tudent obtained the following data for the gas phase decomposition of dinitrogen

Question

tudent obtained the following data for the gas phase decomposition of dinitrogen pentoxide at 335 K. 9.15x102 101 4.58x102 202 2.29x102 303 IN20sl, M 0.183 time, s (1) What is the half-life for the reaction starting at t 0 s? What is the half-life for the reaction starting at t- 101 s? 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? Submit Answer

Explanation / Answer

Ans 1

Half life is the time when the initial concentration of reactant remains half.

At t = 0, CA0 = 0.183 M

CA = CA0/2 = 0.183/2 = 9.15*10^-2 M

Half concentration remains at 101 s

1) half life for the reaction starting (at t = 0s) = 101 s

At t = 101, CA0 = 9.15*10^-2 M

CA = CA0/2 = 9.15*10^-2 /2 = 4.58*10^-2 M

Half concentration remains at 202 s

Half life for the reaction starting (at t = 101s)

= 202 - 101 = 101 s

As the reaction proceeds, half life remains constant

2) When half life does not depend on the the initial concentration, the reaction is first order.

3) rate constant for first order reaction

k = 0.6932/t1/2 = 0.6932/101 = 0.00686 s-1

Ans 2

At t = 0, CA0 = 1.24*10^-2 M

CA = CA0/2 = 1.24*10^-2 /2 = 6.2*10^-3 M

Half concentration remains at 442 s

1) half life for the reaction starting (at t = 0s) = 442 s

At t = 442, CA0 = 6.2*10^-3  M

CA = CA0/2 = 6.2*10^-3 /2 = 3.1*10^-3 M

Half concentration remains at 662 s

Half life for the reaction starting (at t = 442s)

= 662 - 442 = 220 s

As the reaction proceeds, half life decreases

2) When half life decreases with decrease in the initial concentration, the reaction is zero order.

3) rate constant for zero order reaction

k = CA0/2*t1/2 = 1.24*10^-2/2*442

= 1.4027 x 10^-5 Ms-1

Ans 3

At t = 0, CA0 = 2.01 M

CA = CA0/2 = 2.01 /2 = 1.01 M

Half concentration remains at 544 s

1) half life for the reaction starting (at t = 0s) = 544 s

At t = 544, CA0 = 1.01 M

CA = CA0/2 = 1.01 /2 = 0.505 M

Half concentration remains at 1.64*10^3 s

Half life for the reaction starting (at t = 544s)

= 1.64*10^3 - 544 = 1096 s

As the reaction proceeds, half life increases

2) When half life increases with decrease in the initial concentration, the reaction is second order.

3) rate constant for second order reaction

k = 1/(CA0*t1/2) = 1/2.01*544

= 9.145 x 10^-4 M-1s-1

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