A researcher studies the gas-phase reaction 2NO2(g)→2NO(g)+O2(g) at 350K. The researcher collects the following concentration data for NO2 during the first 90s and fits a polynomial trendline to reduce the effect of measurement noise.
Time (s) [NO2] (M)
0.0 0.800
15.0 0.725
30.0 0.660
45.0 0.606
60.0 0.560
75.0 0.520
90.0 0.485
Using a least-squares routine, the trendline is determined to be
[NO2]=0.800−4.10×10−3t−3.20×10−5t2,
where t is in seconds and concentration in molL−1.
(a) Derive an analytical expression for the instantaneous rate of disappearance of NO2 as a function of time based on the fitted trendline.
(b) Use your result from part (a) to calculate the instantaneous rate of disappearance of NO2 at t=50.0s.
(c) Determine the corresponding instantaneous rate of formation of O2 at t=50.0s and comment on the relative magnitudes of the two rates in light of the reaction stoichiometry.
(d) Discuss how the sign and time dependence of the coefficients in the trendline influence the way the reaction rate evolves over the first 90s.