A student investigates the gas-phase decomposition reaction at

CHEMISTRY · Multi-part · AP · Chemistry · Kinetics · Kinetics

Problem

A student investigates the gas-phase decomposition reaction XA0(g)→productsXA_0(g) \to \text{products} at 298 K298\,\text{K}. Using initial rate data, the student constructs a plot of log⁡(rate)\log(\text{rate}) (y-axis) versus log⁡([X]0)\log([X]_0) (x-axis) and obtains the best-fit equation log⁡(rate)=1.50 log⁡([X]0)−0.85.\log(\text{rate}) = 1.50\,\log([X]_0) - 0.85. (The standard error in the slope is ±0.04\pm0.04.) (a) Identify the order of the reaction with respect to XX and state the numerical value of the overall reaction order. (b) Explain, in terms of the mathematical form of the rate law, why the slope of the plotted line corresponds to the reaction order obtained in part (a). (c) Qualitatively predict how the initial rate will change if the initial concentration of XX is tripled, and justify your prediction without performing a numerical calculation.

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