Problem 19SE

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 = k t + 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 measured to be 0.0023 ± 2.0 x 10-4 mol/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 ×10-4 mol/L. Estimate the rate constant k, and find the uncertainty in the estimate.

c. Denote ihe estimates of the rate constant k in parts (a) and (b) by and 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.

Answer :

Step 1 of 5:

Given, the decomposition of nitrogen dioxide (into nitrogen monoxide (NO) and oxygen is a second order reaction.

This means that the concentration C of at time ‘t’ is given by:

….. (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.