The reaction 2 NO1g2 + O21g2S 2 NO21g2 has the thirdorderrate law rate = k3NO423O24, where k = 25 M-2 s-1.Under the condition that 3NO4 = 2 3O24, the integratedrate law is13O242 = 8 kt +113O24022What are the concentrations of NO, O2, and NO2 after100.0 s if the initial concentrations are 3NO4 = 0.0200 Mand 3O24 = 0.0100 M?

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Identify the given reaction and rate law: The reaction is 2 NO(g) + O2(g) -> 2 NO2(g) with a third-order rate law: rate = k[NO]^2[O2].

Note the given rate constant k = 25 M^-2 s^-1 and the condition [NO] = 2[O2].

Use the integrated rate law provided: 1/[O2] = 8kt + 1/[O2]_0^2, where [O2]_0 is the initial concentration of O2.

Substitute the initial concentration of O2 ([O2]_0 = 0.0100 M) and the time (t = 100.0 s) into the integrated rate law to solve for [O2].

Once [O2] is found, use the condition [NO] = 2[O2] to find [NO], and use stoichiometry to find [NO2] based on the initial concentrations and changes in [NO] and [O2].

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Key Concepts

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

Rate Laws

Rate laws express the relationship between the rate of a chemical reaction and the concentration of its reactants. In this case, the rate law is third-order, indicating that the rate depends on the concentrations of NO and O2 raised to the power of their stoichiometric coefficients. Understanding how to interpret and apply rate laws is essential for predicting how changes in concentration affect the reaction rate.

Integrated Rate Laws

Integrated rate laws relate the concentrations of reactants to time, allowing for the calculation of concentrations at any given time during the reaction. The provided integrated rate law for this reaction shows how the concentration of O2 changes over time, which is crucial for determining the concentrations of all species after a specified duration. Mastery of integrated rate laws is vital for solving kinetics problems.

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In this question, the stoichiometric coefficients from the balanced equation are used to relate the initial concentrations of NO and O2 to the concentrations of NO2 produced. A solid understanding of stoichiometry is necessary to accurately calculate the concentrations of all species involved in the reaction.

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Textbook Question

Some reactions are so rapid that they are said to be diffusion-controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H₃O⁺ by OH^-, which has a second-order rate constant of 1.3⨉10¹¹ M^-1 s^-1 at 25 °C. (a) If equal volumes of 2.0 M HCl and 2.0 M NaOH are mixed instantaneously, how much time is required for 99.999% of the acid to be neutralized?

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Textbook Question

The half-life for the first-order decomposition of N2O4 is 1.3 * 10-5 s. N2O41g2S 2 NO21g2 If N2O4 is introduced into an evacuated flask at a pressure of 17.0 mm Hg, how many seconds are required for the pressure of NO2 to reach 1.3 mm Hg?

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Textbook Question

Some reactions are so rapid that they are said to be diffusion-controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H₃O⁺ by OH^-, which has a second-order rate constant of 1.3⨉10¹¹ M^-1 s^-1 at 25 °C. (b) Under normal laboratory conditions, would you expect the rate of the acid–base neutralization to be limited by the rate of the reaction or by the speed of mixing?

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