Rates of Reaction

In chemistry, chemical reactions can take place at different rates. For example, sodium reacts quickly with water to make sodium hydroxide and hydrogen gas (which then ignites and burns, hehe). Iron, on the other hand, oxidizes slowly, and therefore rusts bit by bit over time.

In General Chemistry, you are taught that there are several factors that affect rates of chemical reactions. Temperature, one of the more obvious, can be increased or decreased to make reactions run faster or slower. (Raising temperature increases reaction rate because the molecules will have more energy and will bump into each other more often, which is important for a reaction to take place.) The molecules’ orientation is important for some reactions, since certain parts of certain molecules may only be able to interact with certain parts of other molecules. The properties of the molecules themselves, obviously, play certain roles. Adding a catalyst to a reaction, by definition of catalysis, will speed it up. This whole business of studying the speeds of reactions and the way reactants change into products is called chemical kinetics.

An important factor not mentioned above that determines the rate of a reaction is the concentrations of reactants in aqueous solution. (An aqueous solution is just a solution where something is dissolved in water.) In a solution of higher concentration, there will be more reactant present than in a solution of lower concentration. (A 0.1 M [molar: a standard measure of concentration in moles per liter] solution of NaOH, for example, will only contain 1/10 of a mole of NaOH for every liter of solution, whereas a 1 M solution of NaOH will contain 1 mole per liter, etc.)

An easy way to work with concentrations and rates is to try to determine the rate at which a certain reactant changes over the course of a reaction. Since rate is defined as the change in something over a change in time (driving a rate of 60 mph is driving a distance of sixty miles over an hour), the rate of change of the concentration of reactant B can be thought of like this:

rate = Δ[B]/Δt, where Δ (delta) is read as “change in,” [B] is the concentration of B, and t is time.

Let’s say that the initial concentration of B is 0.1 M, and the final concentration ends up being 0.05 M. Our time, t, is 10 seconds. This equation tells us that the rate of change of the concentration of reactant B is [0.05M-0.1M]/[10-0], or -0.005M/s. By convention (and because chemists like to put little stumbling blocks in the paths of freshman chemistry students), the rate is positive, so the rate of change of reactant B is 0.005 M/s, or 5.0E-3 M/s.

Nifty, huh? That makes logical sense. It gets a little more complicated from there, though, so hang on tight.

Let’s say we have a reaction that runs according to this equation:

2A + B → C

The numbers in front of the reactants and products are referred to as stoichiometric coefficients, and they tell us two things. One, that two molecules of A and one of B react to form one of C, and two, that two moles of A and one mole of B react to form one mole of C.

Say we wanted to know the rate of the reaction. That doesn’t sound too difficult, but remember that two moles of A react with one mole of B to make a mole of products. Just calculating the rate of change of [A] would give us a number that was double the actual rate of the reaction, since A changes at twice the rate of B and C. The reaction rate for this reaction, then, if we were to calculate it from the change in [A], would be half of the rate of change of the concentration of A. The same holds true for other reactions—as a basic rule, the average rate of a reaction is equal to the rate of change of a reactant or product divided by its stoichiometric coefficient.

The rate found by calculating the change in concentration over the change in time of a certain reactant or product is referred to as the average rate of reaction for that particular time interval. However, just as you can speed up or slow down while you’re driving down the interstate (i.e., accelerate or decelerate), so chemical reactions can speed up or slow down as reactants are consumed and concentrations decrease. If you want to know the rate at a specific concentration, you must find the instantaneous reaction rate.

Perhaps this conjures up memories of calculus and physics—the concepts are, indeed, similar. The instantaneous rate of a reaction is the slope of the tangent line to the concentration-time curve at the point corresponding to the concentration and time of interest. This, my friends, involves calculus. Luckily, there is an easier way to do this.

Each reaction at each temperature has a specific rate constant attached to it; the rate constant is simply a value independent of concentration but dependent on temperature and reaction that makes it possible to relate concentrations of reactants with the rate of the reaction. It must be experimentally determined, which means by the time these problems get to us, the hard part is already done. The rate constant is typically denoted k.

To find the instantaneous reaction rate for any concentration of any reactant, a simple equation, called the rate law, may be used. For example, for the reaction A + B + C → D:

rate = k[A]a[B]b[C]c, where the concentrations of A and B are raised to an undetermined power.

Rates can be said to be a certain order with respect to a concentration of a certain reactant. If the concentration of the reactant does not affect the rate, the rate is said to be zeroth order with respect to that reactant, and the concentration is left out of the rate law. If it affects it linearly (by doubling the concentration you double the rate), the rate in respect to the concentration is said to be first order, and the concentration is raised to the first power. If the rate changes as the square of the concentration, it is said to be second order, and the concentration is raised to the second power. 

For the above example, let’s assume that the rate of reaction is in zeroth order in respect to A, first in respect to B and second in respect to C. The final rate law would be as follows:

rate = k[B][C]2

Knowing this piece of information, we can learn many things about this reaction. If given a data table with a rate and the concentrations of B and C, we can find k. Given k and the concentrations of each reactant, we can determine the rate. Using the rate, k, and either concentration, we can find the other. Altogether, a useful little equation.

Another useful set of equations is the set of integrated rate law equations, but that’s a lesson for another day.

Any questions? Feel free to drop them in the comments box. I’m a freshman chemistry student, so I’ll do the best I can.

Complaints? Corrections? Feel free to add those too. Just be gentle.


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