The decomposition of nitrogen dioxide (NO2) into nitrogen monoxide (NO) and oxygen is a second-order reaction. This means that the concentration C of NO2 at time t is given by 1/C = kt + 1/C0, where C0 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 measure to be 0.0023 ± 2.0 × 10−4 mol/Lm 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 × 10−4 mol/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 k1 and k2, respectively. The average (k1 + k2)/2 is used as an estimate of k. Find the uncertainty in this estimate.
d. Find the value of c so that the weighted average c k1 + (1 − c) k2 has the smallest uncertainty.