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Chemistry 2e

12.1 Chemical Reaction Rates

Chemistry 2e12.1 Chemical Reaction Rates
  1. Preface
  2. 1 Essential Ideas
    1. Introduction
    2. 1.1 Chemistry in Context
    3. 1.2 Phases and Classification of Matter
    4. 1.3 Physical and Chemical Properties
    5. 1.4 Measurements
    6. 1.5 Measurement Uncertainty, Accuracy, and Precision
    7. 1.6 Mathematical Treatment of Measurement Results
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  3. 2 Atoms, Molecules, and Ions
    1. Introduction
    2. 2.1 Early Ideas in Atomic Theory
    3. 2.2 Evolution of Atomic Theory
    4. 2.3 Atomic Structure and Symbolism
    5. 2.4 Chemical Formulas
    6. 2.5 The Periodic Table
    7. 2.6 Molecular and Ionic Compounds
    8. 2.7 Chemical Nomenclature
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  4. 3 Composition of Substances and Solutions
    1. Introduction
    2. 3.1 Formula Mass and the Mole Concept
    3. 3.2 Determining Empirical and Molecular Formulas
    4. 3.3 Molarity
    5. 3.4 Other Units for Solution Concentrations
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  5. 4 Stoichiometry of Chemical Reactions
    1. Introduction
    2. 4.1 Writing and Balancing Chemical Equations
    3. 4.2 Classifying Chemical Reactions
    4. 4.3 Reaction Stoichiometry
    5. 4.4 Reaction Yields
    6. 4.5 Quantitative Chemical Analysis
    7. Key Terms
    8. Key Equations
    9. Summary
    10. Exercises
  6. 5 Thermochemistry
    1. Introduction
    2. 5.1 Energy Basics
    3. 5.2 Calorimetry
    4. 5.3 Enthalpy
    5. Key Terms
    6. Key Equations
    7. Summary
    8. Exercises
  7. 6 Electronic Structure and Periodic Properties of Elements
    1. Introduction
    2. 6.1 Electromagnetic Energy
    3. 6.2 The Bohr Model
    4. 6.3 Development of Quantum Theory
    5. 6.4 Electronic Structure of Atoms (Electron Configurations)
    6. 6.5 Periodic Variations in Element Properties
    7. Key Terms
    8. Key Equations
    9. Summary
    10. Exercises
  8. 7 Chemical Bonding and Molecular Geometry
    1. Introduction
    2. 7.1 Ionic Bonding
    3. 7.2 Covalent Bonding
    4. 7.3 Lewis Symbols and Structures
    5. 7.4 Formal Charges and Resonance
    6. 7.5 Strengths of Ionic and Covalent Bonds
    7. 7.6 Molecular Structure and Polarity
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  9. 8 Advanced Theories of Covalent Bonding
    1. Introduction
    2. 8.1 Valence Bond Theory
    3. 8.2 Hybrid Atomic Orbitals
    4. 8.3 Multiple Bonds
    5. 8.4 Molecular Orbital Theory
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  10. 9 Gases
    1. Introduction
    2. 9.1 Gas Pressure
    3. 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
    4. 9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions
    5. 9.4 Effusion and Diffusion of Gases
    6. 9.5 The Kinetic-Molecular Theory
    7. 9.6 Non-Ideal Gas Behavior
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  11. 10 Liquids and Solids
    1. Introduction
    2. 10.1 Intermolecular Forces
    3. 10.2 Properties of Liquids
    4. 10.3 Phase Transitions
    5. 10.4 Phase Diagrams
    6. 10.5 The Solid State of Matter
    7. 10.6 Lattice Structures in Crystalline Solids
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  12. 11 Solutions and Colloids
    1. Introduction
    2. 11.1 The Dissolution Process
    3. 11.2 Electrolytes
    4. 11.3 Solubility
    5. 11.4 Colligative Properties
    6. 11.5 Colloids
    7. Key Terms
    8. Key Equations
    9. Summary
    10. Exercises
  13. 12 Kinetics
    1. Introduction
    2. 12.1 Chemical Reaction Rates
    3. 12.2 Factors Affecting Reaction Rates
    4. 12.3 Rate Laws
    5. 12.4 Integrated Rate Laws
    6. 12.5 Collision Theory
    7. 12.6 Reaction Mechanisms
    8. 12.7 Catalysis
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  14. 13 Fundamental Equilibrium Concepts
    1. Introduction
    2. 13.1 Chemical Equilibria
    3. 13.2 Equilibrium Constants
    4. 13.3 Shifting Equilibria: Le Châtelier’s Principle
    5. 13.4 Equilibrium Calculations
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  15. 14 Acid-Base Equilibria
    1. Introduction
    2. 14.1 Brønsted-Lowry Acids and Bases
    3. 14.2 pH and pOH
    4. 14.3 Relative Strengths of Acids and Bases
    5. 14.4 Hydrolysis of Salts
    6. 14.5 Polyprotic Acids
    7. 14.6 Buffers
    8. 14.7 Acid-Base Titrations
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  16. 15 Equilibria of Other Reaction Classes
    1. Introduction
    2. 15.1 Precipitation and Dissolution
    3. 15.2 Lewis Acids and Bases
    4. 15.3 Coupled Equilibria
    5. Key Terms
    6. Key Equations
    7. Summary
    8. Exercises
  17. 16 Thermodynamics
    1. Introduction
    2. 16.1 Spontaneity
    3. 16.2 Entropy
    4. 16.3 The Second and Third Laws of Thermodynamics
    5. 16.4 Free Energy
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  18. 17 Electrochemistry
    1. Introduction
    2. 17.1 Review of Redox Chemistry
    3. 17.2 Galvanic Cells
    4. 17.3 Electrode and Cell Potentials
    5. 17.4 Potential, Free Energy, and Equilibrium
    6. 17.5 Batteries and Fuel Cells
    7. 17.6 Corrosion
    8. 17.7 Electrolysis
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  19. 18 Representative Metals, Metalloids, and Nonmetals
    1. Introduction
    2. 18.1 Periodicity
    3. 18.2 Occurrence and Preparation of the Representative Metals
    4. 18.3 Structure and General Properties of the Metalloids
    5. 18.4 Structure and General Properties of the Nonmetals
    6. 18.5 Occurrence, Preparation, and Compounds of Hydrogen
    7. 18.6 Occurrence, Preparation, and Properties of Carbonates
    8. 18.7 Occurrence, Preparation, and Properties of Nitrogen
    9. 18.8 Occurrence, Preparation, and Properties of Phosphorus
    10. 18.9 Occurrence, Preparation, and Compounds of Oxygen
    11. 18.10 Occurrence, Preparation, and Properties of Sulfur
    12. 18.11 Occurrence, Preparation, and Properties of Halogens
    13. 18.12 Occurrence, Preparation, and Properties of the Noble Gases
    14. Key Terms
    15. Summary
    16. Exercises
  20. 19 Transition Metals and Coordination Chemistry
    1. Introduction
    2. 19.1 Occurrence, Preparation, and Properties of Transition Metals and Their Compounds
    3. 19.2 Coordination Chemistry of Transition Metals
    4. 19.3 Spectroscopic and Magnetic Properties of Coordination Compounds
    5. Key Terms
    6. Summary
    7. Exercises
  21. 20 Organic Chemistry
    1. Introduction
    2. 20.1 Hydrocarbons
    3. 20.2 Alcohols and Ethers
    4. 20.3 Aldehydes, Ketones, Carboxylic Acids, and Esters
    5. 20.4 Amines and Amides
    6. Key Terms
    7. Summary
    8. Exercises
  22. 21 Nuclear Chemistry
    1. Introduction
    2. 21.1 Nuclear Structure and Stability
    3. 21.2 Nuclear Equations
    4. 21.3 Radioactive Decay
    5. 21.4 Transmutation and Nuclear Energy
    6. 21.5 Uses of Radioisotopes
    7. 21.6 Biological Effects of Radiation
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  23. A | The Periodic Table
  24. B | Essential Mathematics
  25. C | Units and Conversion Factors
  26. D | Fundamental Physical Constants
  27. E | Water Properties
  28. F | Composition of Commercial Acids and Bases
  29. G | Standard Thermodynamic Properties for Selected Substances
  30. H | Ionization Constants of Weak Acids
  31. I | Ionization Constants of Weak Bases
  32. J | Solubility Products
  33. K | Formation Constants for Complex Ions
  34. L | Standard Electrode (Half-Cell) Potentials
  35. M | Half-Lives for Several Radioactive Isotopes
  36. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
    18. Chapter 18
    19. Chapter 19
    20. Chapter 20
    21. Chapter 21
  37. Index
By the end of this section, you will be able to:
  • Define chemical reaction rate
  • Derive rate expressions from the balanced equation for a given chemical reaction
  • Calculate reaction rates from experimental data

A rate is a measure of how some property varies with time. Speed is a familiar rate that expresses the distance traveled by an object in a given amount of time. Wage is a rate that represents the amount of money earned by a person working for a given amount of time. Likewise, the rate of a chemical reaction is a measure of how much reactant is consumed, or how much product is produced, by the reaction in a given amount of time.

The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure. For reactions involving one or more colored substances, rates may be monitored via measurements of light absorption. For reactions involving aqueous electrolytes, rates may be measured via changes in a solution’s conductivity.

For reactants and products in solution, their relative amounts (concentrations) are conveniently used for purposes of expressing reaction rates. For example, the concentration of hydrogen peroxide, H2O2, in an aqueous solution changes slowly over time as it decomposes according to the equation:

2H2O2(aq)2H2O(l)+O2(g)2H2O2(aq)2H2O(l)+O2(g)

The rate at which the hydrogen peroxide decomposes can be expressed in terms of the rate of change of its concentration, as shown here:

rate of decomposition ofH2O2=change in concentration of reactanttime interval=[H2O2]t2[H2O2]t1t2t1=Δ[H2O2]Δtrate of decomposition ofH2O2=change in concentration of reactanttime interval=[H2O2]t2[H2O2]t1t2t1=Δ[H2O2]Δt

This mathematical representation of the change in species concentration over time is the rate expression for the reaction. The brackets indicate molar concentrations, and the symbol delta (Δ) indicates “change in.” Thus, [H2O2]t1[H2O2]t1 represents the molar concentration of hydrogen peroxide at some time t1; likewise,[H2O2]t2[H2O2]t2 represents the molar concentration of hydrogen peroxide at a later time t2; and Δ[H2O2] represents the change in molar concentration of hydrogen peroxide during the time interval Δt (that is, t2t1). Since the reactant concentration decreases as the reaction proceeds, Δ[H2O2] is a negative quantity. Reaction rates are, by convention, positive quantities, and so this negative change in concentration is multiplied by −1. Figure 12.2 provides an example of data collected during the decomposition of H2O2.

A table with five columns is shown. The first column is labeled, “Time, h.” Beneath it the numbers 0.00, 6.00, 12.00, 18.00, and 24.00 are listed. The second column is labeled, “[ H subscript 2 O subscript 2 ], mol / L.” Below, the numbers 1.000, 0.500, 0.250, 0.125, and 0.0625 are double spaced. To the right, a third column is labeled, “capital delta [ H subscript 2 O subscript 2 ], mol / L.” Below, the numbers negative 0.500, negative 0.250, negative 0.125, and negative 0.062 are listed such that they are double spaced and offset, beginning one line below the first number listed in the column labeled, “[ H subscript 2 O subscript 2 ], mol / L.” The first two numbers in the second column have line segments extending from their right side to the left side of the first number in the third row. The second and third numbers in the second column have line segments extending from their right side to the left side of the second number in the third row. The third and fourth numbers in the second column have line segments extending from their right side to the left side of the third number in the third row. The fourth and fifth numbers in the second column have line segments extending from their right side to the left side of the fourth number in the third row. The fourth column in labeled, “capital delta t, h.” Below the title, the value 6.00 is listed four times, each single-spaced. The fifth and final column is labeled “Rate of Decomposition, mol / L superscript negative 1 / h superscript negative 1.” Below, the following values are listed single-spaced: negative 0.0833, negative 0.0417, negative 0.0208, and negative 0.010.
Figure 12.2 The rate of decomposition of H2O2 in an aqueous solution decreases as the concentration of H2O2 decreases.

To obtain the tabulated results for this decomposition, the concentration of hydrogen peroxide was measured every 6 hours over the course of a day at a constant temperature of 40 °C. Reaction rates were computed for each time interval by dividing the change in concentration by the corresponding time increment, as shown here for the first 6-hour period:

Δ[H2O2]Δt=−(0.500 mol/L1.000 mol/L)(6.00 h0.00 h)=0.0833 molL−1h−1Δ[H2O2]Δt=−(0.500 mol/L1.000 mol/L)(6.00 h0.00 h)=0.0833 molL−1h−1

Notice that the reaction rates vary with time, decreasing as the reaction proceeds. Results for the last 6-hour period yield a reaction rate of:

Δ[H2O2]Δt=(0.0625mol/L0.125mol/L)(24.00h18.00h)=0.010molL−1h−1Δ[H2O2]Δt=(0.0625mol/L0.125mol/L)(24.00h18.00h)=0.010molL−1h−1

This behavior indicates the reaction continually slows with time. Using the concentrations at the beginning and end of a time period over which the reaction rate is changing results in the calculation of an average rate for the reaction over this time interval. At any specific time, the rate at which a reaction is proceeding is known as its instantaneous rate. The instantaneous rate of a reaction at “time zero,” when the reaction commences, is its initial rate. Consider the analogy of a car slowing down as it approaches a stop sign. The vehicle’s initial rate—analogous to the beginning of a chemical reaction—would be the speedometer reading at the moment the driver begins pressing the brakes (t0). A few moments later, the instantaneous rate at a specific moment—call it t1—would be somewhat slower, as indicated by the speedometer reading at that point in time. As time passes, the instantaneous rate will continue to fall until it reaches zero, when the car (or reaction) stops. Unlike instantaneous speed, the car’s average speed is not indicated by the speedometer; but it can be calculated as the ratio of the distance traveled to the time required to bring the vehicle to a complete stop (Δt). Like the decelerating car, the average rate of a chemical reaction will fall somewhere between its initial and final rates.

The instantaneous rate of a reaction may be determined one of two ways. If experimental conditions permit the measurement of concentration changes over very short time intervals, then average rates computed as described earlier provide reasonably good approximations of instantaneous rates. Alternatively, a graphical procedure may be used that, in effect, yields the results that would be obtained if short time interval measurements were possible. In a plot of the concentration of hydrogen peroxide against time, the instantaneous rate of decomposition of H2O2 at any time t is given by the slope of a straight line that is tangent to the curve at that time (Figure 12.3). These tangent line slopes may be evaluated using calculus, but the procedure for doing so is beyond the scope of this chapter.

A graph is shown with the label, “Time ( h ),” appearing on the x-axis and “[ H subscript 2 O subscript 2 ] ( mol per L)” on the y-axis. The x-axis markings begin at 0.00 and end at 24.00. The markings are labeled at intervals of 6.00. The y-axis begins at 0.000 and includes markings every 0.200, up to 1.000. A decreasing, concave up, non-linear curve is shown, which begins at 1.000 on the y-axis and nearly reaches a value of 0 at the far right of the graph around 24.00 on the x-axis. A red tangent line segment is drawn on the graph at the point where the graph intersects the y-axis at 1.000. The slope is labeled as “slope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 0 equals initial rate”. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled “capital delta [ H subscript 2 O subscript 2 ]” and the horizontal leg is labeled, “capital delta t.” The slope is labeled as “slope equals negative capital delta [H subscript 2 O subscript 2 ] over capital delta t subscript 12 equals instantaneous rate at 12 h.” A second red tangent line segment is drawn near the middle of the curve at 12.00 on the x-axis. A vertical dashed line segment extends from the left endpoint of the line segment downward to intersect with a similar horizontal line segment drawn from the right endpoint of the line segment, forming a right triangle beneath the curve. The vertical leg of the triangle is labeled “capital delta [ H subscript 2 O subscript 2 ]” and the horizontal leg is labeled, “capital delta t.”
Figure 12.3 This graph shows a plot of concentration versus time for a 1.000 M solution of H2O2. The rate at any time is equal to the negative of the slope of a line tangent to the curve at that time. Tangents are shown at t = 0 h (“initial rate”) and at t = 12 h (“instantaneous rate” at 12 h).

Chemistry in Everyday Life

Reaction Rates in Analysis: Test Strips for Urinalysis

Physicians often use disposable test strips to measure the amounts of various substances in a patient’s urine (Figure 12.4). These test strips contain various chemical reagents, embedded in small pads at various locations along the strip, which undergo changes in color upon exposure to sufficient concentrations of specific substances. The usage instructions for test strips often stress that proper read time is critical for optimal results. This emphasis on read time suggests that kinetic aspects of the chemical reactions occurring on the test strip are important considerations.

The test for urinary glucose relies on a two-step process represented by the chemical equations shown here:

C6H12O6+O2catalystC6H10O6+H2O2C6H12O6+O2catalystC6H10O6+H2O2
2H2O2+2IcatalystI2+2H2O+O22H2O2+2IcatalystI2+2H2O+O2

The first equation depicts the oxidation of glucose in the urine to yield glucolactone and hydrogen peroxide. The hydrogen peroxide produced subsequently oxidizes colorless iodide ion to yield brown iodine, which may be visually detected. Some strips include an additional substance that reacts with iodine to produce a more distinct color change.

The two test reactions shown above are inherently very slow, but their rates are increased by special enzymes embedded in the test strip pad. This is an example of catalysis, a topic discussed later in this chapter. A typical glucose test strip for use with urine requires approximately 30 seconds for completion of the color-forming reactions. Reading the result too soon might lead one to conclude that the glucose concentration of the urine sample is lower than it actually is (a false-negative result). Waiting too long to assess the color change can lead to a false positive due to the slower (not catalyzed) oxidation of iodide ion by other substances found in urine.

A photograph shows 8 test strips laid on paper toweling. Each strip contains 11 small sections of various colors, including yellow, tan, black, red, orange, blue, white, and green.
Figure 12.4 Test strips are commonly used to detect the presence of specific substances in a person’s urine. Many test strips have several pads containing various reagents to permit the detection of multiple substances on a single strip. (credit: Iqbal Osman)

Relative Rates of Reaction

The rate of a reaction may be expressed as the change in concentration of any reactant or product. For any given reaction, these rate expressions are all related simply to one another according to the reaction stoichiometry. The rate of the general reaction

aAbBaAbB

can be expressed in terms of the decrease in the concentration of A or the increase in the concentration of B. These two rate expressions are related by the stoichiometry of the reaction:

rate=(1a)(ΔAΔt)=(1b)(ΔBΔt)rate=(1a)(ΔAΔt)=(1b)(ΔBΔt)

the reaction represented by the following equation:

2NH3(g)N2(g)+3H2(g)2NH3(g)N2(g)+3H2(g)

The relation between the reaction rates expressed in terms of nitrogen production and ammonia consumption, for example, is:

Δmol NH3Δt×1 molN22 molNH3=ΔmolN2ΔtΔmol NH3Δt×1 molN22 molNH3=ΔmolN2Δt

This may be represented in an abbreviated format by omitting the units of the stoichiometric factor:

12ΔmolNH3Δt=ΔmolN2Δt12ΔmolNH3Δt=ΔmolN2Δt

Note that a negative sign has been included as a factor to account for the opposite signs of the two amount changes (the reactant amount is decreasing while the product amount is increasing). For homogeneous reactions, both the reactants and products are present in the same solution and thus occupy the same volume, so the molar amounts may be replaced with molar concentrations:

12Δ[NH3]Δt=Δ[N2]Δt12Δ[NH3]Δt=Δ[N2]Δt

Similarly, the rate of formation of H2 is three times the rate of formation of N2 because three moles of H2 are produced for each mole of N2 produced.

13Δ[H2]Δt=Δ[N2]Δt13Δ[H2]Δt=Δ[N2]Δt

Figure 12.5 illustrates the change in concentrations over time for the decomposition of ammonia into nitrogen and hydrogen at 1100 °C. Slopes of the tangent lines at t = 500 s show that the instantaneous rates derived from all three species involved in the reaction are related by their stoichiometric factors. The rate of hydrogen production, for example, is observed to be three times greater than that for nitrogen production:

2.91×10−6M/s9.70×10−7M/s32.91×10−6M/s9.70×10−7M/s3
A graph is shown with the label, “Time ( s ),” appearing on the x-axis and, “Concentration ( M ),” on the y-axis. The x-axis markings begin at 0 and end at 2000. The markings are labeled at intervals of 500. The y-axis begins at 0 and includes markings every 1.0 times 10 superscript negative 3, up to 4.0 times 10 superscript negative 3. A decreasing, concave up, non-linear curve is shown, which begins at about 2.8 times 10 superscript negative 3 on the y-axis and nearly reaches a value of 0 at the far right of the graph at the 2000 marking on the x-axis. This curve is labeled, “[ N H subscript 3].” Two additional curves that are increasing and concave down are shown, both beginning at the origin. The lower of these two curves is labeled, “[ N subscript 2 ].” It reaches a value of approximately 1.25 times 10 superscript negative 3 at 2000 seconds. The final curve is labeled, “[ H subscript 2 ].” It reaches a value of about 3.9 times 10 superscript negative 3 at 2000 seconds. A red tangent line segment is drawn to each of the curves on the graph at 500 seconds. At 500 seconds on the x-axis, a vertical dashed line is shown. Next to the [ N H subscript 3] graph appears the equation “negative capital delta [ N H subscript 3 ] over capital delta t = negative slope = 1.94 times 10 superscript negative 6 M / s.” Next to the [ N subscript 2] graph appears the equation “negative capital delta [ N subscript 2 ] over capital delta t = negative slope = 9.70 times 10 superscript negative 7 M / s.” Next to the [ H subscript 2 ] graph appears the equation “negative capital delta [ H subscript 2 ] over capital delta t = negative slope = 2.91 times 10 superscript negative 6 M / s.”
Figure 12.5 Changes in concentrations of the reactant and products for the reaction 2NH3N2+3H2.2NH3N2+3H2. The rates of change of the three concentrations are related by the reaction stoichiometry, as shown by the different slopes of the tangents at t = 500 s.

Example 12.1

Expressions for Relative Reaction Rates The first step in the production of nitric acid is the combustion of ammonia:

4NH3(g)+5O2(g)4NO(g)+6H2O(g)4NH3(g)+5O2(g)4NO(g)+6H2O(g)

Write the equations that relate the rates of consumption of the reactants and the rates of formation of the products.

Solution Considering the stoichiometry of this homogeneous reaction, the rates for the consumption of reactants and formation of products are:

14Δ[NH3]Δt=15Δ[O2]Δt=14Δ[NO]Δt=16Δ[H2O]Δt14Δ[NH3]Δt=15Δ[O2]Δt=14Δ[NO]Δt=16Δ[H2O]Δt

Check Your Learning The rate of formation of Br2 is 6.0 ×× 10−6 mol/L/s in a reaction described by the following net ionic equation:

5Br+BrO3+6H+3Br2+3H2O5Br+BrO3+6H+3Br2+3H2O

Write the equations that relate the rates of consumption of the reactants and the rates of formation of the products.

Answer:

15Δ[Br]Δt=Δ[BrO3]Δt=16Δ[H+]Δt=13Δ[Br2]Δt=13Δ[H2O]Δt15Δ[Br]Δt=Δ[BrO3]Δt=16Δ[H+]Δt=13Δ[Br2]Δt=13Δ[H2O]Δt

Example 12.2

Reaction Rate Expressions for Decomposition of H2O2 The graph in Figure 12.3 shows the rate of the decomposition of H2O2 over time:

2H2O22H2O+O22H2O22H2O+O2

Based on these data, the instantaneous rate of decomposition of H2O2 at t = 11.1 h is determined to be
3.20 ×× 10−2 mol/L/h, that is:

Δ[H2O2]Δt=3.20×10−2mol L−1h−1Δ[H2O2]Δt=3.20×10−2mol L−1h−1

What is the instantaneous rate of production of H2O and O2?

Solution The reaction stoichiometry shows that

12Δ[H2O2]Δt=12Δ[H2O]Δt=Δ[O2]Δt12Δ[H2O2]Δt=12Δ[H2O]Δt=Δ[O2]Δt

Therefore:

12×3.20×10−2molL−1h−1=Δ[O2]Δt12×3.20×10−2molL−1h−1=Δ[O2]Δt

and

Δ[O2]Δt=1.60×10−2molL−1h−1Δ[O2]Δt=1.60×10−2molL−1h−1

Check Your Learning If the rate of decomposition of ammonia, NH3, at 1150 K is 2.10 ×× 10−6 mol/L/s, what is the rate of production of nitrogen and hydrogen?

Answer:

1.05 ×× 10−6 mol/L/s, N2 and 3.15 ×× 10−6 mol/L/s, H2.

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