8.1: Introduction to Chemical Reaction Rates

Figure \(\PageIndex{1}\) An agama lizard basks in the sun. As its body warms, the chemical reactions of its metabolism speed up.

Learning Objectives

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
• Describe the effects of chemical nature, physical state, temperature, concentration, and catalysis on reaction rates

Introduction

The lizard in the Figure \(\PageIndex{1}\) photograph is not simply enjoying the sunshine or working on its tan. The heat from the sun’s rays is critical to the lizard’s survival. A warm lizard can move faster than a cold one because the chemical reactions that allow its muscles to move occur more rapidly at higher temperatures. A cold lizard is a slower lizard and an easier meal for predators.

From baking a cake to determining the useful lifespan of a bridge, rates of chemical reactions play important roles in our understanding of processes that involve chemical changes. Two questions are typically posed when planning to carry out a chemical reaction. The first is: “Will the reaction produce the desired products in useful quantities?” The second question is: “How rapidly will the reaction occur?” A third question is often asked when investigating reactions in greater detail: “What specific molecular-level processes take place as the reaction occurs?” Knowing the answer to this question is of practical importance when the yield or rate of a reaction needs to be controlled.

The study of chemical kinetics concerns the second and third questions—that is, the rate at which a reaction yields products and the molecular-scale means by which a reaction occurs. This chapter examines the factors that influence the rates of chemical reactions, the mechanisms by which reactions proceed, and the quantitative techniques used to describe the rates at which reactions occur.

Reaction Rates

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:

$${\text{2H}}_2{\text{O}}_2(aq)⟶{\text{2H}}_2\text{O}(l)+{\text{O}}_2(g)$$

Figure \(\PageIndex{2}\) provides an example of data collected during the decomposition of H₂O₂. 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. The reaction rate between any two measurements is determined by finding the change in concentration, Δ[H₂O₂], and the change in time, Δt. Reaction rates are, by convention, positive quantities, and so this negative change in concentration is multiplied by −1. 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:

$$\frac{-\text{Δ}[{\text{H}}_2{\text{O}}_2]}{\text{Δ}t}=\frac{-(\text{0.500 mol/L}-\text{1.000 mol/L})}{(\text{6.00 h}-\text{0.00 h})}=0.0833\mathrm{mol}{\text{L}}^{}{\mathrm{-1}}^{}{\text{h}}^{\mathrm{-1}}$$

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:

$$\frac{-\text{Δ}[{\text{H}}_2{\text{O}}_2]}{\text{Δ}t}=\frac{-(0.0625\text{mol/L}-0.125\text{mol/L})}{(24.00\text{h}-18.00\text{h})}=0.010\text{mol}{\text{L}}^{\mathrm{-1}}{\text{h}}^{\mathrm{-1}}$$

Figure \(\PageIndex{2}\) The rate of decomposition of H₂O₂ in an aqueous solution decreases as the concentration of H₂O₂ decreases.

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.

Instantaneous Reaction Rate

The change in concentration with time shown in Figure \(\PageIndex{2}\) can also be made into a graph, as shown in Figure \(\PageIndex{3}\). The slope of the curve in this graph is another way to find the rate of a reaction. At any specific time, the slope of this line is the rate of the reaction.

Figure \(\PageIndex{3}\) 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 \(\PageIndex{4}\) ). 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:

\( \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{O}_2 \stackrel{\text {catalyst}}{\longrightarrow} \mathrm{C}_6 \mathrm{H}_{10} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O}_2 \)

\( \mathrm{2 H}_2 \mathrm{O}_{2} +\mathrm{2I}^- \stackrel{\text {catalyst}}{\longrightarrow} \mathrm{I}_2 + \mathrm{2H}_{2} \mathrm{O}+\mathrm{O}_2 \)

$${\mathrm{}}_{}$$

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.

Figure \(\PageIndex{4}\) 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)

Factors Affecting Reaction Rates

The rates at which reactants are consumed and products are formed during chemical reactions vary greatly. Five factors typically affecting the rates of chemical reactions will be explored in this section: the chemical nature of the reacting substances, the state of subdivision (one large lump versus many small particles) of the reactants, the temperature of the reactants, the concentration of the reactants, and the presence of a catalyst.

The Chemical Nature of the Reacting Substances

The rate of a reaction depends on the nature of the participating substances. Reactions that appear similar may have different rates under the same conditions, depending on the identity of the reactants. For example, when small pieces of the metals iron and sodium are exposed to air, the sodium reacts completely with air overnight, whereas the iron is barely affected. The active metals calcium and sodium both react with water to form hydrogen gas and a base. Yet calcium reacts at a moderate rate, whereas sodium reacts so rapidly that the reaction is almost explosive.

The Physical States of the Reactants

A chemical reaction between two or more substances requires intimate contact between the reactants. When reactants are in different physical states, or phases (solid, liquid, gaseous, dissolved), the reaction takes place only at the interface between the phases. Consider the heterogeneous reaction between a solid phase and either a liquid or gaseous phase. Compared with the reaction rate for large solid particles, the rate for smaller particles will be greater because the surface area in contact with the other reactant phase is greater. For example, large pieces of iron react more slowly with acids than they do with finely divided iron powder (Figure \(\PageIndex{5}\)). Large pieces of wood smolder, smaller pieces burn rapidly, and saw dust burns explosively.

Figure \(\PageIndex{5}\) (a) Iron powder reacts rapidly with dilute hydrochloric acid and produces bubbles of hydrogen gas: 2Fe(s) + 6HCl(aq) $⟶$ 2FeCl₃(aq) + 3H₂(g). (b) An iron nail reacts more slowly because the surface area exposed to the acid is much less.

Link to Learning

Watch this video to see the reaction of cesium with water in slow motion and a discussion of how the state of reactants and particle size affect reaction rates.

Temperature of the Reactants

Chemical reactions typically occur faster at higher temperatures. Food can spoil quickly when left on the kitchen counter. However, the lower temperature inside of a refrigerator slows that process so that the same food remains fresh for days. Gas burners, hot plates, and ovens are often used in the laboratory to increase the speed of reactions that proceed slowly at ordinary temperatures. For many chemical processes, reaction rates are approximately doubled when the temperature is raised by 10 °C.

Concentrations of the Reactants

The rates of many reactions depend on the concentrations of the reactants. Rates usually increase when the concentration of one or more of the reactants increases. For example, calcium carbonate (CaCO₃) deteriorates as a result of its reaction with the pollutant sulfur dioxide. The rate of this reaction depends on the amount of sulfur dioxide in the air (Figure \(\PageIndex{6}\)). An acidic oxide, sulfur dioxide combines with water vapor in the air to produce sulfurous acid in the following reaction:

$${\text{SO}}_{\text{2}}(g)+{\text{H}}_2\text{O}\text{(}g)⟶{\text{H}}_2{\text{SO}}_{\text{3}}(aq)$$

Calcium carbonate reacts with sulfurous acid as follows:

$${\text{CaCO}}_{\text{3}}(s)+{\text{H}}_2{\text{SO}}_{\text{3}}(aq)⟶{\text{CaSO}}_{\text{3}}(aq)+{\text{CO}}_{\text{2}}(g)+{\text{H}}_2\text{O}\text{(}l)$$

In a polluted atmosphere where the concentration of sulfur dioxide is high, calcium carbonate deteriorates more rapidly than in less polluted air. Similarly, phosphorus burns much more rapidly in an atmosphere of pure oxygen than in air, which is only about 20% oxygen.

Figure \(\PageIndex{6}\) Statues made from carbonate compounds such as limestone and marble typically weather slowly over time due to the actions of water, and thermal expansion and contraction. However, pollutants like sulfur dioxide can accelerate weathering. As the concentration of air pollutants increases, deterioration of limestone occurs more rapidly. (credit: James P Fisher III)

Link to Learning

Phosphorus burns rapidly in air, but it will burn even more rapidly if the concentration of oxygen is higher. Watch this video to see an example.

The Presence of a Catalyst

Relatively dilute aqueous solutions of hydrogen peroxide, H₂O₂, are commonly used as topical antiseptics. Hydrogen peroxide decomposes to yield water and oxygen gas according to the equation:

$$2{\text{H}}_2{\text{O}}_2(\text{aq})⟶2{\text{H}}_2\text{O}(l)+{\text{O}}_2(\text{g})$$

Under typical conditions, this decomposition occurs very slowly. When dilute H₂O₂(aq) is poured onto an open wound, however, the reaction occurs rapidly and the solution foams because of the vigorous production of oxygen gas. This dramatic difference is caused by the presence of substances within the wound’s exposed tissues that accelerate the decomposition process. Substances that function to increase the rate of a reaction are called catalysts, a topic treated in greater detail later in this chapter.

Link to Learning

Chemical reactions occur when molecules collide with each other and undergo a chemical transformation. Before physically performing a reaction in a laboratory, scientists can use molecular modeling simulations to predict how the parameters discussed earlier will influence the rate of a reaction. Use the PhET Reactions & Rates interactive to explore how temperature, concentration, and the nature of the reactants affect reaction rates.