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Question

Three experiments are performed under identical conditions to measure the initial rate of the reaction described by the equation 2N₂O₅(g)--> 4NO₂(g)+O₂(g). The results of the three experiments, in which only the N₂O₅ concentration is varied, are as follows: 

 

Experiment |   (N₂O₅₎ (M)   |   Rate (M/s) 

        1       |         0.030     |      2.2x10^-2

        2       |         0.060     |      8.8x10^-2

        3       |         0.090     |      1.98x10^-1

 

Write the rate law for the reaction. Find the value and units of the specific rate constant. show work. 

Answer 1

Rate=k[N₂O₅]ⁿ, where k is the rate constant and n is the order of the reaction. In order to figure out what the order of the reaction is, we need to divide 2 experiments.

 

Exp 2/Exp 1= k[0.060]ⁿ/k[0.030]ⁿ=8.8*10^-2/2.2*10-2

Cancel out the "k's"=> [0.060]ⁿ/[0.030]ⁿ=4

Combine the concentrations=> (0.060/0.030)ⁿ=4

Do math=> 2ⁿ=4. At this point it should be clear that the answer is 2, but in case there isn't we will cover that step also.

Solve for n using properties of logs=> n*log(2)=log(4)

Solve for n=> n=log(4)/log(2)=2

 

Now that we know the order of the reaction (n) we can solve for the rate using any experiment (we will use experiment 1).

2.2*10^-2=k*[0.030]²

Solve for k=> 24.4=k, but with appropriate significant figures the answer is 24.

The units of k is always M^1-ns^-1, so for this situation the units are M^-1s^-1.