The reaction 2 NO2¡2 NO + O2 has the rate constant k = 0.63 M- 1s - 1. (b) If the initial concentration of NO2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

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Step 1: Identify the order of the reaction. In this case, the reaction is second order with respect to NO2, as indicated by the stoichiometric coefficient in front of NO2 in the balanced chemical equation.

Step 2: Write down the rate law for the reaction. For a second order reaction, the rate law is given by: \(\frac{1}{[A]_t} - \frac{1}{[A]_0} = kt\), where [A]_t is the concentration of the reactant at time t, [A]_0 is the initial concentration of the reactant, k is the rate constant, and t is the time.

Step 3: Substitute the given values into the rate law. In this case, [A]_0 is the initial concentration of NO2, which is 0.100 M, [A]_t is the final concentration of NO2, which is 0.025 M, and k is the rate constant, which is 0.63 M^-1s^-1.

Step 4: Solve the equation for t. This will give you the time it takes for the concentration of NO2 to decrease from 0.100 M to 0.025 M.

Step 5: Remember to check the units of your answer. The time should be in seconds, as the rate constant k is given in M^-1s^-1.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rate Law and Reaction Order

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. For the reaction 2 NO2 → 2 NO + O2, the rate law can be determined based on the stoichiometry of the reaction, which indicates that it is second-order with respect to NO2. Understanding the reaction order is crucial for calculating how concentration changes over time.

Integrated Rate Laws

Integrated rate laws relate the concentration of reactants to time. For a second-order reaction, the integrated rate law is given by 1/[A] = kt + 1/[A0], where [A] is the concentration at time t, [A0] is the initial concentration, and k is the rate constant. This equation allows us to calculate the time required for the concentration of NO2 to decrease from 0.100 M to 0.025 M.

Units of the Rate Constant

The units of the rate constant (k) provide insight into the order of the reaction. For a second-order reaction, the units of k are M^-1s^-1, indicating that the rate depends on the square of the concentration of the reactant. Understanding these units is essential for correctly applying the integrated rate law and ensuring that calculations are dimensionally consistent.

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