The decomposition of nitrogen dioxide (NO2) into nitrogen

QUESTION:

The decomposition of nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\) into nitrogen monoxide (NO) and oxygen is a second-order reaction. This means that the concentration  of \(\mathrm{NO}_{2}\) at time  is given by \(1 / \mathrm{C}=k t+1 / C_{0}\), where \(C_{0}\) is the initial concentration and  is the rate constant. Assume the initial concentration is known to be  exactly. Assume that time can be measured with negligible uncertainty.

a. After , the concentration  is measured to be \(0.0023 \pm 2.0 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\). Estimate the rate constant , and find the uncertainty in the estimate.

b. After , the concentration  is measured to be \(0.0018 \pm 2.0 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\). Estimate the rate constant , and find the uncertainty in the estimate.

c. Denote the estimates of the rate constant  in parts
(a) and (b) by \(\widehat{k}_{1}\) and \(\widehat{k}_{2}\), respectively. The average \(\left(\widehat{k}_{1}+\widehat{k}_{2}\right) / 2\) is used as an estimate of  Find the uncertainty in this estimate.

d. Find the value of  so that the weighted average \(c\widehat{k}_{1}+(1-c) \hat{k}_{2}\) has the smallest uncertainty.

Equation Transcription:

Text Transcription:

(NO_2)

(NO)

NO2

1/C=kt+1/C_0

C_0

0.03 mol/L

0.0023{+/-}2.010^{-4} mol/L

0.0018{+/-}2.010^{-4} mol/L

hat{k}_1

hat{k}_2

(hat{k}_1+hat{k}_2)/2

c hat{k}_1+(1-c)hat{k}_2