Consider the following data for the gas-phase decomposition of NO2: 2 NO2(g) → 2 NO(g) + O2(g) If 0.0050 mol of NO2 is introduced into a 1.0 L flask and allowed to decompose at 650 K, how many seconds does it take for the NO2 concentration to drop to 0.0010 M?

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Step 1: Determine the initial concentration of NO2. Since 0.0050 mol of NO2 is introduced into a 1.0 L flask, the initial concentration [NO2]_0 is 0.0050 M.

Step 2: Identify the order of the reaction. The problem involves the decomposition of NO2, which is often a second-order reaction. Verify this with the given data or assume second-order if not specified.

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Step 3: Use the integrated rate law for a second-order reaction: \( \frac{1}{[A]} = kt + \frac{1}{[A]_0} \), where [A] is the concentration at time t, k is the rate constant, and [A]_0 is the initial concentration.

Step 4: Substitute the known values into the integrated rate law. Here, [A]_0 = 0.0050 M, [A] = 0.0010 M, and solve for time t. You will need the rate constant k, which should be provided or determined from additional data.

Step 5: Rearrange the equation to solve for t: \( t = \frac{1}{k} \left( \frac{1}{[A]} - \frac{1}{[A]_0} \right) \). Calculate t using the values from the previous steps.

Key Concepts

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

Chemical Kinetics

Chemical kinetics is the study of the rates of chemical reactions and the factors that affect these rates. In this context, understanding how the concentration of NO2 changes over time is crucial for determining the time it takes for the concentration to drop from 0.0050 M to 0.0010 M. The rate of reaction can be influenced by temperature, concentration, and the presence of catalysts.

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Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. For the decomposition of NO2, the rate law can be determined experimentally and is essential for calculating the time required for the concentration to decrease. It typically takes the form rate = k[NO2]^n, where k is the rate constant and n is the order of the reaction.

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Rate Law Fundamentals

Concentration and Molarity

Concentration refers to the amount of a substance in a given volume of solution, commonly expressed in molarity (M), which is moles of solute per liter of solution. In this problem, the initial concentration of NO2 is 0.0050 M, and the goal is to find the time it takes for this concentration to decrease to 0.0010 M. Understanding how to convert between moles and molarity is essential for solving the problem.

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Related Practice

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 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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Textbook Question

A 1.50 L sample of gaseous HI having a density of 0.0101 g>cm3 is heated at 410 °C. As time passes, the HI decomposes to gaseous H2 and I2. The rate law is -Δ3HI4>Δt = k3HI42, where k = 0.031>1M ~ min2 at 410 °C. (b) What is the partial pressure of H2 after a reaction time of 8.00 h?

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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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