Question

The gaseous reaction between hydrogen gas and elemental phosphorus to form phosphor was studied, and the following data were obtained:
0.120   0.180 1.60x10^-2
0.060   0.120   4.36x10^-3
0.030   0.090   1.42x10^-3
0.240   0.090    1.13x10^-2
Determine the rate law for the reaction and calculate the value of the rate constant.

Answer 1

Consider a rate law for the reaction

Rate = K[H2]^x [P]^y -----(1)

K = rate constant, x is order of reaction with respect to hydrogen gas, y is order of reaction with respect to elemental phosphorous

Note :- you have not mentioned, in which column concentration of reactants exist. I am considering, hydrogen gas data is in 1st column and elemental phosphorous data is in 2nd column.

Given:- [H2] = 0.030 M, [P] = 0.090 M, rate = 1.42 * 10^-3 M/s

From(1). 1.42 * 10^-3 M/s = K(0.030 M)^x(0.090 M)^y ---(2)

Given:- [H2] = 0.240 M, [P] = 0.090 M, Rate = 1.13 * 10^-2 M/s

From(1) 1.13 * 10^-2 M/s = K(0.240 M)^x (0.090 M)^y -----(3)

Divide (3) by (2)

1.13 * 10^-2 M/s / 1.42 * 10^-3 M/s = K(0.240 M)^x(0.090 M)^y / K(0.030 M)^x(0.090 M)^y

~ 8.0 = 8.0^x

x = 1

Given:- [H2] = 0.060 M, [P] = 0.120 M, Rate = 4.36 * 10^-3 M/s

From(1) 4.36 * 10^-3 M/s = K(0.060 M)^x(0.120 M)^y ---(4)

Divide (4) by (2)

4.36 * 10^-3 M/s / 1.42 * 10^-3 M/s = K(0.060 M)^x(0.120 M)^y / K(0.030 M)^x(0.090 M)^y

3.07 = 2^x * 1.33^y

3.07 = 2^1 * 1.33^y

3.07 / 2 = 1.33^y

1.535 = 1.33^y

1.33^1.5 = 1.33^y

y = 1.5 = 3/2

From(1) Rate law for the reaction

Rate = K[H2][P]^3/2