17.1 Chemical Reaction Rates
Learning Objectives
- 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 coloured 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. If we measure the concentration of hydrogen peroxide, H2O2, in an aqueous solution, we find that it changes slowly over time as the H2O2 decomposes, according to the equation:
The rate at which the hydrogen peroxide decomposes can be expressed in terms of the rate of change of its concentration, as shown here:
This mathematical representation of the change in species (chemical) 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 represents the molar concentration of hydrogen peroxide at some time t1; likewise, [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, t2 − t1). Since the reactant concentration decreases as the reaction proceeds, Δ[H2O2] is a negative quantity; we place a negative sign in front of the expression because reaction rates are, by convention, positive quantities. Figure 17.1a 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 / h.” Below, the following values are listed single-spaced: negative 0.0833, negative 0.0417, negative 0.0208, and negative 0.0103.](https://ecampusontario.pressbooks.pub/app/uploads/sites/3164/2022/05/CNX_Chem_12_01_KDataH2O2.jpg)
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:
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:
This behaviour 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. If we plot 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 17.1b). We can use calculus to evaluate the slopes of such tangent lines, 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 L superscript negative 1)” on the y-axis. The x-axis markings begin at 0 and end at 24. The markings are labeled at intervals of 6. The y-axis begins at 0 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 10 on the x-axis. A red tangent line segment is drawn on the graph at the point where the graph intersects the y-axis. A second red tangent line segment is drawn near the middle of the curve. 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.”](https://ecampusontario.pressbooks.pub/app/uploads/sites/3164/2023/03/CNX_Chem_12_01_RRateIll.jpg)
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 17.1c). These test strips contain various chemical reagents, embedded in small pads at various locations along the strip, which undergo changes in colour 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:
The first equation depicts the oxidation of glucose in the urine to yield glucolactone and hydrogen peroxide. The hydrogen peroxide produced subsequently oxidizes colourless 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 colour 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 typical glucose test strip for use with urine requires approximately 30 seconds for completion of the colour-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 colour change can lead to a false positive due to the slower (not catalyzed) oxidation of iodide ion by other substances found in urine.
Relative Rates of Reaction
The rate of a reaction may be expressed in terms of the change in the amount of any reactant or product, and may be simply derived from the stoichiometry of the reaction. Consider the reaction represented by the following equation:
The stoichiometric factors derived from this equation may be used to relate reaction rates in the same manner that they are used to relate reactant and product amounts. The relation between the reaction rates expressed in terms of nitrogen production and ammonia consumption, for example, is:
We can express this more simply without showing the stoichiometric factor’s units:
Note that a negative sign has been added to account for the opposite signs of the two amount changes (the reactant amount is decreasing while the product amount is increasing). If the reactants and products are present in the same solution, the molar amounts may be replaced by concentrations:
Similarly, the rate of formation of H2 is three times the rate of formation of N2 because three moles of H2 form during the time required for the formation of one mole of N2:
Figure 17.1d illustrates the change in concentrations over time for the decomposition of ammonia into nitrogen and hydrogen at 1100 °C. We can see from the slopes of the tangents drawn at t = 500 seconds that the instantaneous rates of change in the concentrations of the reactants and products 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:
![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.”](https://ecampusontario.pressbooks.pub/app/uploads/sites/3164/2023/03/CNX_Chem_12_01_NH3Decomp.jpg)
Example 17.1a
Reaction Rate Expressions for Decomposition of H2O2
The graph in Figure 17.1b shows the rate of the decomposition of H2O2 over time:
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:
What is the instantaneous rate of production of H2O and O2?
Solution
Using the stoichiometry of the reaction, we may determine that:
Therefore:
and
Exercise 17.1a
Check Your Learning Exercise (Text Version)
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?
- 5.30 × 10−6 mol/L/s, N2 and 7.52 × 10−6 mol/L/s, H2
- 1.05 × 10−6 mol/L/s, N2 and 3.15 × 10−6 mol/L/s, H2
- 3.15 × 10−6 mol/L/s, N2 and 1.05 × 10−6 mol/L/s, H2
- 2.10 × 10−6 mol/L/s, N2 and 6.30 × 10−6 mol/L/s, H2
Check Your Answer[1]
Source: “Exercise 17.1a” is adapted from “Example 12.1-2” in General Chemistry 1 & 2, a derivative of Chemistry (Open Stax) by Paul Flowers, Klaus Theopold, Richard Langley & William R. Robinson, licensed under CC BY 4.0.
Key Equations
- relative reaction rates for [latex]a\text{A}\;{\longrightarrow}\;b\text{B} = -\frac{1}{a}\;\frac{{\Delta}[\text{A}]}{{\Delta}t} = \frac{1}{b}\;\frac{{\Delta}[\text{B}]}{{\Delta}t}[/latex]
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Attribution & References
- b) 1.05 × 10−6 mol/L/s, N2 and 3.15 × 10−6 mol/L/s, H2 ↵
measure of the speed at which a chemical reaction takes place
can be a group of atoms, molecules, ions etc. that are chemically identical
mathematical representation relating reaction rate to changes in amount, concentration, or pressure of reactant or product species per unit time
rate of a chemical reaction computed as the ratio of a measured change in amount or concentration of substance to the time interval over which the change occurred
rate of a chemical reaction at any instant in time, determined by the slope of the line tangential to a graph of concentration as a function of time
instantaneous rate of a chemical reaction at t = 0 s (immediately after the reaction has begun)
