The decomposition of SO_2Cl_2 is first order in SO_2Cl_2 and has a rate constant

Question

The decomposition of SO_2Cl_2 is first order in SO_2Cl_2 and has a rate constant of 1.42 times 10^-4 s^-1 at a certain temperature. What is the half-life for this reaction? How long will it take for the concentration of SO_2Cl_2 to decrease to 25% of its initial concentration? If the initial concentration of SO_2CI_2 is 1.00 M, how long will it take for the concentration to decrease to 0.78 M? If the initial concentration of SO_2Cl_2 is 0.150 M, what is the concentration of SO_2Cl_2 after 2.00 times 10^2 s? After 5.00 times 10^2 s?

Explanation / Answer

a)

rate - constant k = 1.42 x 10^-4 s-1

half - life t1/2 = 0.693 / k

                     = 0.693 / 1.42 x 10^-4

                     = 4880 sec

half life = 4880 sec

b)

k = 1/t ln (Ao / At)

1.42 x 10^-4 = 1/t ln (100 / 25)

t = 9762.6 sec

time taken = 9762.6 sec

c)

k = 1/t ln (Ao / At)

1.42 x 10^-4 = 1/t ln (1.00 / 0.78)

t - 1750 sec

time taken = 1750 sec

d)

k = 1/t ln (Ao / At)

1.42 x 10^-4 = 1/ 2.00 x 10^2 ln (0.150 / At)

At = 0.146 M

concentration after = 0.146 M

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