The conversion of cyclobutane
to ethylene
is a first-order reaction. This means that the concentration of cyclobutane at time t is given by lnC=ln
?kt, where C is the concentration at time t,
is the initial concentration, t is the time since the reaction started, and k is the rate constant. Assume that
=0.2 mol/L with negligible uncertainty. After 300 seconds at a constant temperature, the
concentration is measured to be C=0.174 ± 0.005 mol/L. Assume that time can be measured with negligible uncertainty.
a. Estimate the rate constant k, and find the uncertainty in the estimate. The units of k will be .
b. Find the relative uncertainty in k.
c. The half-life 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
=(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.
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