The rate constant for the second-order reaction 2 NO2(g) ⟶2 NO(g)+O2(g) is 0.54 / M ·s at 300^∘

step 1 Hello, so today we're going to be looking at this reaction right here. So this is a second order

The rate constant for the second-order reaction 2 NO2(g) ⟶2...

The rate constant for the second-order reaction $$2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$ is $0.54 / M \cdot$ s at $300^{\circ} \mathrm{C}$. How long (in seconds) would it take for the concentration of $\mathrm{NO}_{2}$ to decrease from 0.62 $M$ to 0.28 $M ?$

The rate constant for the second-order reaction
$$2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$
is $0.54 / M \cdot$ s at $300^{\circ} \mathrm{C}$. How long (in seconds) would it take for the concentration of $\mathrm{NO}_{2}$ to decrease from 0.62 $M$ to 0.28 $M ?$

Key Concepts

Calculating Reaction Time Using the Integrated Rate Law

Using the integrated rate law for second-order reactions, one can calculate the time required for a reactant’s concentration to change from an initial value to a desired final value. By rearranging the equation 1/[A] = 1/[A]? + kt to solve for t, the method provides a way to estimate the reaction time under specific conditions.

Rate Constant

The rate constant is a proportionality factor in the rate law that is specific to a given reaction at a certain temperature. Its units vary depending on the reaction order. For a second-order reaction, the rate constant typically has units of inverse molarity per second (1/(M·s)), ensuring the reaction’s rate has consistent units when calculated.

Reaction Order

Reaction order indicates how the rate of a chemical reaction depends on the concentration of its reactants. For example, in a second-order reaction, the rate depends on either the square of one reactant concentration or the product of two different reactant concentrations. Understanding the reaction order is essential for predicting how changes in concentration affect the rate.

Second-Order Reaction Integrated Rate Law

For second-order reactions, the integrated rate law relates the inverse of the reactant concentration to time. It is generally 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 law is useful for determining the concentration of a reactant after a certain time or the time required to reach a specified concentration.

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