]=0.250Mexp(-3.7x10^(-3)s^(-1)*220s)\\\\`

`[A]=0.111M`

Regards.