Many organic compounds can isomerize (turn into another compound with the same molecular formula) when heated. Suppose you are an organic chemist studying cyclopropane. You find that when cyclopropane (C₃H₆, 1) is heated to 500. °C (773 K), it converts into an isomer, propene (2). You collect the following data, which show the concentration of cyclopropane at a series of times after the start of the reaction. Confirm that the reaction is first order in C₃H₆
and calculate the rate constant.

PLAN Plot the natural logarithm of the reactant concentration against t. If a straight line is obtained, the reaction is first order and the slope of the graph is –k_r. If the plot is not linear, then the reaction is not first order in the specified reactant. Use the linear regression methods in the Living Graph section of the textbook Web site, a spreadsheet program, or a graphing calculator to plot the data and determine the slope of the graph.

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Time, t/min [C3H6lt/(mol-L¹) 0 1.50 X 10 3 5 1.24 X 10-3 10. 1.00 × 10 ³ 15 0.83 x 10 3