Question

The following initial rate data are for the reaction of ammonium ion with nitrite ion in aqueous solution:

NH4+ + NO2- N2 + 2 H2O

Experiment [NH4+]o, M [NO2-]o, M Initial Rate, Ms-1

1 0.746 2.54×10-2 6.29×10-6

2 0.746 5.07×10-2 1.26×10-5

3 1.49 2.54×10-2 1.26×10-5

4 1.49 5.07×10-2 2.51×10-5

Complete the rate law for this reaction in the box below.

Use the form k[A]m[B]n , where '1' is understood for m or n and concentrations taken to the zero power do not appear. Don't enter 1 for m or n

Rate =

From these data, the rate constant is _______ M-1s-1.

Answer 1

Sol.

Initial Rate = k [NH4+]o^m [NO2-]oⁿ  

where [NH4+]o is the initial concentration of NH4+ and [NO2-]o is the initial concentration of NO2-

m is the order of reaction with respect to NH4+ and n is the order of reaction with respect to NO2-

k is rate constant  

Now , Taking data of Experiment number 1 and 3 and put in initial rate equation , then , dividing them

( 6.29 × 10^-6 ) / ( 1.26 × 10^-5 )  

= ( 0.746 / 1.49 ) ^m × ( ( 2.54 × 10^-2 ) / ( 2.54 × 10^-2 ) )ⁿ

0.5 = (0.5)^m (1)ⁿ = (0.5)^m  

So , m = 1

Now , Taking data of experiment number 1 and 2 and put in initial Rate equation , then , dividing them ,

( 6.29 × 10^-6 ) / ( 1.26 × 10^-5 )  

= ( 0.746 / 0.746 )^m × ( ( 2.54 × 10^-2 ) / ( 5.07 × 10^-2 ) )ⁿ

0.5 = (0.5)ⁿ  

Therefore , n = 1

So , Initial Rate = k [NH4+]o¹ [NO2-]o¹

= k [NH4+]o [NO2-]o  

Taking the data of experiment number 1 ,

6.29 × 10^-6 = k × 0.746 × 2.54 × 10^-2  

k =  3.32 × 10^-4 M-1 s-1