# Chemical Kinetics: Rate of Reaction

## Concentration Changes

Chemical kinetics is the study of how fast a chemical reaction occurs and the factors that affect how fast the reaction occurs. This information is especially useful for determining how a reaction occurs.

The term reaction rate refers to how fast the chemical reaction occurs. The rate of reaction, r, describes how fast the concentrations of reactants and products change.

Consider the following hypothetical example. The letters A, B and C represent chemical species (in this context, the letters do not represent elements). In a sense, one can think of the symbols A, B and C as chemical variables, analogous to mathematical variables.

A + 2 B   →   3 C

The simulation below illustrates how this reaction can be studied. The apparatus at the left is called a stopped-flow apparatus. The left syringe is filled with a solution containing A and the right syringe is filled with a solution containing B. When the two solutions are forced out of the syringes, they quickly mix in the square mixing block and the reaction starts. The reacting solution passes through the tube at the bottom. After some of the reactant solutions have mixed, the flow is stopped and an analytical technique such as spectrophotometry is used to measure the concentrations of the species in the reaction mixture and how those concentrations change with time.

In this example, the solution of species A has a wine red color. The syringe of species B has a gold color. The product C has a blue color.

The graph at the right shows how the concentration of each species changes as time progresses. Run the simulation and observe the stopped-flow experiment and the shape of the concentration-time plots.

Notice that the color of the reaction mixture changes as the reaction progresses. The reactants are wine red and gold, which when mixed produce an orange color. As the reactants are consumed, the product, which is blue, is produced.

This behavior is reflected in the concentration-time plots. The concentration of A, shown by the wine red line, decreases as time goes by, because the reaction consumes A. The same behavior is observed for B (gold line). Initially the product C is not present (blue line). The reaction produces C, however, so the concentration of C increases as time goes by.

In this simulation, A and B were initially present in stoichiometric amounts. That is, because each mole of A reacts with two moles of B, there was initially twice as much B as A. So when the reaction is complete, neither A nor B remain.

Question: The syringe on the left contains a 0.10 M solution of A. The syringe on the right contains a 0.20 M solution of B. So why is the initial concentration of A equal to 0.050 M and the initial concentration of B equal to 0.10 M, as reported on the graph? The term initial concentration means the concentration at time t = 0.

## Reaction Rate

The rate of change in the concentrations of the reactants and products can be used to characterize the rate of a chemical reaction. The rate of change in the concentration corresponds with the slope of the concentration-time plot. Thus the rate of change in the concentration is used to determine the rate of the reaction. From calculus, the slope is provided by the derivative dC/dt , where C is the molar concentration of a reactant or product and t is time.

The simulation below is the same as that presented above except that the slope of the concentration-time curves are also plotted on the graph. Select the species (A, B, or C) whose slope is shown and use the controls to step through the points on the graph.

In examining the simulation, answer the following questions:

• How does the slope change with time for a given species?
• Is the slope the same for all species?
• What is the sign of the slope for the reactants?
• What is the sign of the slope for the product?

Species:

sec

mole L-1

mole L-1 sec-1

It is usually more convenient to work with positive numbers, so the rate of reaction, r, is defined to be a positive quantity. Also, the rate of change in concentration depends upon the stoichiometric coeffients, as is evident from the graph above. Therefore, the derivative dC/dt is divided by the stoichiometric coefficient of the species. For this reaction, the rate of reaction is defined below. In this mathematical equation, [A] represents the molar concentration of species A. Similarly for [B] and [C].

A + 2 B   →   3 C

r   =   –
d [A] d t
=   –
1 2
d [B] d t
=
1 3
d [C] d t

ReactionRates.html version 3.0
© 2000, 2014, 2023 David N. Blauch