The conversion of cyclobutane (C4H8) to ethylene (C2H4) is a first-order reaction. This

Chapter 3, Problem 18

(choose chapter or problem)

The conversion of cyclobutane \(\left(C_{4} H_{5}\right)\) to ethylene \(\left(C_{2} H_{4}\right)\) is a first-order reaction. This means that the concentration of cyclobutane at time  is given by \(\ln C=\ln C_{0}-k t\), where  is the concentration at time \(t, C_{e}\) is the initial concentration,  is the time since the reaction started, and  is the rate constant. Assume that \(C_{0}=0.2 \mathrm{~mol} / \mathrm{L}\) with negligible uncertainty. After 300 seconds at a constant temperature, the concentration is measured to be \(C=0.174 \pm 0.005 \mathrm{~mol} / \mathrm{L}\). Assume that time can be measured with negligible uncertainty-

a. Estimate the rate constant , and find the uncertainty in the estimate. The units of  will be \(s^{-1}\)

b. Find the relative uncertainty in \(k_{-}\)

c. The half-life \(t_{1 / 2}\) of the reaction is the time it takes for the concentration to be reduced to one-half its initial value. The half-life is related to the rate constant by \(t_{1 / 2}=(\ln 2) / k\) Using the result found in part (a), find the uncertainty in the half-life.

d. Find the relative uncertainty in the half-life.

Equation Transcription:

   

     

   

   

     

         

Text Transcription:

(C4H5)    

(C2H4)    

lnC=lnC0-kt  

t, Ce    

C0=0.2 mol/L    

C=0.174 \pm 0.005 mol/L

s-1

k-

t1/2        

t1/2=(ln2)/k