13.54 The decomposition of XY is second order in XY and has a rate constant of 6

Question

13.54

The decomposition of XY is second order in XY and has a rate constant of 6.90x10-3 M-1 s-1 at a certain temperature.

(a) What is the half-life for this reaction at an initial concentration of .100 M?

(b) How long will it take for the concentration of XY to decrease to 12.5% of it's initial concentration when the initial concentration is .100M?

(c) How long will it take for the concentration of XY to decrease to 12.5% of its initial concentration when the initial concentration is .200M?

(d) If the initial concentration of XY is .140M, how long will it take for the concentration to decrease to 6.00x10-2M? Express answer to two sig figs.

(e) If the initial concentration of XY is 0.050M, what is the concentration of XY after 45.0s? Express answer to two sig figs.

(f) If the initial concentration of XY is 0.050M, what is the concentration of XY after 600s? Express answer to two sig figs.

Explanation / Answer

the rate law for a second order reaction is given as

1/[A] = 1/[Ao] + kt

given

k = 6.9 x 10-3

a)

after half life , half of the initial conc is consumed

so half of the initial conc will remain

so

[A] = [Ao]/2 = 0.1 /2 = 0.05

so

1/[A] = 1/[Ao] + kt

1/0.05 = 1/0.1 + ( 6.9 x 10-3 x t1/2 )

t1/2 = 1449.27 s

so the half life for this reaction is 1449.27 s

b)

given

[Ao] = 0.1 M

also given

final conc is 12.5 % of initial

so

[A] = 0.125 x 0.1 = 0.0125

so

1/0.0125 = 1/0.1 + ( 6.9 x 10-3 x t )

t = 10144.92 s

so the time taken is 10144.92 s

c)

now

[Ao] = 0.2 M

[A] = 0.125 x 0.2 = 0.025

so

1/0.025 = 1/0.2 + ( 6.9 x 10-3 x t )

t = 5072.463

so the time taken is 5072.463

d) given

[Ao] = 0.14

[A] = 0.06

so

1/0.06 = 1/0.14 + ( 6.9 x 10-3 x t )

t = 1380.26

so the time taken is 1.4 x 10^3 s

e)

given

[Ao]= 0.05

t = 45

so

1/[A] = 1/0.05 + ( 6.9 x 10-3 x 45 )

[A] = 0.0492

so the conc after 45 s is 4.9 x 10-2 M

f)

given

[Ao] = 0.05

t = 600

so

1/[A] = 1/0.05 + ( 6.9 x 10-3 x 600)

[A] = 0.0414

so

the conc after 600 s is 4.1 x 10-2 M

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