Gaseous NO, decomposes at 573 K. 2 NO2(g) →2 NO(g)+O2(g) The...

Gaseous NO, decomposes at $573 \mathrm{K}.$ $$2 \mathrm{NO}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$ The concentration of $\mathrm{NO}_{2}$ was measured as a function of time. A graph of $1 /\left[\mathrm{NO}_{2}\right]$ versus time gives a straight line with a slope of $1.1 \mathrm{L} / \mathrm{mol} \cdot$ s. What is the rate law for this reaction? What is the rate constant?

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Key Concepts

Rate Law

The rate law expresses how the reaction rate depends on the concentration of the reactants. For the reaction involving NO? decomposition, the rate law is determined by the kinetic order with respect to NO?. A linear plot of 1/[NO?] versus time indicates that the reaction is second order in NO?, meaning the rate is proportional to the square of the NO? concentration, expressed as Rate = k [NO?]².

Integrated Rate Law (Second Order Reaction)

For a second order reaction where a reactant A is involved, the integrated rate law is written as 1/[A] = 1/[A]? + k·t. This linear relationship between 1/[NO?] and time, with the slope equal to the rate constant k, helps in determining the reaction kinetics and confirms the second order nature of the reaction when the data fits a straight line.

Rate Constant

The rate constant, denoted as k, is a proportionality factor in the rate law that quantifies the speed of the reaction under specific conditions. In the integrated rate law for a second order reaction, the slope of the 1/[NO?] versus time graph gives the value of k. In this particular case, k is determined to be 1.1 L·mol?¹·s?¹, indicating the efficiency with which the reaction proceeds under the experimental conditions.

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