The tabulated data were collected for this reaction at a certain temperature: X₂Y → 2 X + Y a. Determine the order of the reaction and the value of the rate constant at this temperature.

Video transcript

Hello. In this problem we are told for the reaction A. Goes to form be the concentration of a. Is observed over time and tabulated and reported in the table below, we are asked to determine the rate order and calculate the reaction rate constant. In order to do this, we're going to need to make use of the integrated rate laws. Beginning with then Reactions of Order zero. The integrated rate law is given by the concentration of A. At time. T. Is equal to the negative of a reaction rate constant times time plus our initial concentration of A. If we have a zero order reaction and we make a plot of concentration of A versus T. And it's a straight line, the slope will be equal to minus K. And the reason is that this integrated rate law takes the form of a straight line. And so all integrated rate laws take the form of a straight line in case of a first order reaction. If we make a plot of the natural log of A versus time we'll get a straight line and the slope will be equal to the negative of a reaction rate constant. If we have a second order reaction again, the integrated rate law will take the form of a straight line. If we plot one over the concentration of A versus time, we'll get then a straight line with our slope equal to the reaction rate constant. So what we need to do then is take our data and we need to calculate the natural log of concentration of A. And we need to find one over the concentration of A. And then generate three plots within are going to look at which plot as the best fit line. If we make these three plots in a program like Excel, we'll find then the plot of one over the concentration versus time produces a straight line. So this is the best fit line with an R. Squared value of one. And we see then that the slope of the line is equal to 0.0446. So this is then equal to our reaction rate constant. If we then consider our units keep in mind that we're finding the slope of the line, which is the change in Y. Over the change in X. So our units then why are one over more clarity and then change in X. Which is our time is second. So our concentrations work out to per polarity per second. And this is then again a plot for a second order reaction. And so we find our reaction rate constant for the second order reaction is 0.0446 per Moleketi per second. Thanks for watching. Hope this helps