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Ch.14 - Chemical Kinetics
All textbooksBrown 14th EditionCh.14 - Chemical KineticsProblem 46
Chapter 14, Problem 46

From the following data for the first-order gas-phase isomerization of CH3NC at 215 C, calculate the firstorder 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
Table showing time in seconds and corresponding pressure of CH3NC in torr for isomerization.

Verified step by step guidance
1
Step 1: Write down the integrated rate law for a first-order reaction: \( ext{ln} [A]_t = -kt + ext{ln} [A]_0 \).
Step 2: Use the given data to create a plot of \( ext{ln} [CH_3NC] \) versus time (s).
Step 3: Determine the slope of the line from the plot, which is equal to \(-k\).
Step 4: Calculate the first-order rate constant \(k\) from the slope.
Step 5: Use the first-order half-life formula \( t_{1/2} = \frac{0.693}{k} \) to calculate the half-life of the reaction.

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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. This means that as the concentration of the reactant decreases, the rate of the reaction also decreases. The mathematical representation of a first-order reaction is given by the equation: ln([A]0/[A]) = kt, where [A]0 is the initial concentration, [A] is the concentration at time t, k is the rate constant, and t is time.
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Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate equation that provides insight into the speed of a reaction. For first-order reactions, the units of k are typically s⁻¹. The value of k can be determined from experimental data by plotting ln([A]0/[A]) versus time (t), where the slope of the line equals -k. A larger k indicates a faster reaction.
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Half-Life (t1/2)

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. For first-order reactions, the half-life is constant and independent of the initial concentration, calculated using the formula t1/2 = 0.693/k. This property allows for easy comparison of reaction rates and is crucial for understanding the kinetics of the reaction.
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Related Practice
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

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?

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.

Textbook Question

Consider the data presented in Exercise 14.19. (c) What is the half-life for the reaction?