Question

A student obtained the following data for the decomposition of dinitrogen pentoxide in carbon tetrachloride solution at 30 °C.

N2O52 NO2(g) + ½ O2(g) [N2O5],

0.894 time 0 mins 0.447 time 124 mins 0.224 248 mins 0.112 372 minutes

(1a) What is the half-life for the reaction starting at t=0 min?

b) What is the half-life for the reaction starting at t=124 min?

c ) Does the half-life increase, decrease or remain constant as the reaction proceeds? (2) Is the reaction zero, first, or second order? (3) Based on these data, what is the rate constant for the reaction?

Answer 1

when initial concerntration become half, at that point t = t_1/2

(1a) Half-life for the reaction starting at t=0 min is as follow:

at t = 0, let initial conc. = N₀ = 0.894

but at t = 124, conc. become 0.447 = 0.894/2 = N₀/2

t_1/2 for the reaction starting at t=0 min is 124 min.

(b) similarly,

Half-life for the reaction starting at t=124 min is as follow:

at t = 124, let initial conc. = N₀ = 0.447

but at t = 248, conc. become 0.224 = 0.447/2 = N₀/2

t_1/2 for the reaction starting at t=124 min is 248 min.

(c) Half life will increase as the reaction proceeds.

the reaction is first order.

rate constant = 0.693/t_1/2

= 0.693/124

=0.00558