Chemical Kinetics

Introduction:

At this point in your chemistry career, you should be able to predict the products of reactions, the type of reactions, the states of the products, and whether the reaction will occur spontaneously at any given set of conditions. While all of this information is extremely useful, one very important factor is missing: how fast will the reaction occur. Even if a reaction is thermodynamically spontaneous it may occur at a very wide spectrum of rates from glacial to instantaneous.

The branch of chemistry that is concerned with the rates of chemical reactions is known as Chemical Kinetics. Using the Kinetic Molecular Model, you can visualize a chemical reaction as requiring the reactants to come into direct contact via a collision. If the reactants collide with sufficient energy and the proper geometry, then a series of bonds are broken in the reactants and reformed to produce the products. If the collision does not have sufficient energy or the proper geometry is not achieved, then the reactants simply bounce off each other and no reaction occurs. The more successful these reactant collisions are in generating products, the faster the reaction. Studies have shown that several factors influence the rate of successful collisions, and hence the speed of a chemical reaction: the nature of the reactants, the concentration of the reactants, the temperature of the reactants, and the presence of a catalyst. Using this model, we can qualitatively explain how these various factors effect the speed of the reaction:

Concentration: Changing the concentration of a solution alters the number of particles per unit volume. The more particles present in a given volume, the greater the probability of their colliding. Therefore, increasing the concentration of a solution increases the number of collisions per unit time and therefore the rate of the reaction.

Temperature: Since temperature is a measure of the average kinetic energy, an increase in the temperature increases the kinetic energy of the particles. An increase in the kinetic energy increases the velocity of the particles and therefore the number of collisions between them in a given period of time. Thus, the rate of reaction increases. Also, an increase in kinetic energy results in a greater proportion of the collisions having the required activation energy required for the reaction. As a rule of thumb, the reaction rate doubles for each 10° increase in temperature.

Catalyst: Catalysts can increase the rate of reaction through several mechanisms. They may help to bring the reactants together in the proper orientation so that each collision is more successful. They may also provide an alternate route that requires less energetic collisions between the reactant particles. If the activation energy is lowered, then, a larger percentage of the collisions will be successful and the reaction will occur faster.

So, what do we really mean when we use the expression 'rate of reaction'? Let's consider the following general reaction in which 'a' moles of A reacts with 'b' moles of B to produce 'c' moles of C and 'd' moles of D:

a A + b B c C + d D

The rate of this reaction may be determined by observing the rate at which the reactants A and B disappear, or by observing the rate at which the products C and D are formed. In practice, you can determine the rate of the reaction by observing A, B, C, or D. The choice is simply a matter of convenience. Mathematically, the rate of reaction is expressed as the change in concentration with time:

Rate of disappearance of A =	(change in concentration of A) / ('a')(time for change in A) =	- d[A] / 'a'dt
Rate of disappearance of B =	(change in concentration of B) / ('b')(time for change in B) =	- d[B] / 'b'dt
Rate of appearance of C =	(change in concentration of C) / ('c')(time for change in C) =	+ d[C] / 'c'dt
Rate of appearance of D =	(change in concentration of D) / ('d')(time for change in D) =	+ d[D] / 'd'dt

In general, the rate of the reaction, at least initially, will depend solely on the concentration of the reactants. Therefore, the rate of our reaction can be expressed as:

rate = k • [A]^x • [B]^y

where [A] and [B] are the molar concentrations of the reactants. The exponents, x and y, represent the order of the reaction with respect to the reactants A and B. It is important to remember that these exponents are not related at all to the stoichiometry of the reaction and must be determined experimentally. The k term, is called the specific rate constant for the reaction at a particular temperature. One of the objectives of chemical kinetics is to determine the rate law by determining the values of x, y, and k. For example, if we determined that x = 2, and y = 3 for a given reaction, then the rate law would be:

rate = k • [A]² • [B]³

From this we can see that if the [A] were doubled, then the rate of the reaction would increase by a factor of four. Likewise, if the [B] were doubled, then the rate of the reaction would increase by a factor of eight. In this case, we say this reaction is second order with respect to [A] and third order with respect to [B]. The overall order of the reaction is the sum of these exponents and so in this case would be 5, or a fifth order reaction.

We mentioned above that the rate constant for a reaction varies with temperature. For most reactions, the rate constant increases as the temperature increases. The relationship between the temperature of a reaction and the rate of a reaction can be expressed as:

Here, k is the rate constant for a reaction, A is a constant representing the frequency of collisions between the reactants, E_a is the activation energy for the reaction, R is the ideal gas constant (8.314 J/molK), and T is the absolute temperature of the reaction. A more useful form of this equation can be obtained by taking the natural logarithms of both sides:

Now the Arrhenius equation takes on the form of a straight line where m is the slope of the line, and b is the intercept of the y-axis. We need to run this reaction at several temperatures and determine the corresponding k values. Then we can plot this data as (ln k) on the y-axis and (1/T) on the x-axis. This will generate a straight line graph were the slope is equal to (–E_a /R) and the y-intercept is (ln A).

So by running a small set of reactions, we can determine the rate law, the activation energy, and the collision frequency for this reaction.

Purpose:

The purpose of this experiment is to familiarize you with the concept of chemical kinetics. In this experiment the effects of reactant concentration, temperature, and form on the rate of a reaction will be studied. The reaction we will be studying is the reaction of magnesium with the non oxidizing acid, HCl (a displacement reaction):

Mg_(s) + 2 HCl_(aq)

Mg²⁺_(aq) + 2 Cl^-_(aq) + H_2(g)

The rate of this reaction can be determined by visually observing the disappearance of the Mg(s) or the disappearance of the HCl through the use of a pH probe. It can equally be determined by observing the appearance of Mg²⁺, Cl^-, or H₂ (by measuring the volume or pressure of gas generated). Mathematically, the rate of appearance or disappearance of these five species are equivalent:

Note that the coefficients of each of these rates comes from the balanced chemical reaction. These rates can then be used to determine the rate law:

rate = k • [Mg]^x • [HCl]^y

This equation represents the slowest, or rate determining, step in this displacement reaction. Remember that the exponents 'x' and 'y' have nothing at all to do with the stoichiometry of the overall reaction and therefore must be determined experimentally.

You will first run a series of experiments with different concentrations of magnesium and hydrochloric acid. Using the method of initial concentrations, you will be able to determine x and y. This information will then allow you to calculate the value of k.

You will then run a series of experiments at varies temperatures while holding the concentration of magnesium and hydrochloric acid constant. A plot of ln[1/t] on the x-axis versus ln(k) on the y-axis, will generate a straight line plot were the slope is the collision frequency and the y-intercept is related to the activation energy.

Finally, you will run a series of experiments with magnesium ribbon versus magnesium powder to observe the effect of surface area on the reaction rate.

Method:

OK, you have just completed the lab and collected a table full of mass, concentration, slope, and temperature data. What do you do with all this data? Lets work through an example. Assume that you are using 20.00 mL of HCl for each experiment. Remember, this is only an example, YOUR NUMBERS MAY VARY!!

The first thing we need to remember is that we are using an average rate (slope) for the appearance of H₂ instead of the initial rate that we used in class.

Experiment #	Temperature (°C )	[HCl]	Wt. of Mg, (g)	Reaction Rate: +d[H₂]/dt (slope)	State
1	21.8	1.0	0.017	9.04x10^-4	Ribbon
2	21.8	0.8	0.017	5.76x10^-4	Ribbon
3	21.8	0.6	0.017	2.81x10^-4	Ribbon
4	21.8	0.2	0.017	3.67x10^-5	Ribbon
5	21.1	0.6	0.032	4.55x10^-4	Ribbon
6	21.1	0.6	0.048	6.52x10^-4	Ribbon
7	38.1	0.6	0.017	5.38x10^-4	Ribbon
8	5.2	0.6	0.016	1.32x10^-4	Ribbon
9	21.1	0.6	0.016	1.65x10^-3	Powder

By comparing the data from Experiment #2 with that from #1, we see that the amount Mg is constant while the [HCl] increases from 0.8 to 1.0 M. The result is that the reaction rate (as measured from the slot of the H₂ of each graph) almost doubles from 5.76x10^-4 to 9.04x10^-4. Therefore, 'x' must be:

d[HCl]^x = d(Reaction rate)

(1.0 / 0.8)^x = ( -9.04x10^-4 / -5.76x10^-4 )

x • ln[1.25] = ln(1.57)

x = 2.02

This shows that the rate determining step is dependent on [HCl]² . Similarly, we can use Experiments #5 and #3 to determine the value for 'y':

d[Mg]^y = d(Reaction rate)

(0.067 / 0.035)^y = (-4.55x10^-4 / -2.81x10^-4)

y • ln(1.91) = ln(1.62)

y = 0.75

Within experimental error, this shows that the rate determining step is dependent on [Mg]¹. Now we know that this reaction is first order with respect to Mg, second order with respect to HCl, and third order overall.

Now we have use this information to calculate 'k'. The concentration of magnesium, [Mg], is calculated using the moles of magnesium dissolved in 20 mL (0.02 l) of solution. Using the data from Experiment #1 (although any experiment at the same temperature would do), we find k to be:

rate = k • [Mg] • [HCl]²

9.04x10^-4 = k • [0.035] • [1.0]²

k = 0.026

Now we can put all of this together to obtain the complete rate law:

rate = 0.026 • [Mg] • [HCl]²

Finally, we can use the Arrhenius equation and the reaction rate data from Experiments #3, #7, and #8 to calculate the collision frequency, A, and the activation energy, E_a for this reaction. To determine these values, you must plot the inverse of each Experiment's absolute temperature (x-axis) against the natural log (ln) of the corresponding k value (y-axis):

By extrapolating the line connecting our three data points (via linear regression), we can calculate the slope and the y-intercept. The R² of 0.986 shows that we generated very good data which gives us a high degree of confidence in the extrapolated values. The y-intercept of 8.308 represents the natural log of the collision frequency, A. By taking the inverse natural log, we obtain a value of 4055 for the collision frequency. The slope of -3555.2 represents -E_a/R. Multiplying by the ideal gas constant, R (8.314 J/mol •K), we obtain a value of -29.6 kJ/mol for the activation energy.

Procedure:

In today's lab, you will be using laptop computers to collect and print out your data (your Technology Access Fee at work). The reaction vessel you will be using consists of a 250 mL brown glass bottle. The cap has been modified so that a standard tire stem (with the guts removed) fits snuggly. A teflon tube is then used to connect the vessel to the PASCO absolute presure gauge so hydrogen is not lost. The pressure gauge is then plugged into the PASCO interface box, which in turn, is plugged into the serial port of the computer. Not to worry, your instructor will show you exactly how to setup the PASCO interface box, pressure probe and software neccessary to collect the data for this experiment.

Preparation of Reagents:

Solutions of approximately 1.0 M, and 2.0 M hydrochloric acid will be prepared for you (be sure to note their exact concentration).
Obtain a piece of magnesium ribbon (~30 cm) and gently sand it to remove any oxide that may have formed. DO NOT sand it on the bench tops!
Cut the cleaned ribbon into 2 cm pieces. Note: Although not absolutely necessary, it will make your calculation easier if each of these magnesium strips weigh the same (0.001 g).

Conducting the HCl concentration experiments:

Accurately weigh (0.001 g) a 2 cm piece of magnesium ribbon. Do not touch it since oils from your fingers will coat the surface and slow the reaction. It may be prudent to wear gloves or use tweezers to ensure that the magnesium is not contaminated.
Using the repippetters, add 20.00 mL of the 1.0 M HCl solution to your reaction vessel.
Use a thermometer to determine the initial temperature of the HCl.
Start acquiring data with the PASCO software.
Add the magnesium strip to the reaction vessel and quickly screw on the top. If the seal is tight, you should notice the pressure rising on the graph. If not, you may have a leak and will have to repeat this run.
Gently swirl the contents of the reaction vessel as you watch the pressure increase.
When the graph flattens out or starts to decrease, the reaction is complete and you can stop acquiring data.
Use a thermometer to determine the final temperature of the solution. If this temperature is different from the initial temperature, average them.
Pour the contents of the reaction vessel down the drain with a large amount of water and repeat Steps 1-8 (duplicate run).
Repeat Steps 1-9 with the 2.0 M HCl solution.

Conducting the Magnesium concentration experiments:

Accurately weight (0.001 g) two, 2 cm pieces of magnesium ribbon. Do not touch it any more than is necessary since oils from your fingers will coat the surface and slow the reaction.
Using the repippetters, add 20.00 mL of the 1.0 M HCl solution to your reaction vessel.
Use a thermometer to determine the starting temperature of the HCl
Start acquiring data with the PASCO software.
Add the magnesium strips to the reaction vessel and quickly screw on the top. If the seal is tight, you should notice the pressure rising on the graph. If not, you may have a leak and will have to repeat this run.
Gently swirl the contents of the reaction vessel as you watch the pressure increase.
When the graph flattens out or starts to decrease, the reaction is complete and you can stop acquiring data.
Use a thermometer to determine the final temperature of the solution. If the temperature is different from the initial temperature, average them.
Pour the contents of the reaction vessel down the drain with a large amount of water and repeat Steps 1-8 (duplicate run).
Repeat Steps 1-9 with three strips of magnesium ribbon.

Conducting the above room temperature experiment:

Heat a beaker of water to 15-20 degrees above room temperature. Make sure it is large enough to fit your reaction vessel.
Using the repippetters, add 20.00 mL of the 1.0 M HCl solution to your reaction vessel and place it in the hot water bath.
Use a thermometer to monitor the temperature of the HCl. When it is 10-15 degrees above room temperature, you are ready to proceed.
Start acquiring data with the PASCO software.
Add a magnesium strip to the reaction vessel and quickly screw on the top. If the seal is tight, you should notice the pressure rising on the graph. If not, you may have a leak and will have to repeat this run.
Gently swirl the contents of the reaction vessel as you watch the pressure increase.
When the graph flattens out or starts to decrease, the reaction is complete and you can stop acquiring data.
Use a thermometer to determine the final temperature of the solution. If the temperature is different from the initial temperature, average them.
Pour the contents of the reaction vessel down the drain with a large amount of water.

Conducting the below room temperature experiment:

Add ice to a beaker of water to until it is 10-15 degrees below room temperature. Make sure it is large enough to fit your reaction vessel.
Using the repippetters, add 20.00 mL of the 1.0 M HCl solution to your reaction vessel and place it in the ice bath.
Use a thermometer to monitor the temperature of the HCl. When it is 10-15 degrees below room temperature, you are ready to proceed.
Start acquiring data with the PASCO software.
Add a magnesium strip to the reaction vessel and quickly screw on the top. If the seal is tight, you should notice the pressure rising on the graph. If not, you may have a leak and will have to repeat this run.
Gently swirl the contents of the reaction vessel as you watch the pressure increase.
When the graph flattens out or starts to decrease, the reaction is complete and you can stop acquiring data.
Use a thermometer to determine the final temperature of the solution. If the temperature is different from the initial temperature, average them.
Pour the contents of the reaction vessel down the drain with a large amount of water.

Conducting the Mg surface area experiment:

Accurately weight (0.001 g) a quantity of magnesium powder that is equivalent to that of a single magnesium strip used in the above experiments.
Using the repippetters, add 20.00 mL of the 1.0 M HCl solution to your reaction vessel.
Use a thermometer to determine the initial temperature of the HCl.
Start acquiring data with the PASCO software.
Add the magnesium powder to the reaction vessel as quickly as possible and quickly screw on the top. If the seal is tight, you should notice the pressure rising on the graph. If not, you may have a leak and will have to repeat this run.
Gently swirl the contents of the reaction vessel as you watch the pressure increase.
When the graph flattens out or starts to decrease, the reaction is complete and you can stop acquiring data.
Use a thermometer to determine the final temperature of the solution. If this temperature is different from the initial temperature, average them.
Pour the contents of the reaction vessel down the drain with a large amount of water.

Results/Calculations:

Set up a table that includes the mass of magnesium, [HCl], [Mg], slope of the pressure curve, and temperatures for all of the experiments.
Using the method of initial concentrations and your data from Experiments #1 through #8, calculate the order of this reaction with respect to HCl and Mg. What is the overall order of this reaction?
Given the order of the reaction, calculate k for each experiment. How does k vary with temperature?
Using your data from experiments #3, #9, and #10 (one ribbon in 1.0 M HCl at three different temperatures), create a plot of (1/T) vs (ln k). Use Excel, MR. PLOT, or some other program to generate a least squares fit for your data. From this least squares analysis, you should be able to calculate the collision frequency, A, and the activation energy, E_a, for this displacement reaction.
What effect did you notice when powdered magnesium was used instead of the magnesium ribbon? How do you explain this?

(Updated 6/5/07 by C.R. Snelling)