# Unit 1: Kinetics

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## The rate of reaction

The rate of reaction is the change in concentration (of the products or reactants) per unit time.

Calculation:       rate of reaction       = [products] / time              = [reactants] / time

[products] means the concentration of products

[reactants] means the concentration of reactants

Units for rate of reaction are moldm-3s-1

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## Concentration against time graphs

X axis will be time /s                            (x is across)

Y axis will be concentration /moldm-3   (y is up)

The gradient of the graph will give us the rate of reaction ( concentration / time = rate of reaction)

For reactants, their concentrations will decrease as the reaction occurs.

For products, their concentrations will increase as the reaction occurs.

The line on the graph will most likely be a curve. So to calculate the rate at a particular instant in time you will find that point on the line and then draw  tangent to the curve (drawing a straight line in parallel to the point). You will then calculate the gradient from the tangent as it is a straigh line.

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## The rate expression

For the imaginary reaction of       X + Y --> Z     the rate ∝ [X] [Y]  meaning the rate is proportional to the concentrations of X and Y multiplied together. So both X and Y have an effect on the rate.

Double X or Y will double the rate of reaction. Double both and the rate will quadrupal.

If the reaction is       2A + B --> C  the rate ∝ [A]² [B]

Doubling B will still double the rate but doubling A will quadrupal the rate.

To get rid of the ∝ symbol we use a constant called the rate constant (k)

X + Y --> Z

rate = k [X] [Y]

The rate constant is NOT the same for all reactions.

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## Order of reactions

For    X + 2Y --> Z      rate = k [X] [Y]²

The order of a species is equal to the power it is raised to in the rate equation.

So X's order is 1 (or first order) and Y's order is 2 (or second order)

The overall order for this reaction is found by adding the single orders together.

Overall order of reaction = 1 + 2 = 3 (or third order).

However, sometimes a species is zero order. Meaning it has no effect on the rate of reaction.

e.g. rate = k [A] [B]² [C]0                 [C] is to the power of zero, so it is zero order.

actually for this instance    rate = k [A] [B]²      and [C] can be ignored. Doubling or halving [C] will have no effect on the rate of reaction.   The overall order of the reaction = 1 + 2 + 0 = 3 (third order)

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## Units of the rate Constant, K

rate = k [reactants]       so      k = rate / [reactants]                                                               The units of k change with the overall order of the reaction:

e.g. rate = k [X] [Y]         k = rate / [X] [Y]     rate units: moldm-3s-1  [X] and [Y] units: moldm-3

moldm-3s-1 / moldm-3 moldm-3

The red areas cancel out leaving the units as     s-1 / moldm-3   or     mol-1 dm3 s-1

So for a second order reaction, the units of k are mol-1 dm3 s-1

When working out the units of k, remember to check to see if you can cancel out!

Units of k for a first order reaction are   M s-1 / M        or     s-1

Units of k for a third order reaction are M s-1 / M M M  or mol-2 dm6 s-1

Units of k for a fourth order reaction are M s-1 / M M M M or mol-3 dm9 s-1

note: M stands for moldm-3 above

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## Rate against concentration graphs

X axis will give the concentration of a species e.g. [A]   /moldm-3    (X is across)

Y axis will give the rate of reaction  / moldm-3 s-1

You can tell the order of the species from a rate against concentration graph.

Zero order: A horizontal line

First order: A directly proportional line (a slanted line)

Second order or above: a sloped line (curving straight up)

With a slopped line we can not be certain if it is second order or above. If it is second order plot a graph of rate against [A]² and the line will be straight.

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## Initial rate of reaction

For a concentration against time graph, the initial rate is the gradient at time 0 (use a tangent).

We can find orders of species and thus calculate k with initial concentrations and initial rates.

e.g.     Initial [X] /moldm-3                   Initial [Y]  /moldm-3                Initial rate /mold-3 s-1

1                                              1                                           1

2                                              1                                           2

1                                              2                                           4

When [X] is doubled and [Y] is kept the same the inital rate doubles so [X] is first order.

When [Y] is doubled and [X] is kept the same the initial rate quadrupals so [Y] is second order.

so,    k = rate / [X] [Y]²    The values from the table can then be used to calculate k (use values from the same row!)   You can check your answer by using different values from other rows.

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## The effect of temperature on k

Changing the temperature rapidly effects the rate of reaction and thus will also effect the rate constant. That is why rate and reaction and k are often quoted at a certain temperature.

e.g. 2HI (g) --> I2 (g) + H2 (g)

Temperature /K                 k /moldm-3 s-1              Be careful, big K means Kelvin and little k                633                         0.0178 x10 -3                means the rate of reaction.

666                         0.107 x10 -3

697                         0.501 x10 -3

715                         1.05 x10 -3

Increasing the temperature, increases the rate of reaction (k)

Decreasing the temperature, decreases k

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## Why temperature effects k

Particles will only react if they have enough energy. The energy they need must be above the activation energy (Ea).

The temperature is a measure of the average kinetic energy. So increasing the temperature will increase the average energy of particles. This means more particles have energy above Ea and so can react, leading to an increase in rate of reaction. In contrast, lowering the temperature decreases the average energy of particles, so less particles have energy above Ea leading to the decrease in rate of reaction.

Increasing Temperature                                         Decreasing Temperature

Rate of reaction increases                                     Rate of reaction decreases

k = rate / [reactants]                                             k= rate / [reactants]

As rate has increased                                          As rate has decreased

k increases                                                         k decreases

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## The rate-determining step

A lot of reactions involve multiple steps before they are completed. These steps do not all occur at the same speed. So it stands to reason that the slowest step is the one that determines the rate of the overall reaction.

e.g.   A + B + C --> Y + Z

A + B --fast--> D  first intermediate

D --slow--> E      second intermediate                      As the second intermediate is the slowest

E + C --fast--> Y + Z                                              step, it is the rate-determining step.

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