The reaction of NOBr(g) to form NO(g) and Br2(g) is second order: 2 NOBr(g) ⟶2 NO(g)+Br2(g) The

step 1 So here we're given information about a second order chemical reaction where the rate is equival

The reaction of NOBr(g) to form NO(g) and Br2(g) is second...

The reaction of $\mathrm{NOBr}(g)$ to form $\mathrm{NO}(g)$ and $\mathrm{Br}_{2}(g)$ is second order: $$2 \mathrm{NOBr}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$ The rate constant is $0.556 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at some temperature. If the initial concentration of NOBr in the container is $0.25 M$, how long will it take for the concentration to decrease to $0.025 \mathrm{M}$ ?

Key Concepts

Second Order Reactions

In second order reactions, the rate of reaction depends on the square of the concentration of a single reactant or on the product of the concentrations of two different reactants. This order of reaction signifies that the overall rate is proportional to the concentration raised to the second power, resulting in a unique time-concentration relationship that can be analyzed using specific kinetic models.

Integrated Rate Law for Second Order Reactions

For a single reactant following second order kinetics, the integrated rate law is expressed as 1/[A] = 1/[A]? + kt, where [A] is the concentration at time t, [A]? is the initial concentration, k is the rate constant, and t is time. This equation is instrumental in calculating the time required for the concentration to drop from an initial value to a final value and provides insight into the reaction’s progression over time.

Rate Constant and its Units

The rate constant, k, quantifies the speed of a chemical reaction and is specific to the reaction and its conditions. In second order reactions, the units of k are typically L mol?¹ s?¹, ensuring that when it is multiplied by the square of the concentration (in mol/L), the overall units of the rate are consistent with mol L?¹ s?¹. The rate constant is a crucial parameter in kinetic calculations using the integrated rate law.

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