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Ch.14 - Chemical Kinetics
All textbooksBrown 15th EditionCh.14 - Chemical KineticsProblem 50a
Chapter 14, Problem 50a

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?

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We need to determine the order of the reaction with respect to sucrose (C_{12}H_{22}O_{11}). The data provided shows the concentration of sucrose at different times. We will use this data to determine if the reaction is first order or second order.
For a first-order reaction, the rate law is: \( \text{Rate} = k [\text{C}_{12}\text{H}_{22}\text{O}_{11}] \). For a second-order reaction, the rate law is: \( \text{Rate} = k [\text{C}_{12}\text{H}_{22}\text{O}_{11}]^2 \).
For a first-order reaction, the integrated rate law is: \( \ln [\text{C}_{12}\text{H}_{22}\text{O}_{11}] = -kt + \ln [\text{C}_{12}\text{H}_{22}\text{O}_{11}]_0 \). For a second-order reaction, the integrated rate law is: \( \frac{1}{[\text{C}_{12}\text{H}_{22}\text{O}_{11}]} = kt + \frac{1}{[\text{C}_{12}\text{H}_{22}\text{O}_{11}]_0} \).
Plot \( \ln [\text{C}_{12}\text{H}_{22}\text{O}_{11}] \) versus time for a first-order reaction and \( \frac{1}{[\text{C}_{12}\text{H}_{22}\text{O}_{11}]} \) versus time for a second-order reaction. The plot that results in a straight line indicates the order of the reaction.
Determine which plot is linear. If the plot of \( \ln [\text{C}_{12}\text{H}_{22}\text{O}_{11}] \) versus time is linear, the reaction is first order. If the plot of \( \frac{1}{[\text{C}_{12}\text{H}_{22}\text{O}_{11}]} \) versus time 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, indicating a more complex relationship.
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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. Determining the rate law is essential for understanding how changes in concentration affect the speed of the reaction.
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Integrated Rate Laws

Integrated rate laws provide a mathematical relationship between the concentration of reactants and time, allowing for the determination of reaction order through experimental data. For first-order reactions, the integrated form is ln[A] = -kt + ln[A]0, while for second-order reactions, it is 1/[A] = kt + 1/[A]0. Analyzing concentration versus time data using these equations helps identify the order of the reaction.
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Related Practice
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

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

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Textbook Question

(b) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature?

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