## 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}.