The rate constant for the second-order reaction 2 NOBr(g) ⟶2 NO(g)+Br2(g) is 0.80 / M ·s at 10^∘

step 1 Okay, so in this question, they want us to calculate the final concentration of NOBR after 22 se

The rate constant for the second-order reaction 2 NOBr(g) ⟶2...

The rate constant for the second-order reaction $$2 \mathrm{NOBr}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$ is $0.80 / M \cdot$ s at $10^{\circ} \mathrm{C}$. (a) Starting with a concentration of $0.086 M,$ calculate the concentration of NOBr after 22 s. (b) Calculate the half-lives when $[\mathrm{NOBr}]_{0}=0.072 M$ and $[\mathrm{NOBr}]_{0}=0.054$ $M$.

The rate constant for the second-order reaction
$$2 \mathrm{NOBr}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$
is $0.80 / M \cdot$ s at $10^{\circ} \mathrm{C}$. (a) Starting with a concentration of $0.086 M,$ calculate the concentration of NOBr after 22 s. (b) Calculate the half-lives when $[\mathrm{NOBr}]_{0}=0.072 M$ and $[\mathrm{NOBr}]_{0}=0.054$ $M$.

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Key Concepts

Integrated Rate Law for Second Order Reactions

The integrated rate law for a second order reaction provides a relationship between concentration and time. For a reaction where a single reactant is involved with a rate constant k, the law can be expressed as 1/[A] = 1/[A]_0 + kt. This equation is used to calculate the concentration of the reactant at a given time and is fundamental in solving time-dependent kinetics problems.

Half-life for Second Order Reactions

In second order kinetics, the half-life of a reaction is not constant but depends on the initial concentration. It is calculated using the formula t1/2 = 1/(k[A]_0), indicating that as the initial concentration decreases, the half-life increases. This dependency distinguishes second order reactions from first order reactions, where the half-life is independent of the initial concentration.

Second Order Reaction Kinetics

In chemical kinetics, a second order reaction involves a rate that depends on the product of two reactant concentrations or the square of the concentration of a single reactant. The overall rate is proportional to [A]^2 or [A][B]. This concept is crucial for understanding how the concentration of reactants decreases over time in reactions following this order.

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