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

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Start by understanding the order of a reaction, which can be determined by analyzing how the concentration of reactants changes over time. For a first-order reaction, a plot of the natural logarithm of concentration versus time will yield a straight line. For a second-order reaction, a plot of the inverse of concentration versus time will yield a straight line.

Gather the concentration data from Exercise 14.19. You will need the initial concentration and the concentration at various time intervals.

Create a graph plotting the natural logarithm of concentration (ln[Concentration]) on the y-axis against time on the x-axis. If the data points form a straight line, the reaction is first order.

Create another graph plotting the inverse of concentration (1/[Concentration]) on the y-axis against time on the x-axis. If the data points form a straight line, the reaction is second order.

Compare the two graphs. The graph that results in a straight line indicates the order of the reaction. If the ln[Concentration] vs. time graph is linear, the reaction is first order. If the 1/[Concentration] vs. time graph is linear, the reaction is second order.

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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 has a linear relationship between the concentration of one reactant and the rate, while a second-order reaction involves a squared concentration term, leading to a different graphical representation.

Rate Laws

Rate laws express the relationship between the rate of a chemical reaction and the concentration of its reactants. They are determined experimentally and can be used to identify the order of a reaction. For example, a first-order rate law is expressed as rate = k[A], while a second-order rate law can be expressed as rate = k[A]^2 or rate = k[A][B], depending on the number of reactants involved.

Graphical Analysis

Graphical analysis involves plotting data to visually interpret relationships between variables. For reaction order, specific plots can be used: a plot of concentration versus time for first-order reactions yields a straight line when plotted as ln[A] versus time, while a plot of 1/[A] versus time gives a straight line for second-order reactions. Analyzing these graphs helps determine the order of the reaction based on the linearity of the plots.

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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

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

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.