Question

Substance Q reacts according to a first order rate law with k = 5.0 x 10-5 s -1 .

a. If the initial concentration of the reaction is 1.00 M for Q, what is the initial rate of the reaction?

b. What is the rate after 1.00 hr?

Answer 1

The reaction is first order with substrate Q with a rate constant .

a.

We can write the rate expression for the reaction as follows:

  

Hence, given that , we can calculate the initial rate as follows:

Hence, the initial rate of the reaction is .

b.

Now, we have to find the rate at t = 1.00 hr = 3600 s.

Hence, first we must find the concentration of Q at t = 3600 s.

Now, the integrated first order rate equation is written as

Where

Hence, putting in the values,

Hence, the concentration of substrate Q is 0.835 M after 1.00 hr.

Hence, the rate after 1.00 hr can be calculated as follows:

Hence, the rate of the reaction after 1.00 hr is

Note: Answers are rounded to three significant figures.