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Chapter 13

Q. 13.3

The First-Order Integrated Rate Law: using Graphical analysis of Reaction Data
Consider the equation for the decomposition of SO_{2}Cl_{2}.
SO_{2}Cl_{2}(g) → SO_{2}(g) + Cl_{2}(g)
The concentration of SO_{2}Cl_{2} is monitored at a fixed temperature as a function of time during the decomposition reaction, and the following data are tabulated:

Time (s) [SO_{2}Cl_{2} ] (M) Time (s) [SO_{2}Cl_{2} ] (M)
0 0.100 800 0.0793
100 0.0971 900 0.0770
200 0.0944 1000 0.0748
300 0.0917 1100 0.0727
400 0.0890 1200 0.0706
500 0.0865 1300 0.0686
600 0.0840 1400 0.0666
700 0.0816 1500 0.0647

Show that the reaction is first order and determine the rate constant for the reaction.

Step-by-Step

Verified Solution

In order to show that the reaction is first order, prepare a graph of ln [ SO_{2}Cl_{2} ] versus time as shown here.

The plot is linear, confirming that the reaction is indeed first order. To obtain the rate constant, fit the data to a line. The slope of the line is equal to -k. Since the slope of the best fitting line (which is most easily determined on a graphing calculator or with spreadsheet software such as Microsoft Excel) is -2.90 × 10^{-4} s^{-1}, the rate constant is therefore +2.90 ×10^{-4} s^{-1}.

Screenshot 2022-10-08 150836