Ch 203 Problem 14.31

14.31 The following data were measured for the reaction BF3(g) + NH3(g) ----> F3BNH3(g):

Experiment [BF3] [NH3] Initial rate, M/s

1 0.250 0.250 0.2130

2 0.250 0.125 0.1065

3 0.200 0.100 0.0682

4 0.350 0.100 0.1193

5 0.175 0.100 0.0596

(a) What is the rate law for the reaction?

The rate law for this reaction has the general form

rate = k[BF3]m[NH3]n

where m and n are the orders with respect to BF3 and NH3, respectively. We must use the experimental data above to determine these quantities. First, we will look for two experiments in which [BF3] is constant, and [NH3] is changed, and we will look at the effect of the reaction rate when [NH3] is varied. We can use experiments 1 and 2 for this purpose: [BF3] is constant, and [NH3] is changed. The ratio of the rates is

experiment 1 / experiment 2

the ratio of the NH3 concentrations is

experiment 1 / experiment 2

So, when we double [NH3], the rate of the reaction doubles. This means that the order of the reaction with respect to NH3 must be 1, so we set n=1 in the above rate law.

Now, we find the value of a. We want to find two experiments where NH3 is constant and BF3 is varied. Experiments 4 and 5 will do nicely; in these experiments, the ratio of BF3 concentrations is

experiment 4 / experiment 5

and the ratio of rates is

experiment 4 / experiment 5

so we notice that when the concentration of BF3 is doubled, the reaction rate doubles. We conclude that m = 1, and the reaction is first order in BF3 also.

Based on our results above, the rate law is rate = k[BF3][NH3] (both m and n = 1).

(b) What is the overall order of the reaction?

The reaction is first order in BF3, first order in NH3, and second order overall

(c) What is the value of the rate constant for the reaction?

here, we choose any experiment, and use the rate and concentration data in the rate law to find the value of k. I'll use experiment 5 (feel free to plug in numbers from other experiments below)

we solve the rate law for k:

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