Question

The decomposition of XY is second order in XYand has a rate constant of 6.92×10−3 M−1⋅s−1at a certain temperature.

Part A What is the half-life for this reaction at an initial concentration of 0.100 M? t1/2 = .0125   s   Part B How long will it take for the concentration of XY to decrease to 12.5% of its initial concentration when the initial concentration is 0.100 M? t =   s   Part 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 0.200 M? t = ________ s   Part D If the initial concentration of XY is 0.160 M , how long will it take for the concentration to decrease to 6.80×10−2 M ? Express your answer using two significant figures. t = _______   s   Part E If the initial concentration of XY is 0.050 M, what is the concentration of XY after 55.0 s ? Express your answer using two significant figures. [XY]t = ______   M   Part F If the initial concentration of XY is 0.050 M, what is the concentration of XY after 600 s ? Express your answer using two significant figures. [XY]t = _______   M   Please explain and show work with the answers, I have been struggling for the past hour trying to solve the problem!!! Thanks for your help

Answer 1

a)

1. We know that for second order reaction the half life will be

Part B

How long will it take for the concentration of XY to decrease to 12.5% of its initial concentration when the initial concentration is 0.100 M?

Answer: Let initial concentration =[A0] = 0.10 then [At] = 0.125 [A0] = 0.125 X 0.1 = 0.0125 M

0.00692 X t

time = 10115.61 seconds

Part 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 0.200 M?

40 = 5 + 0.00692 t

t = 5057.81 seconds = 5.1 X 10³ seconds

D) If the initial concentration of XY is 0.160 M , how long will it take for the concentration to decrease to 6.80×10⁻² M ?

At = 0.068 M A0 = 0.160 k = 0.00692

time = 1222.54 seconds = 1.2 X 10³ seconds

E) If the initial concentration of XY is 0.050 M, what is the concentration of XY after 55.0 s

A0 = 0.050 t = 55 s K = 0.00692

At = 0.0491 M = 0.049 M

Part F

If the initial concentration of XY is 0.050 M, what is the concentration of XY after 600 s ?

A0 = 0.050 t = 600 s K = 0.00692

At = 0.041 M