Unit 8: Reaction Rates

Introduction

A match is a chemical reaction ready to go, but unless a little heat is added by friction the reaction will not start. Water can be made with hydrogen and oxygen, but just mixing the gases is not enough, a catalyst must be used. Kinetics is the study of the rates of reactions. Understanding the reaction rate is just as important as understanding if the thermodynamics of a reaction—the energy calculations—are favorable (see unit 7). Some reactions, like the match, are ready to go but are stable until enough energy is added, other reactions have driving forces that keep the reaction going forward, and other reactions need a third-party to negotiate the terms of the reaction like the catalytic reaction of hydrogen and water. This unit is about rates of reaction, how concentration affects the rate of reaction, catalysts, and the role of an activated complex in every reaction.

Fire

A fire is a good example of our intuitive understanding of the factors governing the rate of a reaction. If you want a fire to burn fiercely and rapidly, then you need lots of wood, heat, and oxygen. This is why one of the first things done before starting a fire is to gather lots of wood—then you’ll have a big fire. But, as seen on TV shows so often, starting the fire requires little bits of wood called kindling, because the match to light the fire is not going to burn the bigger pieces of wood. Kindling is small so it exposes a lot of the wood’s surface to the match flame. It also changes the heat from the match to a temperature change because the mass is low. Still, like in the TV shows, often all the kindling does is smoke and smolder, until someone blows gently on the kindling pile. This adds extra oxygen, increasing its concentration. Now the fire can start. First the little kindling pile, then some sticks, then the logs, and finally the roaring fire.

This scenario introduces the key elements of reaction rate. 1) higher concentrations, like the added oxygen, lead to greater rates of reaction; 2) some energy is needed to get the reaction started even if it is exothermic, which is why a match is needed to start a fire, even though it does just fine after it is started; and 3) there are factors that change the concentration and increase the rate of reaction, like using kindling instead of logs of wood.

Reaction Rate

Rate is a term usually used to show the change in something over change in time. The rate of travel is the change in distance over time, and the rate of interest on your savings is change in dollars over time. The rate of reaction, or reaction rate, is the change in molar concentration of reactants or products over change in time. On a graph concentration vs. time, the rate of reaction is the slope of the line. For example, in the reaction H2 + I2➔ 2HI, the reaction rate is ∆[H2]/∆t or ∆[I2]/∆t or –½∆[HI]/∆t.

On the graph the change in the concentration of the product HI is increasing twice as fast as the H2 and I2 are disappearing. The coefficients of the balanced equation shows the same doubling of HI: H2 + I2➔ 2HI. In order for the rate of reaction to be the same regardless of whether a product or reactant concentration is used, the inverse of the coefficient is multiplied by the change in concentration over change in time; that is if the concentration is twice as large then the rate will be multiplied by 1/2 to balance the larger change in concentration. Moreover, the change for the production of products will be positive, because the final concentration is larger than the starting concentration. But the change in the disappearance of the reactants will be negative, because the final concentration is smaller than the starting concentration. Therefore, the rate based on the reactant concentrations is made positive by multiplying by –1.

Example, “List the rates of reaction for the chemical equation 2Al + 3O2➔ 2Al2O3, in terms of the product and the reactants.”

Rate = – 1 ∆[Al] Rate = – 1 ∆[O2] Rate = 1 ∆[Al2O3]

2 ∆t 3 ∆t 2 ∆t

Example. “Write the rate of reactions based on products and reactants for the balanced chemical equation : C2H6 + 5⁄2 O2 ➔ 2 CO2 + 3 H2O

Rate = – ∆[C2H6] Rate = – 2 ∆[O2] Rate = 1 ∆[CO2]Rate = 1 ∆[H2O]

∆t 5 ∆t 2 ∆t3 ∆t

Determining Rate of Reaction

To determine the rate of a reaction the experimental data is collected and then the changes in concentration over time are calculated to give the rate.

For example, “Given the following data determine the average rate of reaction during the first 15 seconds for 2N2O5 ➔ 4NO2 + O2. Show how to calculate the same rate with the products and the reactant.”

Time
(s) / [N2O5]
mol/L / [NO2]
mol/L / [O2]
mol/L
0.0 / 0.55 / 0.00 / 0.00
15 / 0.41 / 0.28 / 0.07
30 / 0.31 / 0.48 / 0.12
45 / 0.23 / 0.64 / 0.16

Rate = – 1 ∆[N2O5] = – (0.41 - 0.55) = 0.0047 M/s

2 ∆t 2•(15 - 0)

Rate = 1 ∆[NO2] = (0.28 - 0) = 0.0047 M/s

4 ∆t 4•(15 - 0)

Rate = ∆[O2] = (0.07 - 0) = 0.0047 M/s

∆t (15 - 0)

All calculations of the rate give the same answer.

But if the rate was calculated at a different time the rate of reaction is slower. For the last 15 seconds the rate of formation of oxygen, O2, is: Rate = ∆[O2] = (0.16 - 0.12) = 0.0027 M/s.

∆t (45 - 30)

This is because the amount of reactant is decreasing and the rate of reaction is dependent upon the concentration of the substance measured. This means that the rate of reaction is usually given as the beginning rate when the concentration changes are largest. In our example we used an average rate of reaction based on the initial conditions and the first measured value. The rate would be faster if the first measurement was closer to the beginning of the experiment, say the first 5 seconds. Using calculus, it is possible to get the slope of a single point on the curve and determine the instantaneous reaction rate. Usually, the average reaction rate is sufficient for most problems and experiments, but keep in mind that the rate is an average and that the rate becomes slower over time.

Pressure instead of Concentration.

Many reactions happen in the gas phase like the reaction used above, 2N2O5 ➔ 4NO2 + O2, . Instead of concentration, it would be possible to measure amount of each substance in terms of pressure. This is because all gases follows the ideal gas law in typical reaction conditions and the formula for the ideal gas law can be manipulated so that molar concentration is proportional to pressure.

Ideal Gas Law: PV = nRT rearrange to give P = n n/V is molarity so P• 1 = Molarity, M

RT V RT

For each gas in the container there is a partial pressure, which is the pressure of only that gas in a container; whereas, the total pressure in the container is the sum of all the partial pressures of the substances in the container. To determine the rate of reaction from the partial pressure, the partial pressure measurements must be multiplied by 1/RT to convert them to molar concentrations, which can then be used to determine the reaction rate.

Factors that Change the Reaction Rate

Concentration or pressure, temperature, and a catalyst are factors that determine the reaction rate. The concentration or pressure changes seem obvious based on the previous discussion because of their direct relationship to rate: rate = ∆[concentration, M] = 1 ∆ P .

∆t RT ∆t

But to understand the reasons for the change, we need a model of the behavior of free moving particles as gases, liquids, or those in solution.

Kinetic Molecular Theory

Kinetic energy is the energy of motion, and is the energy of the motion of the atoms, molecules, and ions of matter. Kinetic molecular theory, KMT, states that particles of matter are in constant and random motion regardless of their state of matter. KMT also proposes that the motion of particles is directly proportional to temperature, such that, at high temperatures the particles (on average) are moving faster. Moreover, with regard to gases, KMT hypothesizes that particles are too small for their volume to interfere with the properties of a gas and that the distance between the particles of a gas is so great that the intermolecular forces are insignificant between the particles.

Maxwell-Boltzmann Distribution

The movement of particles is random and constant, so particles in a container do not all have the same velocity (speed and direction). The Maxwell-Boltzmann Distribution graphs the number of particles at specific velocity at different temperatures. Each temperature curve shows a peak near the average energy, which corresponds to the idea that temperature is a measure of the average kinetic energy, since higher temperatures have higher average kinetic energies. But what is most important for rate of reaction is that high temperature curves show more and more particles with high energy. So at -100°C on the graph almost no particle reach 1000 m/s, but at 600°C many particles have velocities of 1000 m/s or more .

Collision Theory

Collision theory assumes that colliding particles are responsible for the reactions between substances. Collision theory proposes that a reaction can only occur between particles if three conditions are met: 1) particles must collide for a reaction to happen, 2) colliding particles have sufficient energy to initiate the reaction, 3) the particles must be “aimed” or orientated in a specific way for the reaction to occur.

Collision Theory Summary

Particles must Collide

Collisions Must be of Sufficient Energy

Particles must have Appropriate Orientation

/
Lines, —, represent amount of kinetic energy / H2 + I2 ➔ 2HI

Factors Affecting Reaction Rate

A reaction will increase in rate when the concentration, pressure, and temperature increase. With collision theory we can explain the increase in rate due to increase in the number of particles as measured by concentration or pressure and the increase in the rate of reaction with the increase in temperature. If there are more particles in a reaction container then the likelihood of a collision goes up. It also increases the odds that the collision will take place with sufficient energy and in the correct orientation. If the temperature increases then the number of particles with sufficient energy to cause a reaction will increase, as shown in the Maxwell-Boltzmann distribution.

Activated Complex

When a match sits in a box the chemical energy is ready and willing to react, but it stays stable until the little heat of friction is added. Like in many reactions some energy must be added before the reaction can begin. The activation energy is the amount of energy needed start a reaction. In the graphs of an exothermic and endothermic reaction, the activation energy is the energy needed to get the reaction started.

Ea is the activation energy for a reaction. ** is the energy of the activated complex

Once an exothermic reaction starts the activation energy is supplied by the reaction itself, which is why a match remains lit without adding more friction. For an endothermic reaction the energy to overcome the activation energy must come from the surroundings, so the container and whatever else is connected to the reaction mixture become colder as they lose energy.

Activated Complex

An activated complex is a combination of the atoms in the reactants that is halfway between full bond breaking of the reactants and full bond forming to make products. This species has the highest energy of any combination of atoms from the reactants that leads to the products. The collision theory helps explain the nature of the activated complex: if the particles are not arranged to form the activation complex then the collision does not lead to products, and if the collision occurs with enough energy then the bond breaking and bond forming of the complex cannot occur.

Catalyst

A catalyst is a substance that causes a reaction to increase in rate without being consumed by the reaction. Cells require enzymes, which are proteins, to act as catalysts in biological processes, and many industrial processes are not possible without a catalyst. When hydrogen peroxide is added to a cut, it begins foaming or bubbling as it produces oxygen that will kill bacteria in the wound. The catalase in blood acts as a catalyst and speeds up the decomposition of the hydrogen peroxide. The catalytic converter in a car usually contains platinum, palladium, or rhodium as a catalyst, to changes toxic gases in the exhaust fumes into more benign substances, like NO into N2 and O2.

A catalyst works by providing a new pathway for the reactants to form products so the activated complex is different than the activated complex of the uncatalyzed reaction. The reaction rate increases because the new pathway has a lower activation energy so the sufficient energy required by collision theory is lower and more particles can combine successfully. A graph of a catalyzed reaction shows a “tunnel” through the barrier from the reactants to the products.

Summary

The rate of a reaction, or reaction rate, is the change in molar concentration over time and can be calculated from the data provided by an experiment. The rate of a reaction can be calculated with either data from the reactants or from the products, but it must be equal for any substance used. For this reason rates are adjusted to be equal. For the model reaction, aA+bB ➔ cC + dD, the reaction rate = – 1 ∆[A] = – 1 ∆[B] = 1 ∆[C] = 1 ∆[D] .

a ∆tb ∆t c ∆t d ∆t

The reaction rate is an average rate from the initial point where data was collected to the final point that data was collected, so the formulas above calculate average reaction rate. Using calculus a reaction rate at a point can be calculated which is called the instantaneous reaction rate.

Collision theory explains the factors affect a reaction. Collision theory states that 1) particles must collide for a reaction to happen, 2) collisions must have sufficient energy for the reaction to happen, and 3) only collisions with particles “aimed” or oriented in the correct geometry will lead to a reaction.

Increasing concentration increases a reaction, because it increases the number of collisions, which must lead to a greater number of successful collisions. Since the partial pressure of a gas is related to the concentration of the gas in a container (P/RT = n/V = Molarity), then increasing pressure also increases the reaction rate. Temperature is a measure of the average kinetic energy of the particles, so some particles can have high energy and some can have low energy. When the temperature increases the number of particles with high energy increases. This causes more collisions between particles with sufficient energy and reaction rate will increase.

The activation energy for a reaction is the little bit of energy that is needed to make the reaction proceed to products. Like the friction for striking a match or the dropping of nitroglycerin, the activation energy will start an exothermic reaction, but the energy that is produced by the reaction will continue to supply the needed activation energy so the reaction can continue. For endothermic reactions, the activation energy is supplied by the surroundings that become colder as energy is removed. The activated complex is the species produced by the activation energy. It is a combination of the reactant and product with the bonds half broken and half formed.

A catalyst is a substance that increases the rate of reaction when it is present and is unchanged at the end of the reaction. Enzymes are used in many cellular processes and industry makes extensive use of catalysts. A catalyst provides another pathway for a reaction and another lower activated complex. Because the pathway has a lower activation energy, there are more successful collisions and the reaction rate increases.

Reaction Rates

8. Chemical reaction rates depend on factors that influence the frequency of collision of reactant molecules. As a basis for understanding this concept:

a. Students know the rate of reaction is the decrease in concentration of reactants or the increase in concentration of products with time.

b. Students know how reaction rates depend on such factors as concentration, temperature, and pressure.

c. Students know the role a catalyst plays in increasing the reaction rate.

d.*Students know the definition and role of activation energy in a chemical reaction.

Starred standards are non-tested standards on the California Standards Test

Contributed by Kenneth Pringle

Edited by Kathleen Duhl

Formatted and Wiki Contribution by Christine Mytko