The decomposition of dinitrogen pentoxide in carbon tetrachloride solution at 30 °C N2O5 2 NO2 + ½ O2 is first order in N2O5 with a rate constant of 0.00410 min-1. If the initial concentration of N2O5 is 0.393 M, the concentration of N2O5 will be M after 315.0 min have passed. The rearrangement of cyclopropane to propene at 500 °C (CH2)3CH3CH=CH2 is first order in (CH2)3 with a rate constant of 0.000670 s-1. If the initial concentration of (CH2)3 is 0.126 M, the concentration of (CH2)3 will be 0.0296 M after s have passed.


To calculate the concentration of N2O5 after 315.0 minutes have passed, we can use the first-order rate equation:

ln⁡(N2O5t)N2O5=−kt

Where:

  • N2O5t is the concentration of N2O5 at time t
  • N2O5 is the initial concentration of N2O5
  • k is the rate constant
  • t is the time

Rearranging the equation, we have:

N2O5t=N2O5×e−kt

Given:

  • N2O5=0.393M
  • k=0.00410min−1
  • t=315.0min

Substituting these values into the equation:

N2O5t=0.393e−0.00410315.0

Calculating this expression:

N2O5t=0.162M

Explanation:

Therefore, the concentration of N2O5 after 315.0 minutes have passed is approximately 0.162 M.

Step 3 of 3

Now, let’s calculate the concentration of (CH2)3 after s seconds have passed using a similar approach.

The first-order rate equation for the rearrangement of cyclopropane to propene is:

ln⁡((CH2)3t)/(CH2)3)=−kt

Where:

  • (CH2)3t is the concentration of (CH2)3 at time t
  • (CH2)3 is the initial concentration of (CH2)3
  • k is the rate constant
  • t is the time

Rearranging the equation, we have:

(CH2)3t=(CH2)3×e−kt

Given:

  • (CH2)3 = 0.126 M
  • k=0.000670s−1
  • (CH2)3t=0.0296M

Substituting these values into the equation:

0.0296=0.126e−0.000670s

Solving for s:

s=−ln⁡(0.0296/0.126)/0.000670

Calculating this expression:

s=6,545sec⁡

Explanation:

using the first-order approach we can find the seconds.

Final solution

Therefore, the concentration of (CH2)3 will be 0.0296 M after 6,545 sec⁡ have passed.

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