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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1

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.

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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

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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Textbook Question

The reaction 2 NO1g2 + O21g2S 2 NO21g2 has the thirdorder rate law rate = k3NO423O24, where k = 25 M-2 s-1. Under the condition that 3NO4 = 2 3O24, the integrated rate law is 13O242 = 8 kt +113O24022 What are the concentrations of NO, O2, and NO2 after 100.0 s if the initial concentrations are 3NO4 = 0.0200 M and 3O24 = 0.0100 M?

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Open Question

Use the following initial rate data to determine the activation energy (in kJ/mol) for the reaction A + B ⇌ C.

Textbook Question

The following experimental data were obtained in a study of the reaction 2 HI1g2S H21g2 + I21g2. Predict the concentration of HI that would give a rate of 1.0 * 10-5 M>s at 650 K.

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.