Write a rate law for this reaction and calculate the value of the rate constant

Question

Write a rate law for this reaction and calculate the value of the rate constant k with correct unit symbols

Some measurements of the initial rate of a certain reaction are given in the table below. N2 H initial rate of reaction 0.438 M 1.54M 0.501 M/s 0.0937 M/s 0.438 M 0.666 M 0.739 M/s 0.532 M 1.54 M Use this information to write a rate law for this reaction and calculate the value of the rate constant k. Round your value for the rate constant to 2 significant digits. Also be sure your answer has the correct unit symbol rate k X n

Explanation / Answer

let the rate law be

rate = k [N2]^a [H2]^b

now

for trail 1 and trail 2 , [N2] = constant

so

rate 2 / rate1 = ( [H2]2 / [H2]1)^b

0.0937 / 0.501 = ( 0.666 / 1.54)^b

0.187 = ( 0.432)^b

b = 2

so

the reaction is 2nd order with respect to H2

now

for trail 1 and trail 3 , [H2] = constant

so

rate 3 / rate 1 = ( [N2]3 / [N2]1)^a

0.739 / 0.501 = ( 0.532 / 0.438)^a

1.475 = ( 1.2146)^a

a = 2

so

the reaction is 2nd order with respect to N2

so

the rate law is

rate = k [N2]^2 [H2]^2

now

consider trail 1

0.501 = k [0.438]^2 [1.54]^2

k = 1.1

we know that

for a reaction with order n , the units of rate constant are M^(1-n) s-1

in this case

order = 2 + 2 = 4

so

the rate constant is 1.1 M-3 s-1

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