The first-order rate constant for the decomposition of N 2 O 5 , 2 N 2 O 5 (g) → 4 NO 2 (g) + O 2 (g), at 70°C is 6.82×10 -3 s -1 . Suppose we start with 0.0250 mol of N 2 O 5 (g) in a volume of 2.0 L. (c) What is the half-life of N 2 O 5 at 70°C?

Hello everyone. Today, we have the following problem. The thermal d hydrogenation of propane is a first order process and has a rate constant of 4.86 times 10 to the negative second seconds to the negative one at 873. Kelvin, Calculate the Half Life of Propane at 873 Kelvin. So the first thing you wanna do is you want to write our formula for half life And it's going to be the natural log of two divided by a constant K. And so we have our constant K, our rate constant given us in the question stem. So we simply plug it in, we have our natural log two divided by our constant, which was 4.86 times 10 to the negative two seconds to the negative one. And this is going to give us a half life of 14.3 seconds. And with that, we have answered the question overall, I hope this helped. And until next time.

Ch.14 - Chemical Kinetics

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Brown 15th Edition

Ch.14 - Chemical Kinetics

Problem 44c

Chapter 14, Problem 44c

The first-order rate constant for the decomposition of N₂O₅, 2 N₂O₅(g) → 4 NO₂(g) + O₂(g), at 70°C is 6.82×10^-3 s^-1. Suppose we start with 0.0250 mol of N₂O₅(g) in a volume of 2.0 L. (c) What is the half-life of N₂O₅ at 70°C?

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Step 1: Understand that the half-life of a first-order reaction is given by the formula t1/2 = 0.693/k, where k is the rate constant.

Step 2: Identify the given rate constant (k) from the problem, which is 6.82 * 10^-3 s^-1.

Step 3: Substitute the given rate constant into the half-life formula.

Step 4: Solve the equation for t1/2 to find the half-life of N2O5 at 70 C.

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Key Concepts

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

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. In these reactions, the rate constant (k) remains constant, and the concentration of the reactant decreases exponentially over time. The half-life of a first-order reaction is independent of the initial concentration, making it a key characteristic for calculations involving such reactions.

Half-Life

The half-life of a substance is the time required for half of the initial amount of that substance to undergo a reaction or decay. For first-order reactions, the half-life can be calculated using the formula t1/2 = 0.693/k, where k is the rate constant. This concept is crucial for understanding how quickly a reactant is consumed in a reaction and is particularly useful in kinetics.

Rate Constant

The rate constant (k) is a proportionality factor in the rate equation that relates the rate of a reaction to the concentration of reactants. It is specific to a given reaction at a particular temperature and is essential for calculating reaction rates and half-lives. In the context of first-order reactions, the rate constant directly influences the duration of the half-life and the speed of the reaction.

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Rate Constant Units

Related Practice

Textbook Question

As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO₂Cl₂) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10^-2 s^-1. (a) If we begin with an initial SO₂Cl₂ pressure of 450 torr, what is the partial pressure of this substance after 60 s?

Textbook Question

As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO₂Cl₂) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10^-2 s^-1. (b) At what time will the partial pressure of SO₂Cl₂ decline to one-tenth its initial value?

Textbook Question

The first-order rate constant for the decomposition of N₂O₅, 2 N₂O₅(g) → 4 NO₂(g) + O₂(g), at 70°C is 6.82×10^-3 s^-1. Suppose we start with 0.0250 mol of N₂O₅(g) in a volume of 2.0 L. (a) How many moles of N₂O₅ will remain after 5.0 min?

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Textbook Question

From the following data for the first-order gas-phase isomerization of CH3NC to CH3CN at 215°C, calculate the first-order rate constant and half-life for the reaction:

Time (s) Pressure CH3NC (torr)

0 502

2000 335

5000 180

8000 95.5

12,000 41.7

15,000 22.4

Textbook Question

Consider the data presented in Exercise 14.19. (a) By using appropriate graphs, determine whether the reaction is first order or second order.

The first-order rate constant for the decomposition of N2O5, 2 N2O5(g) → 4 NO2(g) + O2(g), at 70°C is 6.82×10-3 s-1. Suppose we start with 0.0250 mol of N2O5(g) in a volume of 2.0 L. (c) What is the half-life of N2O5 at 70°C?

Verified video answer for a similar problem:

Key Concepts

First-Order Reactions

Half-Life

Rate Constant

The first-order rate constant for the decomposition of N₂O₅, 2 N₂O₅(g) → 4 NO₂(g) + O₂(g), at 70°C is 6.82×10^-3 s^-1. Suppose we start with 0.0250 mol of N₂O₅(g) in a volume of 2.0 L. (c) What is the half-life of N₂O₅ at 70°C?