Determine the rate law, including the values of the orders and rate law constant, for the following reaction using the experimental data provided. A + B yield

Question

Determine the rate law, including the values of the orders and rate law constant, for the following reaction using the experimental data provided.

A + B yields products


Trial [A] [B] Rate
1 0.15 M 0.12 M 1.3 × 10-2 M/min
2 0.30 M 0.12 M 2.6 × 10-2 M/min
3 0.15 M 0.24 M 5.2 × 10-2 M/min

Answer 1

Hello Billy

 

The rate law expression for this reaction is:

 

Rate = k [A]^x [B]^y

 

where x and y are the orders of the reaction with respect to each reactant.

 

To determine the order for A, look at the data and select the Trials where the concentration of B remains constant.  In this case, it is Trials #1 and #2.  The concentration of A in Trial #1 is 0.15 M and in Trial #2, it is 0.30 M.  Now we can setup a ratio of these 2 trials as:

 

(Rate₂ / Rate₁) = ([A]₂ / [A]₁)^x

 

Plug in the numbers from the data.

 

(2.6 x 10^-2 / 1.3 x 10^-2) = (0.30 / 0.15)^x

 

(2) = (2)^x

 

What is the value of the exponent x?  x = 1.  Therefore, the reaction is 1st order with respect to reactant A.

 

Now repeat the above process for reactant B.  In Trials #1 and #3, the concentration of A remains constant.  The concentration of B in Trial #1 is 0.12 M and in Trial #3, it is 0.24 M. Now we can setup a ratio of these 2 trials as:

 

(Rate₃ / Rate₁) = ([B]₃ / [B]₁)^y

Plug in the numbers from the data.

(5.2 x 10^-2 / 1.3 x 10^-2) = (0.24 / 0.12)^y

(4) = (2)^y

What is the value of the exponent y? y = 2. Therefore, the reaction is 2nd order with respect to reactant B.

 

The rate law can now be written as:  Rate = k [A] [B]²

 

To determine the value of the rate constant, k, you can take the data from any of the 3 trials, and plug in the values into the above rate law.  Let's choose Trial #1.

 

[A] = 0.15 M

[B] = 0.12 M

Rate = 1.3 x 10^-2 M min^-1

 

1.3 x 10^-2 M min^-1 = k (0.15 M) (0.12 M)²

 

1.3 x 10^-2 M min^-1 = k(2.2 x 10^-3 M³)

 

k = 1.3 x 10^-2  M min^-1 / 2.2 x 10^-3  M³ = 5.9 M^-2 min^-1