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The rate expression
That’s
where the
rate
expression
comes in
We know how to work out the rate of
reaction …
… but that do...
The rate expression
When you see square brackets around
a formula it means concentration of
[HCl]
… means concentration of...
The rate expression
rate ∝ [X][Y]
This suggests that X and Y
both have an equal affect on
the rate of this reaction
What w...
The rate constant
Unfortunately, proportionality signs aren’t
very useful to us, so we need to replace it
with a constant ...
The order of a reaction
rate = k[X][Y]2
Let’s look at the rate equation for X and Y again …
… means that Y has
double the ...
The rate expression
So, taking into account the rate constant and the reaction order, the
overall rate expression is …
rat...
Orders of Reaction
The order can be determined
experimentally using the initial rate
method, but …
… to do so, the concent...
First order reactions
If rate doubles because the
concentration is doubled,
then it is a first order reaction
[X]
mol dm-3...
First order reactions
[X]
mol dm-3
[Y]
mol dm-3
Rate
mol dm-3 s-1
0.01 0.02 0.0004
0.01 0.04 0.0008
0.005 0.04 0.0004
Let’...
First order reactions
If the concentrations are not simple whole numbers, then it may be
easier to draw a graph of rate ag...
Second order reactions
[X]
mol dm-3
[Y]
mol dm-3
Rate
mol dm-3 s-1
0.01 0.02 0.0004
0.01 0.04 0.0016
Question …
What is th...
Second order reactions
In this case the rate is [X]2, giving a curve through the origin
Rate
Concentration
Reaction orders
[X]
mol dm-3
[Y]
mol dm-3
Rate
mol dm-3 s-1
0.2 0.1 0.0004
0.4 0.1 0.0008
0.8 0.2 0.0064
Question …
What i...
Zero order reactions
Concentration
Rate
In a zero order reaction you
get a straight line as
concentration does not
change ...
Units of k
The units of the rate constant (k) vary depending on the order of the
reaction …
First order reaction …
rate = ...
Units of k
rate = k[A][B]2
What about this reaction?
Question …
rate (mol dm-3 s-1)
[A] (mol dm-3)
[B] (mol dm-3)2
mol dm-...
Temperature and k
As a rule when the temperature increases so does the rate
Generally, for every 10oC increase the rate do...
Temperature and k
Because k varies with temperature it can be used to compare the
same reaction at different temperatures
...
Temperature and k
Remember, temperature is
a measure of the average
kinetic energy
Particles will only react if
they colli...
Questions …
Write down the rate expression for a reaction that is first order
with respect to [A] and [B] and second order...
Questions …
For the reaction:
BrO3
-
(aq) + 5Br-
(aq) + 6H+
(aq) → 3Br2(aq) + 3H2O(l)
The rate expression is:
rate = k[BrO...
Questions …
For the reaction:
BrO3
-
(aq) + 5Br-
(aq) + 6H+
(aq) → 3Br2(aq) + 3H2O(l)
The rate expression is:
rate = k[BrO...
Questions …
In the reaction L + M → N the rate expression is found to be:
rate = k[L]2[H+]
What is k?
L H+
What is the ord...
Questions …
In the reaction G + 2H → I + J, which is the correct rate
expression?
rate = k[G][H]2
rate = k
[I][J]
[G][H]
r...
Rate Expression and Order of Reaction
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Rate Expression and Order of Reaction

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A-level chemistry notes on rate expression and order of reaction

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Rate Expression and Order of Reaction

  1. 1. The rate expression That’s where the rate expression comes in We know how to work out the rate of reaction … … but that doesn’t tell us if the all the reactants make the same contribution to the overall reaction X + Y → Z Look at this reaction … X may make more contribution to the rate of the reaction than Y Or X may make no contribution to the rate of the reaction – instead it depends on Y The only way to find this out is through experimentation
  2. 2. The rate expression When you see square brackets around a formula it means concentration of [HCl] … means concentration of HCl So, we could say that the rate is proportional to the concentrations of the reactants … rate ∝ [X][Y]
  3. 3. The rate expression rate ∝ [X][Y] This suggests that X and Y both have an equal affect on the rate of this reaction What would happen if we double the concentration of X or Y? Question … The rate of reaction would also double What would happen if we had [Y]2? Question … Doubling the concentration of Y would quadruple the reaction rate
  4. 4. The rate constant Unfortunately, proportionality signs aren’t very useful to us, so we need to replace it with a constant … rate = k[X][Y] k is the symbol for the rate constant k is different for every reaction k varies with temperature so temperature must be stated when quoting k
  5. 5. The order of a reaction rate = k[X][Y]2 Let’s look at the rate equation for X and Y again … … means that Y has double the effect of X on the rate of reaction This is the order with respect to Y X must have an order of 1 [X] and [X]1 are the same The overall reaction order of X + Y is … 1 + 2 3rd order
  6. 6. The rate expression So, taking into account the rate constant and the reaction order, the overall rate expression is … rate = k[X]m[Y]n … where m and n are the orders of the reaction with respect to X and Y The overall reaction order is m + n
  7. 7. Orders of Reaction The order can be determined experimentally using the initial rate method, but … … to do so, the concentration of the reactant under investigation should be changed – the other reactant’s concentration should remain the same The initial rate method involves plotting the data obtained from an experiment and using the tangent from time 0 to calculate the rate [A] time
  8. 8. First order reactions If rate doubles because the concentration is doubled, then it is a first order reaction [X] mol dm-3 [Y] mol dm-3 Rate mol dm-3 s-1 0.01 0.02 0.0004 0.01 0.04 0.0008 Concentration remains the same Concentration doubled Rate of reaction doubled Since the rate is doubled when [Y] is doubled the order with respect to Y is 1 Note: we don’t know the order of X and would have to do another experiment to find out
  9. 9. First order reactions [X] mol dm-3 [Y] mol dm-3 Rate mol dm-3 s-1 0.01 0.02 0.0004 0.01 0.04 0.0008 0.005 0.04 0.0004 Let’s add another result … Question … What is the order of X? 1 So, the overall rate equation is … rate = k[X][Y] Question … What is the value of the rate constant? k = [X][Y] rate 0.0004 0.01 x 0.04 = = 1.0 mol-1 dm-3 s-1
  10. 10. First order reactions If the concentrations are not simple whole numbers, then it may be easier to draw a graph of rate against concentration Rate Concentration A first order reaction will be a straight line through 0 The gradient in this case is the rate constant (k)
  11. 11. Second order reactions [X] mol dm-3 [Y] mol dm-3 Rate mol dm-3 s-1 0.01 0.02 0.0004 0.01 0.04 0.0016 Question … What is the order of Y? Concentration remains the same Concentration doubled Rate of reaction quadrupled Order of reaction with respect to Y is 2 0.02 0.02 0.0032 Question … What is the order of X? 3 Question … What is rate equation? rate = k[X]3[Y]2
  12. 12. Second order reactions In this case the rate is [X]2, giving a curve through the origin Rate Concentration
  13. 13. Reaction orders [X] mol dm-3 [Y] mol dm-3 Rate mol dm-3 s-1 0.2 0.1 0.0004 0.4 0.1 0.0008 0.8 0.2 0.0064 Question … What is the order of X? 1 We cannot work out Y straight away – instead let’s look at the whole reaction … Both reactant concentrations have doubled … … the reaction rate has increased by x8 Question … What is the overall reaction rate? 3 So, the order of reaction with respect to Y is … overall order = X order + Y order = 2
  14. 14. Zero order reactions Concentration Rate In a zero order reaction you get a straight line as concentration does not change with rate In this case the rate = rate constant This means the reactant has no influence over the rate of reaction
  15. 15. Units of k The units of the rate constant (k) vary depending on the order of the reaction … First order reaction … rate = k[A] rate (mol dm-3 s-1) [A] (mol dm-3) mol dm-3 s-1 k x mol dm-3= s-1 = k Second order reaction … rate = k[A][B] [A] & [B] (mol dm-3) rate (mol dm-3 s-1) mol dm-3 s-1 = k x mol dm-3 x mol dm-3 mol-1 dm3 s-1 = k
  16. 16. Units of k rate = k[A][B]2 What about this reaction? Question … rate (mol dm-3 s-1) [A] (mol dm-3) [B] (mol dm-3)2 mol dm-3 s-1 k x mol dm-3 x mol dm-3 x mol dm-3= k = mol-2 dm6 s-1 Remember, the units of k vary depending on the order of the reactants
  17. 17. Temperature and k As a rule when the temperature increases so does the rate Generally, for every 10oC increase the rate doubles Look at the following rate equation … rate = k[A][B] If we increase the temperature of A or B what happens to the concentration? Nothing Therefore, the temperature only affects k Question …
  18. 18. Temperature and k Because k varies with temperature it can be used to compare the same reaction at different temperatures Temperature (K) Rate Constant (mol-1 dm3 s-1) 633 0.0178 x 10-3 666 0.107 x 10-3 697 0.501 x 10-3 715 1.05 x 10-3 781 15.1 x 10-3 Question … What can we deduce from the table? As temperature increases so does the value of k This only works if the concentration of the reactants remains the same
  19. 19. Temperature and k Remember, temperature is a measure of the average kinetic energy Particles will only react if they collide and have enough energy to start breaking bonds. This energy is known as … activation energy (Ea) Energy Particleswithenergy Ea Only the particles above Ea will react Notice there are more particles above Ea at the higher temperature
  20. 20. Questions … Write down the rate expression for a reaction that is first order with respect to [A] and [B] and second order with respect to [C]. rate = k[A][B][C]2
  21. 21. Questions … For the reaction: BrO3 - (aq) + 5Br- (aq) + 6H+ (aq) → 3Br2(aq) + 3H2O(l) The rate expression is: rate = k[BrO3 - (aq)][Br- (aq)][H+ (aq)]2 What is the order with respect to … BrO3 - (aq) Br- (aq) H+ (aq) What would happen to the rate if we doubled the concentration of … BrO3 - (aq) Br- (aq) H+ (aq) 1 1 2 x2 x2 x4
  22. 22. Questions … For the reaction: BrO3 - (aq) + 5Br- (aq) + 6H+ (aq) → 3Br2(aq) + 3H2O(l) The rate expression is: rate = k[BrO3 - (aq)][Br- (aq)][H+ (aq)]2 What are the coefficients of the following in the chemical equation above? BrO3 - (aq) Br- (aq) H+ (aq) Work out the units for the rate constant Br2(aq) H2O(l) 1 5 6 3 3 mol-3 dm9 s-1
  23. 23. Questions … In the reaction L + M → N the rate expression is found to be: rate = k[L]2[H+] What is k? L H+ What is the order of the reaction with respect to … MN What is the overall order of the reaction? The rate is measured in mol dm-3 s-1. What are the units of k? Suggest the function of H+ in the reaction. the rate constant 2 0 01 3 mol-2 dm6 s-1 A catalyst - since it isn’t in the original equation
  24. 24. Questions … In the reaction G + 2H → I + J, which is the correct rate expression? rate = k[G][H]2 rate = k [I][J] [G][H] rate = k[G][H] It is impossible to say without experimental data

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