Ch.14 - Chemical Kinetics

Problem 48

Chapter 14, Problem 48

Consider the data presented in Exercise 14.20. (a) Determine whether the reaction is first order or second order.

Verified step by step guidance

Step 1: Review the data from Exercise 14.20, which should include concentration and time information for the reaction. This data is crucial for determining the order of the reaction.

Step 2: Plot the concentration of the reactant versus time to visually inspect if the reaction follows a first-order or second-order kinetic model. For a first-order reaction, a plot of ln(concentration) versus time should yield a straight line.

Step 3: Alternatively, plot 1/concentration versus time. For a second-order reaction, this plot should yield a straight line.

Step 4: Calculate the slope of the line from the plot that appears linear. For a first-order reaction, the slope of the ln(concentration) versus time plot is equal to -k, where k is the rate constant. For a second-order reaction, the slope of the 1/concentration versus time plot is equal to k.

Step 5: Compare the linearity of the two plots to determine the order of the reaction. The plot that results in a straight line indicates the order of the reaction: first-order if ln(concentration) versus time is linear, and second-order if 1/concentration versus time is linear.

Key Concepts

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

Reaction Order

Reaction order refers to the power to which the concentration of a reactant is raised in the rate law of a chemical reaction. It indicates how the rate of reaction depends on the concentration of reactants. A first-order reaction depends linearly on the concentration of one reactant, while a second-order reaction depends on the square of the concentration of one reactant or the product of the concentrations of two reactants.

Rate Law

The rate law is an equation that relates the rate of a chemical reaction to the concentration of its reactants. It is typically expressed in the form Rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B, respectively. Analyzing the rate law helps determine the reaction order by examining how changes in concentration affect the reaction rate.

Integrated Rate Laws

Integrated rate laws provide a mathematical relationship between the concentration of reactants and time for different orders of reactions. For first-order reactions, the integrated rate law is ln[A] = -kt + ln[A]₀, while for second-order reactions, it is 1/[A] = kt + 1/[A]₀. By plotting concentration data over time and analyzing the resulting graphs, one can determine the order of the reaction based on which plot yields a straight line.

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Rate Law Fundamentals

Related Practice

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.

Textbook Question

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

Textbook Question

The gas-phase decomposition of NO₂, 2 NO₂(g) → 2 NO(g) + O₂(g), is studied at 383°C, giving the following data:

Time (s) [NO₂] (M)

0.0 0.100

5.0 0.017

10.0 0.0090

15.0 0.0062

20.0 0.0047

(a) Is the reaction first order or second order with respect to the concentration of NO₂?

(c) Predict the reaction rates at the beginning of the reaction for initial concentrations of 0.200 M, 0.100 M, and 0.050 M NO₂.

Textbook Question

Sucrose 1C12H22O112, commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6. At 23 C and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose: Time (min) 3C12H22o11 4 1M2 0 0.316 39 0.274 80 0.238 140 0.190 210 0.146 (a) Is the reaction first order or second order with respect to 3C12H22O114?

Textbook Question

(a) What factors determine whether a collision between two molecules will lead to a chemical reaction?

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