1. 13.2-13.3: The Rate of a Chemical Reaction and the Rate Law

2. The Rate of a Chemical Reaction
A chemical reaction’s rate is a measure of how fast the reaction occurs and is expressed with a positive value
Rates are measured in change of in some quantity over unit of time
Ex. speed is a rate that is measured as change in distance over change in time
The rate of chemical reactions is measured as the change in amount of product or reactant (usually in concentration units) over the change in time
All rates of the same reaction are equal and must be in stoichiometric proportion
When the change in reactants is being measured, it will always be negative (because the concentration of reactant decreases as the concentration of product increases), so a negative sign is included in the equation to make the final rate positive
A negative sign is not included in the equation if the concentration of products is being measured because that will always be positive
Δdistance
Δtime
Δ[concentration of product or reactant]
Δtime
Concentration is expressed in brackets
Rate = (-)

3. Practice! [ΔH₂] [H₂]t2-[H₂]t1 Δt [ΔHI] [ΔI₂] Δt Δt = -
Notice that the rate of HI concentration is POSITIVE because it is a product, so its concentration will always increase as a reaction occurs. It has a coefficient of 0.5 because when one mole of both H2 and I2 is used, 2 moles of HI are produced. To keep the rates at equal values and in stoichiometric proportion, the change in HI concentration must be multiplied by 0.5.
Practice!
Consider the reaction: H₂(g)+ I₂(g)→2HI(g)
The rate, in terms of the reactant H₂(g), on the interval of time (t₁ to t₂), can be expressed as:
Rate = -
[ΔH₂] Δt
[H₂]t2-[H₂]t1
t₂-t₁
= -
What would the rate of the reaction be in terms of I2 ? In terms of HI?
I2 :
Rate = -
[ΔHI] Δt
[ΔI₂] Δt
HI:
Rate = 1 2
Notice that the rate of HI concentration is POSITIVE because it is a product. It has a coefficient of 0.5 because when one mole of both H2 and I2 is used, 2 moles of HI are produced. To keep the rates in stoichiometric proportion, change in HI must be multiplied by 0.5.

4. The Rate of a Chemical Reaction (Continued)
If a chemical reaction has a fast rate, then a large fraction of reactant molecules will combine to form products in a given period of time
If a chemical reaction has a slow rate, then only a small fraction of reactant molecules will combine to form products in a given period of time

6. Measuring Reaction Rates
In order to study the kinetics of a reaction, we must know the concentration of one of the products or one of the reactants over time
This can only be determined experimentally through any one of the following methods:
Polarimetry: a method in which the experimenter shoots a beam of polarized light,which has an electric field oriented along a plane, through the sample and measures how much light passes through (some molecules will rotate the light)
Spectrometry: the most common way to study the kinetics of a reaction; a machine passes light through a reacting sample and it measures how strongly the light is absorbed; this only works for colored samples; if the reactant is colored, absorbency will decrease over time, but if the product is colored, absorbency will increase over time
Pressure measurement: the pressure of a reacting sample of gases is measured; a rise in pressure will determine the relative amounts of reactants and products over time

7. Expressing Reaction Rates
We can generalize the definition of a reaction rate using a generic reaction:
aA + bB → cC + dD
Where A and B are reactants, C and D are products, and a, b, c, and d are the stoichiometric coefficients
The rate at any one specific point in time can be expressed as:
Rate = = = = + 1 a
Δ[A] Δt 1 b
Δ[B] Δt 1 c
Δ[C] Δt 1 d
Δ[D] Δt

8. Change in Reactant and Product Concentrations
Reactant concentrations decrease with time because they are being consumed by the reaction
Product concentrations increase with time because they are being created by the reaction
These changes occur in stoichiometric proportion
For example, H2 concentration decreases at half of the rate that HI concentration increases, because one mole of H2 produces 2 moles of HI.

9. The Average Rate of the Reaction
The average rate of a reaction can be calculated using change in reactant/product concentration over change in time, plugging values into the basic rate equation discussed earlier

10. The Instantaneous Rate of the Reaction
Calculating the instantaneous rate at 50 seconds:
Using [H2]:
= = M/s
Using [HI]:
= =0.0070M/s
The instantaneous rate is always the same, whether it is calculated using reactants or products.
The Instantaneous Rate of the Reaction
Δ[H2] Δt
-0.28M
40s
The instantaneous rate of the reaction is the rate at any one point in time and is represented by the instantaneous slope of the curve at the point
It is determined by calculating the slope of the tangent to the curve at the point of interest
Δ[HI] Δt
0.56M
40s

11. Practice!
Calculate the average rate of the reaction, H₂(g)+ I₂(g)→2HI(g), using values of the [H2] between 10 and 20 seconds and 20 and 30 seconds . What is happening to the rate as the reaction progresses?
Rate10s-20s= = = = M/s
Rate20s-30s= = = = M/s
The rate is decreasing as the reaction proceeds.
Δ[H2] Δt
0.670M M
20s-10s
-0.149M
10s
Δ[H2] Δt
0.549M-0.670M
30s-20s
-0.121M
10s

12. The Rate Law: the Effect of Concentration on Reaction Rate
The rate law is the relationship between the rate of the reaction and the concentration of its reactants, since the rate of a reaction often depends on the concentration of one or more of its reactants
Holds true as long as the reverse reaction (where products return to reactants) is so slow or insignificant that it is negligible
Consider a reaction where the reactant, A, decomposes into products (A→products), the rate law would be:
Rate = k[A]n
Where k is the rate constant, a constant of proportionality
And n is the reaction order (usually an integer) which determines the relationship between the concentration of reactant and the rate of the reaction.

13. Zero Order Reactions rate= k[A]0; n=0
The rate of the reaction is independent of the concentration of the reactants
k[A]0 = k[1]=k
So, k=k, regardless of the concentration of A, and the rate will remain unchanged
As the reaction progresses, the concentration of reactant decreases at a constant rate (linearly), because the reaction rate doesn’t slow as the concentration of reactant decreases
Conditions:
The amount of reactant available for the reaction must be unaffected by changes in the overall quantity of the reactant, like in sublimation, where when a particle sublimes, there is another layer of particles below it, unaffected by the sublimation of the other particles
Rate constant (k) unit: M⋅s-1

14. First Order Reactions rate=k[A]1; n=1
The rate of the reaction is directly proportional to the concentration of the reactants
As[ A ]doubles, the reaction’s rate will also double, etc.
The rate increases/decreases linearly as the concentration of reactant increases/decreases
The rate slows as the reaction proceeds because the concentration of reactant decreases
Rate constant (k) units: s-1

15. Second Order Reactions
rate=k[A]2; n=2
The rate of the reaction is proportional to the square of the concentration of the reactants
As [A] doubles, the reaction’s rate will quadruple (22=4)
The rate of the reaction will quickly decrease as concentration decreases
Rate constant (k) units: M-1⋅ s-1

17. Determining the Order of a Reaction
The order of a reaction can be determined only by experiment!
During experimentation, the method of initial rates is often used
The initial rate (the rate for a short period of time at the beginning of the reaction) is determined by running the reaction several different times with different reactant concentrations to determine the effect of concentration on rate.
If the data has been given, one must find the rate of change between each increment:
= ( )n
Rate 1
Rate 2
k[A]1
k[A]2

18. This reaction is of the first order.
Practice!
A researcher gets the following data after studying two different reactions. To which order to they belong?
Concentration (M)
Initial Rate (M/s)
0.10
0.005
0.20
0.01
0.40
0.02
0.80
0.04
Concentration (M)
Initial Rate (M/s)
0.10
0.0006
0.20
0.0048
0.40
0.0384
0.80
0.3072
This reaction is of the first order.
This reaction is of the third order and is relatively uncommon. Most reactions are of the zero, first, or second order.

19. Reaction Order for Multiple Reactants
The rate law of multiple reactants for a reaction aA + bB → cC + dD is:
rate =k[A]m[B]n
Where m is the reaction order in respect to A, and n is the reaction order in respect to B
The overall order of the reaction is the sum of the exponents (m+n)