Graphical Method: Order and k from Slope and Intercept

Question

In a study of the decomposition of dinitrogen pentoxide in carbon tetrachloride solution at 30 °C

N₂O₅2 NO₂ + ½ O₂

the concentration of N₂O₅ was followed as a function of time.

It was found that a graph of ln[N₂O₅] versus time in minutes gave a straight line with a slope of -5.95×10^-3 min^-1 and a y-intercept of 0.122 .

Based on this plot, the reaction is _______(zero,first,second) order in N₂O₅ and the rate constant for the reaction is _______min^-1.

Answer 1

If ln[N₂O₅] vs time is a straight line, that tell you that the reaction is first order in [N₂O₅]. This is derived from the fact that the integrated rate law for a 1st order reaction is ln[A] = -kt + ln[A]_o which is in the form of a straight line. In this equation, the slope = -kt and the y-intercept = [A]_o

So, the answer to the question is:

The reaction is first order in N₂O₅

The rate constant for the reaction is 5.95x10^-3 min^-1