Concentration Dependence

The measure of how fast a reaction proceeds is called the reaction rate. For a single-step reaction, the rate is equal to the change in concentration of each reactant or product over time multiplied by the inverse of the corresponding stoichiometric coefficient. You can think of the change in concentration over time as the concentration at time t minus the starting concentration divided by t. Reaction rates are always positive, so the reactant expressions have negative signs. These rates may not be equal in multi-step reactions, but we can still use this relationship as an estimate for the overall reaction.

The rate law, or rate equation, describes the relationship between the speed of the reaction and the reactant concentrations. In this equation, k is the rate constant, A and B are the two reactants, and m and n are their respective reaction orders. Reaction order describes the relationship between the concentration of a reactant and the rate and is not related to stoichiometry. It is vital to remember that the reaction order is not the same as the coefficient of the reactant in the balanced equation.

When a reaction involves two or more reactants, we must consider the reaction order for each reactant. The overall reaction order is equal to the sum of the reactants' reaction orders. For example, if reactant A is first-order and reactant B is zero-order, the overall reaction order is one. The most common reaction orders in simple reactions are zero-order, first-order, and second-order. Let's go through them using a unimolecular reaction as an example.

If the reaction is zero order, the reactant concentration has no effect on the reaction rate. Thus, the reaction rate is equal to k, the rate constant. A graph of the reaction rate with respect to concentration is a horizontal line.

In first order relationships, the reactant concentration is linearly related to the reaction rate. Thus, the rate is equal to the rate constant times the reactant concentration. A graph of the reaction rate with respect to concentration will be linear, with k as the slope.

If the reaction is second order, there is a quadratic relationship between the concentration and the rate. Thus, the rate is equal to the rate constant times the concentration squared. A graph of the rate with respect to concentration will be parabolic, with k as the slope.

The rate constant, k, is a temperature-dependent value that relates the activation energy of the reaction to the reaction rate. You will explore this in the next lab experiment.

Reaction rates are typically given in moles per liter per second. The rate has the same units, regardless of the reaction order. Thus, the rate constant has different units, depending on the reaction order. For example, if A is first order and B is zero order, then we have one instance of moles per liter in the rate equation. Therefore, the rate constant must be in inverse seconds.

So how do we determine reaction order? The reaction order must be determined experimentally using a series of tests. If you have two reactants, one method is to hold the concentration of one reactant constant, vary the other, and time how long it takes to make a certain amount of product. The same process is repeated for the second reactant. You can then estimate the order for each reactant by plotting rate versus the reactants' varying concentration, and seeing whether it looks like a zero, first, or second-order graph. Matching your data to the corresponding rate equation will also let you calculate k.

In this lab, you will determine the reaction orders of two reactants by varying their concentrations and timing how long it takes the reaction to progress to turning the solution opaque.