Question

Nitrogen dioxide, NO2 decomposes into nitrogen monoxide (NO) and oxygen gas O2 , according to the following reaction. 2 NO2 (g) 2 NO (g) + O2 (g) A sample of nitrogen dioxide in a sealed vessel, and the total pressure in the vessel was measured to be 0.0980 atm before any reaction had occurred. The total pressure in the vessel was monitored over time during the reaction at 575 K, giving the following data. Time (s) Ptotal (atm) 0.0 0.0980 35.0 0.1298 45.0 0.1325 79.0 0.1375 (a) Determine the rate law (in pressure) for this reaction at 575 K. Include the rate constant (with the correct unit) and reaction order.

Answer 1

Write the reaction as follows: NO, NO+-02 2 Given initial pressure, P, = 0.0980 atm Draw the ICE table as follows: NO → NO + 2 1(atm): 0.0980 0 C(atm):-p + P E (atm): 0.0980-P + P + Total pressure, Point = 0.0980-p+p+=p = 0.0980+ p= 2Proa) -2(0.0980) Parti al pressure of NO, is PNO, = 0.0980-P = 0.0980 – 2 Porta +2(0.0980) = 0.294 - 2 Poprad = for zero order reaction, the integrated equation is Prvo= P - kt for first order reaction, the integrated equation is in (Piros) = 1n Po - kot for second order reaction, the integrated equation is 1 1 +lt PAOL Draw the graphs between Pro, vs tfor zeroth order InPno, vs tfor first order 1 -vs t for second order as follows: PANO

Time(s) Ptotal(atm) P(NO2) In(P(NO2)) 1/PINO2) 01 0.098 0.098 -2.3227878 10.20408163 35 0.1298 0.0344 -3.369698715) 29.06976744 45 0.1325 0.029 -3.540459449 34.48275862 791 0.1375 0.019 -3.9633163 52.63157895 P(NO2) vs t 0.12 0.1 Zeroth order 0.08 P(NO2) 0.06 0.04 -P(NO2) vst 0.02 0 0 20 40 60 80 100 Time, t(s) In(P(NO2)) vs t first order 0 -0.5 0 20 40 60 100 -1 -1.5 -2 In(P(NOW)) -2.5 In(P(NO2)) vs t -3 -3.5 -4 -4.5 Time, t(s) 1/P(NO2) vs t y = 0.537x + 10.24 60 second order 50 40 1/PINO2) 30 20 1/P(NO2) vst Linear (1/P(NO2) vs t) 10 0 0 20 40 60 80 100 time, t(s)

From the graph, the straight line is observed in the graph drawn between Vst Po Therefore, the order of the reaction is 2 The straight line from the graph is y = 0.537x + 10.24 1 Compare the above equation with equation = + let P NO - slope, k = 0.537 atm -1 S Write theratelaw as follows: rate = k( Pero, rate = (0.537 atm -1 3-")( Pero, 2 rate = 0.537 atm -1 -1 S 1x PRO -1 -1 Therefore, the required solution is rate = 0.537 atm S Explor