The reaction is thought to follow second order kinetics which follows the relati

Question

The reaction is thought to follow second order kinetics which follows the relationship 1/[A]=1/[A]0+kt where [A] is the molarity at time, t, and [A]0 is the initial concentration. k is the rate constant. In this case the following data was obtained. Time (min) [A] (molarity) 10 0.51 20 0.42 30 0.36 40 0.31 Analysis a. Transform the data given above so that it would show linear dependence in the case of a second order reaction. b. Make a plot of the data with the appropriate variables as x and y consistent with the second order equation given. c. From the plot, draw by eye a best fit through the data and estimate the slope and y-intercept of the best linear fit of the data. Be sure to include units! d. Using linear regression calculations, determine the slope and the y-intercept of the best fit of the data. Be sure to include units! e. Do the two determinations of linear relationship in the data agree? f. From your analysis, determine best values of k and [A]0.

Explanation / Answer

Data In another experiment, the rate of a reaction is monitored by measuring the concentration of a reactant versus time. Here time is the independent variable. The reaction is thought to follow second order kinetics which follows the relationship kt A A o = + [ ] 1 [ ] 1 where [A] is the molarity at time, t, and [A]0 is the initial concentration. k is the rate constant. In this case the following data was obtained. Time (min) [A] (molarity) 10 20 0.51 0.42 30 0.36 40 0.31 Analysis a. Transform the data given above so that it would show linear dependence in the case of a second order reaction. b. Make a plot of the data with the appropriate variables as x and y consistent with the second order equation given. c. From the plot, draw by eye a best fit through the data and estimate the slope and y-intercept of the best linear fit of the data. Be sure to include units! d. Using linear regression calculations, determine the slope and the y-intercept of the best fit of the data. Be sure to include units! e. Do the two determinations of linear relationship in the data agree? f. From your analysis, determine best values of k and [A]0. Graphing in Excel • Open an EXCEL spreadsheet. • Input data in the form (x,y) • Highlight the two columns of data • Click on the plotting icon • Choose x,y scatter plot • Follow the screens to add title, x-legend, and y-legend • Right-click on one of the data points in the plot (it will turn yellow). • Click on trendline. • Choose “linear” on type; on options choose to show equation, R2 value, ( and intercept through zero, if applicable.) • The equation gives you the general slope-intercept form: y = mx + b, where m = slope of the line plotted and b = the y-intercept. • Clicking on the border of the plot will allow you to copy and paste it into a Word document such as your lab report.

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