Question

At 500 ∘C, cyclopropane (C3H6) rearranges to propene (CH3−CH=CH2). The reaction is first order, and the rate constant is 6.7×10−4s−1. If the initial concentration of C3H6 is 5.50×10−2 M .

What is the molarity of C3H6 after 30 min ?

How many minutes does it take for the C3H6 concentration to drop to 1.00×10−2 M ?

How many minutes does it take for 25% of the C3H6 to react?

Express all the answers in two significant figures.

Answer 1

let [A] represents cyclopropane concentration

for 1st order reaction, rate of reaction is - dA/dt = K[A], where K is rate constant, K= 6.7*10-4 sec

with the boundary conditions at t=0, [A]o= 5.5*10-2M, at t=30 min= 30*60 =1800sec, the integrated expression becomes

ln[A] =ln[A]0- Kt

ln[A] = ln (5.5*10^-2)- 1800*6.7*10^-4

[A] = 0.01646 M

2. Given [A] = 1*10^-2M, ln (1*10^-2)= ln (5.5*10^-2)- 6.7*10-4t

t= 2544.4 seconds

3. when 25% of C3H6 react, remaining [A] = (1-0.25)*5.5*10^-2=0.04125

hence ln(0.04125)= ln(0.055) - 6.7*10-4t

t= 429.4 seconds