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Reactions Rates and Temperature

- Reactions happen when reactants collide.
- The more reactants colliding (the higher the concentration), the faster the reaction.
- When reactants DO collide, they must have enough energy and in the right orientation for the reaction, which generally involves the breaking of bonds and the forming of new bonds.

NO

Cl + NOCl

ClClNO‡

Cl2

transition state

Transition State Theory

This energy requirement is shown in the graph below. Transition state theory says that energy is needed to form an transition statethat can then break down into products.

ClClNO‡

EA, the activation energy

Cl + NOCl

Cl2

NO

ClClNO‡

transition state

Activation Energy

The activation energyEAis the minimum energy needed to initiate the chemical reaction. This energy is different than the overall energy change for the reaction. The value of the activation energy depends on the mechanism for the reaction.

ClClNO‡

EA, the activation energy

ΔE, the energy change for the reaction

Reactions Rates and Temperature

- The kinetic theory of gases says that the average kinetic energy of a gas depends on its temperature. It also says that the kinetic energies of the gas molecules themselves are not all the same but follow a distribution like the one below.

average kinetic energy

fraction of molecules

Reactions Rates and Temperature

- If the activation energy for a reaction is EAthen, for a given temperature, only a fraction of the molecules will have kinetic energies ≥EA.
- At a higher temperature, more reactant molecules will have kinetic energies ≥EA.

Activation energy

EA

Reactions Rates and Temperature

- The reaction rate increases with increasing temperature.
- Where in the rate equation does this dependence on T occur? In the rate constant k. k is a function of temperature. For the reaction shown below,
- rate = k(T)[Cl][NOCl]

NO

Cl + NOCl

ClClNO‡

Cl2

transition state

The Arrhenius Equation

- The dependence of the rate constant k on temperature was found by Arrhenius to have following form for a large number of reactions.
- Arrhenius equation
- This equation is based on experimental results.
- A is a constant, R is the gas constant = 8.3145 J/mol-K, and T is the temperature in kelvin.

The Arrhenius Equation

How does the rate constant k vary with T?

or

ln k = - EA+ ln A

RT

As T increases, EA/RT decreases, and k increases. When k increases, the rate increases.

The Arrhenius Equation

How does the rate constant k vary with EA?

or

ln k = - EA+ ln A

RT

As EAincreases, EA/RT increases, and k decreases. When k decreases, the rate decreases.

Getting Ea from Rate Constant Data

The following table shows the rate constants for the rearrangement of methyl isonitrile at various temperatures.

1. What is the activation energy for the reaction?

2. What is the value of the rate constant at 430.0 K?

Getting EAfrom Rate Constant Data

- What is the activation energy for the reaction?
- ln k = - EA+ ln A
- RT
- A plot of ln k vs 1/T will have a slope = -EA/R.
- So, we change T to kelvin and invert, and change k to ln k:

Getting EAfrom Rate Constant Data

slope = -EA/R

ln k = -EA+ ln A

RT

The slope (and therefore EA) can be found from any two pairs of data points, either from the plot or from a calculation.

Getting EAfrom Rate Constant Data

EAcan also be computed directly:

ln k2 = - EA + ln A

RT2

ln k1 = - EA + ln A

RT1

Subtracting the second equation from the first gives

ln k2 - ln k1 = -EA- -EA

RT2 RT1

Getting Ea from Rate Constant Data

rearranging ln k2 - ln k1 = - EA- -EAleads to:

RT2 RT1

This equation is helpful for comparing rates at different temperatures. It only applies to systems with the same activation energy.

Getting EAfrom Rate Constant Data

Now, any two pairs of k and T will allow EAto be calculated.

Getting EAfrom Rate Constant Data

EA= 156 kJ

Getting a Rate Constant at a New Temperature

2. What is the value of the rate constant at 430.0 K?

We can again use:

Since we know the activation energy:

EA= 156 kJ,

we can use any value of T and k already known:

T1 = 503.4 K

k1 = 6.30 x 10-4 s-1

Getting a Rate Constant at a New Temperature

2. What is the value of the rate constant at 430.0 K?

EA= 156 kJ

T1 = 503.4 K

k1 = 6.30 x 10-4 s-1

k2 = 1.09x10-6 s-1

The Arrhenius Equation

For the reaction C + B Z

If the rate is found by experiment to be second order, then the rate equation would be

rate = ΔZ = k[C][B]

Δt

Substituting the Arrhenius equation for k shows the T and Ea dependence of the reaction rate:

Catalysts and Rates

Catalysts change the rate of a reaction by providing an alternate mechanism that has a lower activation energy.

Original reaction

Potential

catalyzed reaction

This means the rate constant () for the catalyzed reaction will be larger, and the rate for the catalyzed reaction will be faster than the uncatalyzed rate.

How the Rate Constant Changes with Activation Energy

Fumarase lowers the activation energy of the fumarate to malate reaction from 156 kJ to 25 kJ. Calculate the factor by which the enzyme increases the reaction rate at body temperature.

ln k2 - ln k1=

How the Rate Constant Changes with Activation Energy

Fumarase lowers the activation energy of the fumarate to malate reaction from 156 kJ to 25 kJ. Calculate the factor by which the enzyme increases the reaction rate at body temperature.

How the Rate Constant Changes with Activation Energy

Fumarase lowers the activation energy of the fumarate to malate reaction from 156 kJ to 25 kJ. Calculate the factor by which the enzyme increases the reaction rate at body temperature.

The presence of fumarase increases the reaction rate by a factor of 1.2x1022. In effect, the reaction does not happen unless catalyzed by fumarase.

Reaction Profile for a Reaction with a Multistep Mechanism

Potential

The reaction profiles you have seen so far are those for elementary reactions. Elementary reactions are reactions that occur in a single collision step.

Reaction Profile for a Reaction with a Multistep Mechanism

Many reactions occur by mechanisms that involve more than one elementary step. Each step has its own activation energy and rate constant.

Reaction Profile for a Reaction with a Multistep Mechanism

Step 1 has the larger EA, so it is slower than step 2. Step 1 is called the rate-determining step.

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