A student investigates the thermal decomposition of gaseous species C at 525 K. The student measures the initial concentration of C and its corresponding half-life for six different trials. A plot of half-life (vertical axis, units = s) versus initial concentration (horizontal axis, units = mol L⁻¹) is described as follows:
• The data points lie on a straight line that passes through the origin.
• The best-fit line has a slope of 140 s·L·mol⁻¹.
Assume a single rate law applies over the entire concentration range studied.
(1) State the overall order of the reaction with respect to C. Justify your answer with reference to the functional relationship revealed by the graph.
(2) Using the slope given, determine the numerical value and units of the rate constant k at 525 K.
(3) Predict the half-life for a trial in which [C]₀ = 0.800 mol L⁻¹. Show your work.