D18.1 Reaction Rate

The rate of a chemical reaction is usually defined as the change in concentration of a reactant or a product per unit time. Rates can be determined by measuring the concentration of a reactant or product at each of a series of times after the reaction is started.

Often, it is easier to measure some property related to a substance’s concentration instead. For example, for a reaction involving a colored reactant, light absorption can be measured at different times after the start of the reaction. Then the reactant’s concentration at a given time can be calculated from the proportionality between light absorption and concentration.

Consider the decomposition reaction of cyclobutane to ethene in the gas phase:

The rate at which cylcobutane decomposes can be expressed in terms of the rate of change of its concentration:

In this equation, square brackets represent concentration in mol/L (M), so Δ[C₄H₈] represents the change in concentration of cyclobutane during the time interval Δt (that is, t₂ − t₁). The minus sign in front of the fraction is there because reaction rate is defined to be positive. The reactant concentration decreases as the reaction proceeds, making Δ[C₄H₈] a negative quantity, so a negative sign is needed to make the calculated rate positive.

Table 1 provides an example of data collected during the decomposition of C₄H₈.

Notice that the reaction rate varies with time, decreasing as the reaction proceeds and [C₄H₈] decreases. An average rate over a given time period can be calculated using the concentrations at the beginning and end of the period. For example, the average rate for the first and last 20-second period are:

The rate of reaction at any specific time is known as the instantaneous rate. The instantaneous rate when the reaction starts (at t₀), is the initial rate. The instantaneous rate of a reaction may be determined one of two ways:

• If concentration changes can be measured over very short time intervals, then average rates over these very short time intervals provide reasonably good approximations of instantaneous rates.
• If we plot concentration vs. time, the instantaneous rate at any time t is given by the negative of the slope of a straight line that is tangent to the curve at that time (Figure 1).

D18.2 Relative Rates of Reaction

The reaction rate can be expressed in terms of the change in concentration of any reactant or product, and therefore depends on the stoichiometry of the reaction. Let’s use the ammonia decomposition reaction as an example:

From the balanced reaction, we can see that one N₂ molecule is produced for every two NH₃ molecules that have reacted. Therefore, the formation of N₂ is half as fast as disappearance of ammonia:

The negative sign accounts for the fact that NH₃ (reactant) concentration is decreasing while N₂ (product) concentration is increasing. The fraction ½ accounts for the stoichiometry.

Similarly, because 3 mol H₂ forms during the time required for formation of 1 mol N₂:

Figure 2 plots concentrations vs. time for this reaction. At any time, the instantaneous rates for reactants and products are related by the reaction stoichiometry. For example, at 500 s the rate of H₂ production is three times greater than that for N₂ production.

The rate of a reaction is therefore defined by taking the change in concentration per unit time of a reactant or product and multiplying by the reciprocal of the stoichiometric coefficient for that reactant or product. The reaction rate determined this way is the same regardless of which reactant or product is measured during an experiment. For a generic reaction:

where lower-case letters are stoichiometric coefficients and upper-case letters represent chemical formulas, the rate of the reaction is:

D18.3 Factors Affecting Reaction Rates

During a chemical reaction, reactant molecules are changed into product molecules. This involves changes in bonding (i.e. bonds broken and bonds formed), and typically this requires molecules to come into close contact; that is, atomic-scale particles must collide to react. Anything that affects the number and/or effectiveness of those collisions will affect the rate of reaction.

Chemical Nature of the Reacting Substances

Some substances react faster than others. For example, potassium and calcium, which are next to each other in the fourth row of the periodic table, both react with water to form H₂ gas and a basic solution. Yet calcium reacts at a moderate rate, whereas potassium reacts so rapidly that the reaction is almost explosive. One factor affecting these different rates is that the reactions involve loss of electrons from potassium or calcium atoms, and potassium has a smaller first ionization energy, making loss of an electron easier.

Temperature

Chemical reactions typically occur faster at higher temperatures. At higher temperatures atomic-scale particles move faster, so they collide harder and more often, both of which increase the probability that they will react. For example, methane (CH₄) does not react rapidly with air at room temperature, but strike a match and POP!

Concentrations

Reaction rates usually increase when the concentration of one or more of the reactants increases. In some cases, rates depend on the concentrations of products as well. For example, calcium carbonate (CaCO₃) deteriorates as a result of its reaction with the pollutant sulfur dioxide (SO₂). Specifically, sulfur dioxide reacts with water vapor to produce sulfurous acid:

Sulfurous acid then reacts with calcium carbonate:

The rate of the overall reaction depends on the concentration of sulfur dioxide in the air. In a more polluted atmosphere where the concentration of sulfur dioxide is higher, calcium carbonate deteriorates more rapidly (Figure 3).

In another example, a cigarette burns slowly in air, which contains about 21% oxygen by volume, but burns much more rapidly in pure oxygen, as shown in the video below.

Presence and Concentration of a Catalyst

A catalyst is a substance that increases the rate of a chemical reaction by providing an alternative reaction pathway but is not consumed by the reaction. The greater the concentration of a catalyst the more the catalyst can speed up a reaction. How catalysts work will be discussed in detail later on in this course. Watch the video below to see how a catalyst can speed up the decomposition of hydrogen peroxide to oxygen and water.

Surface Area

The factors discussed so far apply to homogeneous reactions, reactions that occur in a single phase (solid, liquid, or gas). If a reaction occurs at a surface, an increase in surface area of the intersection of two phases (such as the surface of a solid in contact with a gas) can increase the rate. Reactions that take place at a surface are called heterogeneous reactions. A finely divided solid (like a powder) has more surface area available for reaction than one large solid piece of the same substance. For example, large pieces of wood smolder, smaller pieces burn rapidly, and sawdust burns explosively. The video below shows how large pieces of iron can be held in a burner flame for a long time and hardly react, whereas iron powder blown into the flame sparkles as the tiny particles burn.

D18.4 Effect of Concentration: Rate Laws

Rate laws or rate equations are mathematical expressions that relate the rate of a chemical reaction to the concentrations of reactants (and sometimes products or catalysts). Often the rate of reaction is proportional to the concentration, or to a power of the concentration, of a substance involved in the reaction:

Here, k is the rate constant, a proportionality constant independent of reactant concentrations that is specific for a particular reaction at a particular temperature.

Each exponent, m, n, or p, defines the order of a reaction with respect to each reactant, A, B, or C. It is the power to which a concentration must be raised to correctly calculate the rate. For example, if m = 1, the reaction is first-order with respect to A; if n = 2, the reaction is second-order with respect to B; if p = 0, the reaction is zeroth-order with respect to C, which means that the rate of the reaction is not affected by the concentration of C, because [C]⁰ = 1. The overall reaction order is the sum of the individual orders, m + n + p + … Reaction orders are usually positive integers, although they can be fractions or negative numbers.

D18.5 Method of Initial Rates

The rate constant and the reaction orders must be determined experimentally by observing how the rate of a reaction changes as the concentrations of the reactants are changed. One way to do this is the method of initial rates. To use this method, select two sets of rate data where all concentrations but one are the same and set up a ratio of the two rates and the two rate laws. This will yield an equation that contains only one unknown: the reaction order of the substance whose concentration varies.

D18.6 Reaction Order and Rate Constant Units

It is often true that, as in the last activity, the reaction orders in the rate law are different from the coefficients in the chemical equation for the reaction. It is important to note that rate laws must be determined by experiment and are not reliably predicted by reaction stoichiometry.

Reaction orders play a role in determining the units for the rate constant—the units for k are whatever is needed so that substituting into the rate law expression affords the appropriate units for the rate.

The units for the rate constant for common reaction orders are summarized below.