## Chemical Kinetics

Chemical Kinetics

The article in the March 2010 TCS http://sas.org/tcs/weeklyIssues_2010/2010-03-05/feature2/index.html on chemical kinetics inspired me to learn more about the subject. Chemical kinetics is not something that I had encountered in my meager chemistry education.

Background

Basically chemical kinetics is the study of the rate at which chemical reactions occur
and what factors affect that rate. Temperature and for reactions in solutions the concentration of the chemicals involved are big factors. To keep things simple this experiment is investigating the concentration effects at a fixed temperature. Chemical reactions can occur over a wide range of rates from almost instantaneous to many
months or years. Reaction between oxalic acid and potassium permanganate is convenient to use as an educational experiment because it occurs slowly enough to easily observe but not too slow that it would take months to complete the experiment. A dramatic example of a very fast reaction would be burning hydrogen. Concrete setting, which can take years to complete, would be an example of a slow reaction. Knowledge of chemical kinetics has a lot of practical applications. For example designing epoxies with specific setting times.

The Math

For many chemical reactions a general equation has been developed that can be used to describe the rate at which the reaction occurs based on the concentration of the reactants. Other equations take into account other factors like temperature. For this experiment only the concentration will be studied. The equation is: r = kAmBn In this equation r is the rate of change of the concentration of the reactant. The constant k is used to make the numbers come out right. The concentrations of the two reactants are A and B. The exponents m
and n describe the shape of the curve or how sensitive the rate is to the concentration. In the case of the exponent being zero the concentration of the reactant has no effect on the rate of the reaction. This is called a zero-order rate. This happens because A0 = 1. The concentration is no longer in the equation. If the exponent is 1 the reaction rate is called a first-order. In this case there is linear relation between the concentration and the reaction rate. For example if you double the concentration of a reactant the rate will also double. A third case is where the exponent is 2. This is called a second order rate equation. Here the rate of the reaction is more sensitive to the concentration than in the first order. The rate will vary with the square of the concentration. The equation is general and would allow for any exponent but only zero, first and second order are likely to occur. When the reaction occurs the reactants are consumed and over time the rate of the reaction changes for first and second order reactions.

Integrated rate equation

We have an equation that shows the relationship between rate and concentration but what
we really need for the experiment is an equation that shows the relationship between concentration and time. Rate is the change in concentration per time, often expressed in units of moles per liter second. This is similar to speed expressed in miles per hour, for
example. If we were traveling at a constant speed, the distance traveled can be computed by multiplying the speed by the time spent traveling at that speed. Things get a bit more complicated if the speed is not constant. This is where calculus comes in handy. To further simplify things we will assume one of the concentrations in the rate equation is constant. Then by applying some calculus and integrating the rate equation with respect to time we come up with equations describing the concentration vs. time for the three orders of interest.

The concentration of the reactant is A. A0 is the initial concentration at time = 0. k is the same constant as in the rate equation. T is time and e is the number e.

In the graph below I have made plots of what the concentration verses time would look like
for zero, first and second order reactions with some arbitrary numbers for A0 and k. The green trace is the zero order plot and as you can see it is a straight line. The blue trace is the first order plot. The red trace is the second order plot. As the order gets higher the traces become steeper. The zero order plot shows the reaction continuing beyond zero concentration. This actually cannot happen in real life as there is no more reactant to
consume at this point. The first and second order plots never actually reach zero concentration. But in reality when the graph says the concentration is less than one molecule in the solution there is really zero concentration because you cannot have less than one molecule of a substance. Design of the Experiment

The goal of the experiment I want to perform is to determine the order of the rate
equation with respect to potassium permanganate and the value of k
for the reaction of acidified potassium permanganate and oxalic acid.

• To keep the temperature from affecting the results, the solutions will be
allowed to settle to room temperature before proceeding with the
experiment.

• To eliminate the effect of the concentration of oxalic acid on the rate, the oxalic
acid concentration will be made large with respect to the potassium
permanganate concentrations.

• To get an idea of the color change expected, perform a pre-experiment just to observe the color change.

• To ensure enough data to plot, take at least four data points.

• To keep possible contaminants from affecting the experiment, use distilled water to make up the solutions.

In a future post I will describe the results of my experiment.

1. s khanum says: