## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## Tip our Team

Our Website is free to use.
To help us grow, you can support our team with a Small Tip.

## Holooly Tables

All the data tables that you may search for.

## Holooly Help Desk

Need Help? We got you covered.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

Products

## Textbooks & Solution Manuals

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

## Holooly Arabia

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

## Holooly Help Desk

Need Help? We got you covered.

## 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.

## 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$^{-4} s^{-1}$.