The decomposition of nitrogen dioxide 
into nitrogen monoxide 
and oxygen is a second-order reaction. This means that the concentration C of 
at time t is given by 1/C=kt+1/
, where is the initial concentration and k is the rate constant. Assume the initial concentration is known to be 0.03 mol/L exactly. Assume that time can be measured with negligible uncertainty.
a. After 40 s, the concentration C is measured to be 0.0023 ± 2.0 ×10–4mol/L. Estimate the rate constant k, and find the uncertainty in the estimate.
b. After 50 s, the concentration C is measured to be 0.0018 ± 2.0 ×10–4mol/L. Estimate the rate constant k, and find the uncertainty in the estimate.
c. Denote the estimates of the rate constant k in parts (a) and (b) by 
, respectively. The average 
is used as an estimate of k. Find the uncertainty in this estimate.
d. Find the value of c so that the weighted average 
has the smallest uncertainty.
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