Chemistry: Please help me understand how to do this equation step by step

Question

Nitrogen reacts with hydrogen to form ammonia. This reaction is described by the following equation:

N2 3 H2 2 NH3

The reaction was studied at 35oC and the data in the table were collected.

[N2] [H2] Initial rate of reaction (M sec-1)

0.56 0.26 0.00832

0.28 0.13 0.00416

0.28 0.39 0.00416

0.56 0.13 0.00832

The rate law for the reaction can be written as: rate = k[N2]x.[H2]y

Determine the orders x and y and calculate the rate constant k. Enter these values in the boxes below and select the correct units for the rate constant.

x = y = k =

Answer 1

if [N2] = 0.28 or 0.56, costant, initial rate no changes then

rate depends on [N2] but no on [H2]

so

y = 0

and

rate = v = k*[N2]^x

then

v(a) = k*[N2]a^x =

= 0.00832 = k*(0.56)^x

v(b) = k*[N2]b^x =

= 0.00416 = k*(0.28)^x

v(a) / v(b) = ([N2]a / [N2]b)^x =

= 0.00832/0.00416 = (0.56/0.28)^x =

= 2 = 2^x

true if only x = 1

then

rate = k*[N2]

and

k = rate/[N2] = 0.00416/0.28 or 0.00832/0.56 = 1.5*10^-2 sec^-1