The rate law or rate equation expresses the rate of a reaction is proportional to the concentration of the reactants raised to various powers.
aA + bB → cC + dD
Rate = k[A]m [B]n
where [A] and [B] express the concentration of the species A and B, respectively (usually in moles per liter (molarity)).
k is the rate coefficient or rate constant of the reaction.
It has a fixed value which is characteristic of a given reaction.
For elementary reactions, the rate equation can be derived from first principles using collision theory.
The exponents m for A and n for B represent order of the reaction. m and n are NOT always derived from the balanced equation.
Again, m and n are NOT always derived from the balanced equation.
- The rate law can be determined by keeping the concentration of all but one reactant constant while measuring the reaction rate for various concentrations of the reactant. This process is repeated for each reactant.
Consider the equation:
Br2(aq)+HCOOH(aq) → 2Br(aq) + 2H+(aq)+CO2(g)
Applying the general rate law equation to the reaction gives:
Rate = k[Br2]m [HCOOH]n
- x = 1 and y = 0
- The reaction is first order with respect to Br2
- The reaction is zeroth order with respect to HCOOH
- The overall order of the reaction (reaction order) is equal to 1
Reaction Order
The order of the reaction can only be determined from the experimental data, and it is not related to the stoichiometric coefficients.
- First order - rate directly proportional to concentration.
- Second order - exponential relationship.
- Zeroth order - no relationship.
- The sum of exponents (orders) indicates the overall reaction order.
The order of the reaction is always defined in terms of reactant (and not product) concentrations.
How is a Reaction Order Determined?
F2(g)+2ClO2(g) → 2FClO2(g)
Initial rate is the instantaneous rate at the beginning of the reaction (time = 0 s). The initial rate of the reaction changes by varying the initial concentrations of the reactants.
Initial Rate Data for the Reaction Between F2 and ClO2
Experiment | [F2](M) | [ClO2](M) | Initial rate (M/s) |
1 | 0.10 | 0.010 | 1.2x10-3 |
2 | 0.10 | 0.040 | 4.8x10-3 |
3 | 0.20 | 0.010 | 2.4x10-3 |
Experiment | [F2](M) | [ClO2](M) | Initial rate (M/s) |
→1 | 0.10 | 0.010 | 1.2x10-3 |
2 | 0.10 | 0.040 | 4.8x10-3 |
→3 | 0.20 | 0.010 | 2.4x10-3 |
Rate = k[F2]m [ClO2]n
The reaction order with respect to F2 can be determined by
holding[ClO2] constant.
m = log rate ratio / log concentration ratio
log rate ratio
F2 = log 2.4 x 10-3 m/s / 1.2 x 10-3 m/s = log 2
= 0.310
log concentration ratio
F2 = log 0.20 / 0.10
= log 2
= 0.310
m = 0.310 / 0.310
m = 1
Rate = k[F2]1 [ClO2]n
Experiment | [F2](M) | [ClO2](M) | Initial rate (M/s) |
→1 | 0.10 | 0.010 | 1.2x10-3 |
→2 | 0.10 | 0.040 | 4.8x10-3 |
3 | 0.20 | 0.010 | 2.4x10-3 |
The reaction order with respect to [ClO2] can be determined by
holding F2 constant.
n = log rate ratio / log concentration ratio
log rate ratio
ClO2 = log 4.8 x 10-3 m/s / 1.2 x 10-3 m/s
= log 4
= 0.6021
log concentration ratioClO2 = log 0.040M / 0.010M
= 0.6021
n = 0.6021 / 0.6021
n = 1
Rate = k[F2]1 [ClO2]1
F2(g)+2ClO2(g) → 2FClO2(g)
The rate law of the reaction is:
Rate = k[F2] [ClO2]
The reaction is:
- First order with respect to F2
- First order with respect to ClO2
- Second order overall
Rate constant can be calculated (Expt. 1 or any of the expt.)
Experiment | [F2](M) | [ClO2](M) | Initial rate (M/s) |
1 | 0.10 | 0.010 | 1.2x10-3 |
k = rate / [F2] [ClO2]
= 1.2 x 10-3 M/s / (0.10M)(0.010M)
k = 1.2M-1s-1
Units of Rate Constant
- For order zero, the rate coefficient has units of mol·L-1·s-1
- For order one, the rate coefficient has units of s-1
- For order two, the rate coefficient has units of L·mol-1·s-1
- For order n, the rate coefficient has units of mol1-n·Ln-1·s-1
* The units of the rate constant (k) depend on the
overall reaction order.
overall reaction order.
Exercises:
2NO(g) + 2H2(g) → N2(g) + 2H20(g)
The following experiments were run at 1280°C
Experiment | [NO] (M) | [H2] (M) | Initial Rate (M/s) |
1 | 5.0 x 10-3 | 2.0 x 10-3 | 1.3 x 10-5 |
2 | 10.0 x 10-3 | 2.0 x 10-3 | 5.0 x 10-5 |
3 | 10.0 x 10-3 | 4.0 x 10-3 | 10.0 x 10-5 |
(a) Write down the correct rate law.
(b) Determine the rate constant.
(c) What is the rate of the reaction when [NO] is 4.8 x 10-3 M and [H2] is 6.2 x 10-3 M?
For a reaction 2A + B → 2C, with the rate equation: Rate = k[A]2[B]
(a) the order with respect to A is 1 and the order overall is 1.
(b) the order with respect to A is 2 and the order overall is 2.
(c) the order with respect to A is 2 and the order overall is 3.
(d) the order with respect to B is 2 and the order overall is 2.
(e) the order with respect to B is 2 and the order overall is 3.
What are the units of k for the rate law: Rate = k[A][B]2, when the concentration unit is mol/L?
(a) s-1
(b) s
(c) L mol-1 s-1
(d) L2 mol-2 s-1
(e) L2 s2 mol-2
Given: A + 3B → 2C + D
This reaction is first order with respect to reactant A and second order with respect to reactant B. If the concentration of A is doubled and the concentration of B is halved,
the rate of the reaction would _____ by a factor of _____.
(a) increase, 2
(b) decrease, 2
(c) increase, 4
(d) decrease, 4
(e) not change
