Factor Affecting Reaction Rate

Factor Affecting Reaction Rate

Objectives

1.    Explain factors affecting reaction rate;

              -Concentration / Pressure   -Temperature

              -Catalyst                                   -Particle size

    2. Explain the effect of temperature on reaction

        rate using Maxwell-Boltzmann distribution

        curve.

    3. Explain the effect of catalyst on activation

       energy based on energy profile diagram for

       exothermic and endothermic reactions.

   4. Relate rate constant to temperature and activation energy using the Arrhenius   

       equation

      

       k = Ae-Ea/RT or ln k = ln A –Ea/RT

   5. Determine k, Ea, T and A using Arrhenius

       equation by calculation and graphical method.

Ln (k1 / k2) = Ea/R (1/T2 – 1/T1)

Factors Affecting Reaction rate

a) Effect of Concentration

o When concentration of reactant increases, frequency

of collision also increases.

o More particles present in the same volume, they are more likely to collide

o The probability of effective collisions increase

frequency of effective collision = collision frequency x fraction of molecules with sufficient energy

o Rate of reaction increases.

   [reactants] increases,the frequency of collision increases

o This observation correlates with the RATE LAW

    Reaction rate = k [ A ]x [ B ]y …

                             (A & B = reactants)

                            (x & y = rate order)

o Based upon this equation,

                       Reaction rate directly proportional to the concentration of reactants

o REMINDER!

    Only in zero order reactions, the rate of reaction is not

    dependant upon the concentration of the reactants.

    (depending on its rate order)

    Reaction rate = k [ A ]0 = k (constant)

b) Effect of Temperature

o At a higher temperature, molecules have higher kinetic energy and move at higher speed

o more collisions will occur in a given time

o Furthermore, the higher the KE, the higher the energy of the collisions

o So more molecules will have energy greater than Ea

o effective collision also will be increased

o thus the reaction rate increases.

Distribution of Kinetic of Molecules(Maxwell-Boltzmann Distributions)

The collision frequency is higher temperature because the fraction of reactant molecules with activation energy is higher.

Maxwell-Boltzmann Distributions

• The figure shows the distribution KE of gaseous molecule at temperature T1 and T2.

• At higher temperature, the fraction of molecules with energy greater than Ea increases.axwel-Boltzmann Distributions

• Thus, rate of reaction increase with increase of

temperature.

Take note:

• Area under the curve ∝ to the total number of molecules

area under the curve is the same, bcoz no. of molecules is the same.

Maxwel-Boltzmann Distributions

• There are a wide range of molecular energy

A few molecules have low and high KE, most have value in the middle.

• The shape of the graph changes with temperature

At higher temperature the peak of the graph moves towards the right to a higher KE value as the curve broadens out.

• At higher temperatures, the fraction of molecules with higher energy increase

Average energy increase at higher temperature, but fraction of molecules with low energy decreases. At higher temperature, fraction of molecules with energy

greater than Ea increase.

c). Effect Of Temperature

ARRHENIUS EQUATION

• the effect of temperature on the rate constant, k:

                                k = A e -Ea⁄RT

Where…

k = rate constant

A = frequency factor

(is a measure of the probability of a favorable collision)

e = natural log exponent

Ea = activation energy for the reaction (kJ/mol)

R = universal gas constant (8.314 J mol-1 K-1)

T = absolute temperature (T in Kelvin)

Arrhenius Equation - Derivation

  k = A e^ -Ea⁄RT

ln k = ln (A.e^ –Ea/RT)

ln k = ln A – Ea/RT

ln k = ln A - Ea / R (1/T)

   y = C + mx

Example

The table below gives the rate constants, k for the reaction between potassium hydroxide and bromoethane at different temperatures.

K(M^-1s^-1)	T(k)
0.63	322
2.50	331
10.0	347
22.6	353

a) Using a graphical method, calculate the activation energy (kJmol-1) for this reaction.

b) What is the overall order of reaction? Explain

c) Calculate the initial rate of reaction at 330 K when the concentrations for both KOH and   CH3CH2Br are 0.1M.

Solution……

1/T	0.0031	0.0030	0.0029	0.0028
ln k	-0.46	0.92	2.30	3.12

a) Slope = Ea/R

              = 12492

Ea = 12492 × 8.314

     = 1.04 ×105 Jmol-1

     = 104 kJmol-1

b) Second order, unit of k = M-1s-1

 c) ln k = -Ea/R(1/T) + ln A

     ln k = -12492 (1/330) + 38.45

         k = 1.81 M^-1s^-1

Rate = k [KOH][CH3CH2Br]

        = 1.81 x 0.1 x 0.1

        = 1.81 x 10-2 Ms-1

Arrhenius Equation – Further Derivation

Rate constant, k varies with T.

The ratio of rate constant at two different T can be calculated.

ln k1 = ln A – Ea / RT1……………………….(1)

ln k2 = ln A – Ea / RT2……………………….(2)

Equation (1) minus (2) gives :

ln ( k1/k2) = Ea / R (1/T2-1/T1)

d). Effect Of Catalyst

• A catalyst is a substance that increases the rate of a chemical reaction without itself being consumed.

• It increases the reaction rate by providing an alternative reaction pathway of which having lower activation energy.

• A catalyst provides a different reaction mechanism.

A catalyst provides an alternative pathway for the reaction to occur (----curve) which has a lower activation energy.

When Ea decreases, k increases, reaction rate increases

e). Effect Of Surface Area

• For reactions that occur on a surface that is for solid, the rate increases as the surface

area is increased.

• A larger surface area increases the contact area between the reactants thus increases

the frequency of collision and the probability of effective collision between the molecules

of the reactants.

Defination of Terms Used in Reaction Kinetics Chapter

Activation Energy  -  The difference in energy between the reactants and the transition state that is the energy barrier the reactants must overcome to achieve a chemical reaction.

Catalyst  -  A substance that lowers the activation energy for a chemical reaction without being chemically altered by the reaction.

Elementary Step  -  A reaction that represents a single collision or intramolecular step in a reaction mechanism.

Integrated Rate Law  -  The integral (a calculus operation) of the rate law, this form of the rate law shows the dependence of the concentration of reactants on time of reaction.

Intermediate  -  A species that is both produced and consumed in a chemical reaction. An intermediate does not appear in the overall reaction expression but is proposed to be produced in one elementary step and consumed in another.

Kinetics  -  The study of the rates and mechanisms of chemical reactions.

Mechanism  -  The series of elementary steps that combine to produce the path molecules take from reactant(s) to product(s) in a chemical reaction.

Method of Initial Rates  -  A series of experiments wherein the concentration of one reagent at a time is varied and the initial rate (rate at time zero) of the reaction is measured. By comparing the change in concentration to the change in rate, it is possible to determine the order of each reagent in a reaction.

Order  -  In the rate law of a reaction, the power to which the concentration of a reagent is raised. Or, the sum of the powers on the concentration terms in the rate law.

Rate  -  The speed of a reaction measured in amount of reagent consumed or product produced per unit time.

Rate Law  -  An expression of the dependence of the rate of a reaction on the concentrations of reactants.

Reaction Coordinate Diagram  -  A plot of free energy versus the reaction coordinate for a reaction that provides a pictorial representation of the lowest energy path from reactants to products.

Transition State  -  The species with the highest energy between reactant and product on a reaction coordinate diagram, it is a short-lived species that represents a combination of product-like and reactant-like properties.

NTRODUCTION TO REACTION KINETICS

Chemical Kinetics - Reaction Rates

Kinetics, the study of the rates of chemical reactions, has a profound impact on our daily lives. Even though some reactions are thermodynamically favorable, such as the conversion of diamonds into graphite, they do not occur at a measurable rate at room temperature. Other reactions, like the explosive reaction between vinegar and baking soda, occur almost instantaneously. Imagine a world where all thermodynamically favored processes occurred at the same rate--life could not exist under such circumstances because biological processes rely on the kinetic stability of many unstable compounds. Kinetics answers questions about rate, how fast reactions go, and mechanisms, the paths molecules take in going from reactants to products.

To describe the rate of a reaction, we will derive the rate law for a chemical reaction and discuss the factors affecting rate. Additionally, we will describe the experimental techniques, such as the method of initial rates and fitting data to plots based on the integrated rate law, used to determine the rate law for an unknown reaction.

In our discussion on mechanisms, we will discuss how to determine the path a reaction takes by analyzing and predicting the series of elementary steps that comprise a mechanism. By comparing the rate law for a proposed mechanism and other mechanistic predictions to experimental data, we can test the validity of a mechanism. Mechanisms can never be proven exactly, but we can rule out mechanisms that disagree with experimental observations. We will use reaction coordinate diagrams to understand and to visualize reaction mechanisms, thermodynamics, and activation energies. Catalysts and intermediates can be important factors in reaction mechanisms, and they provide interesting examples of mechanism problems.

Chemical kinetics is the branch of chemistry which addresses the question: "how fast do reactions go?" Chemistry can be thought of, at the simplest level, as the science that concerns itself with making new substances from other substances. Or, one could say, chemistry is taking molecules apart and putting the atoms and fragments back together to form new molecules. (OK, so once in a while one uses atoms or gets atoms, but that doesn't change the argument.) All of this is to say that chemical reactions are the core of chemistry.

If Chemistry is making new substances out of old substances (i.e., chemical reactions), then there are two basic questions that must be answered:

1. Does the reaction want to go? This is the subject of chemical thermodynamics.

2. If the reaction wants to go, how fast will it go? This is the subject of chemical kinetics.

Here are some examples. Consider the reaction,

2 H₂(g) + O₂(g) → 2 H₂O(l).

We can calculate Δ_rG^o for this reaction from tables of free energies of formation (actually this one is just twice the free energy of formation of liquid water). We find that Δ_rG^o for this reaction is very large and negative, which means that the reaction wants to go very strongly. A more scientific way to say this would be to say that the equilibrium constant for this reaction is very very large.

However, we can mix hydrogen gas and oxygen gas together in a bulb or other container, even in their correct stoichiometric proportions, and they will stay there for centuries, perhaps even forever, without reacting. (If we drop in a catalyst - say a tiny piece of platinum - or introduce a spark, or even illuminate the mixture with sufficiently high frequency uv light, or compress and heat the mixture, the mixture will explode.) The problem is not that the reactants do not want to form the products, they do, but they cannot find a "pathway" to get from reactants to products.

Another example: consider the reaction,

C(diamond) → C(graphite).

If you calculate Δ_rG^o for this reaction from data in the tables of thermodynamic properties you will find once again that it is negative (not very large, but still negative). This result tells us that diamonds are thermodynamically unstable. Yet diamonds are highly regarded as gem stones ("diamonds are forever") and are considered by some financial advisors as a good long-term investment hedge against inflation. On the other hand, if you were to vaporize a diamond in a furnace, under an inert atmosphere, and then condense the vapor, the carbon would come back as graphite and not as diamond.

How can all these things be?

The answer is that thermodynamics is not the whole story in chemistry. Not only do we have to know whether a reaction is thermodynamically favored, we also have to know whether the reaction can or will proceed at a finite rate. The study of the rate of reactions is called chemical kinetics.

The study of chemical kinetics requires new definitions, new types of experimental data, and new theories and equations to organize the data. We begin with the definition of reaction rate in next post.

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Second Order Reaction

http://www.youtube.com/watch?v=a_ZozD3eSw4&feature=related

First Order Reaction

Reaction rates with change in temperature

Maxwell-Boltzman Distribution Curve

What is the Maxwell-Boltzmann Distribution??

All the molecules of a particular chemical, compound or element have the same mass, so their kinetic energy is only dependent on the speed of the particles.

Remember Kinetic Energy = ½mv²

In any particular mixture of moving molecules, the speed will vary a great deal, from very slow particles (low energy) to very fast particles (high energy). Most of the particles however will be moving at a speed very close to the average.

The Maxwell-Boltzmann distribution shows how the speeds (and hence the energies) of a mixture of moving particles varies at a particular temperature.

 Points to notice:

• No molecules at zero energy
• Few molecules at high energy
• No maximum energy value

For the reaction to occur, the particles involved need a minimum amount of energy - the Activation energy (E_ACT). If a particle is not in the shaded area, then it will not have the required energy so it will not be able to participate in the reaction.

The Facts 

What happens?
As you increase the temperature the rate of reaction increases. As a rough approximation, for many reactions happening at around room temperature, the rate of reaction doubles for every 10°C rise in temperature.
You have to be careful not to take this too literally. It doesn't apply to all reactions. Even where it is approximately true, it may be that the rate doubles every 9°C or 11°C or whatever. The number of degrees needed to double the rate will also change gradually as the temperature increases.

Examples
Some reactions are virtually instantaneous - for example, a precipitation reaction involving the coming together of ions in solution to make an insoluble solid, or the reaction between hydrogen ions from an acid and hydroxide ions from an alkali in solution. So heating one of these won't make any noticeable difference to the rate of the reaction.
Almost any other reaction you care to name will happen faster if you heat it - either in the lab, or in industries.

The Explanation  Increasing the collision frequency Particles can only react when they collide. If you heat a substance, the particles move faster and so collide more frequently. That will speed up the rate of reaction. That seems a fairly straightforward explanation until you look at the numbers! It turns out that the frequency of two-particle collisions in gases is proportional to the square root of the kelvin temperature. If you increase the temperature from 293 K to 303 K (20°C to 30°C), you will increase the collision frequency by a factor of: That's an increase of 1.7% for a 10° rise. The rate of reaction will probably have doubled for that increase in temperature - in other words, an increase of about 100%. The effect of increasing collision frequency on the rate of the reaction is very minor. The important effect is quite different . . .   The key importance of activation energy Collisions only result in a reaction if the particles collide with enough energy to get the reaction started. This minimum energy required is called the activation energy for the reaction. You can mark the position of activation energy on a Maxwell-Boltzmann distribution to get a diagram like this: Only those particles represented by the area to the right of the activation energy will react when they collide. The great majority don't have enough energy, and will simply bounce apart. To speed up the reaction, you need to increase the number of the very energetic particles - those with energies equal to or greater than the activation energy. Increasing the temperature has exactly that effect - it changes the shape of the graph. In the next diagram, the graph labeled T is at the original temperature. The graph labeled T+t is at a higher temperature. If you now mark the position of the activation energy, you can see that although the curve hasn't moved very much overall, there has been such a large increase in the number of the very energetic particles that many more now collide with enough energy to react. Remember that the area under a curve gives a count of the number of particles. On the last diagram, the area under the higher temperature curve to the right of the activation energy looks to have at least doubled - therefore at least doubling the rate of the reaction. Summary Increasing the temperature increases reaction rates because of the disproportionately large increase in the number of high energy collisions. It is only these collisions (possessing at least the activation energy for the reaction) which result in a reaction.