Rate Laws

2/26/25

Topics

• Rate laws
• Stoichiometric relationships
• Reaction order (0th, 1st,2nd,3rd)
• Differential vs integrated
• Half-life
• Graphs vs tables
• Collision theory
• Factors affecting rate of reaction (concentration/surface area, temperature, catalyst)
• Reaction mechanisms
• Intermediates
• Rate determining step (slow step)
• Molecularity

Rate Laws

Stoichiometric Relationships

-1 Δ[A] -1 Δ[B] 1 Δ[C] 1 Δ[D]

a Δt b Δt c Δt d Δt

= = =

aA + bB ------> cC + dD

Rate of consumption Rate of formation

-Δ[A]/Δt or -Δ[B]/Δt Δ[C]/Δt or -Δ[D]/Δt

(doesn’t include coefficients) (doesn’t include coefficients)

Finds average rate of reaction over a period of time

Overall rate of reaction

includes coefficients (like -1/a, 1/d, etc)

EX: -1/a [A]/Δt

Reaction Order

Rate = k [A]^m[B]ⁿ

Reaction order= m+n

0th order Rate=k

1st order Rate= k[A]

2nd order Rate= k[A]² Rate= k[A][B]

Order Rate Law

• Shows the degree of impact the concentrations of reactants will have on the reaction rate.
• Higher order=greater impact on rate

Rate Laws (aka Differential Rate Law)

Rate = k [A]^m[B]ⁿ

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Rate constant

• Deals with the impact of the concentration of reactants on the rate of rxn
• Often has tables showing rate of reaction at different concentrations

Concentrations of reactants A and B

Integrated Rate Law

• Often has tables showing rate of reaction at different times
• Turn it into a graph to find order of reaction

Half-Life

• The time it takes for the concentration of a reactant to decrease to half its initial value
• The only important one is the first order one

Tables

• Use to find rate law
• See effect when one reactant’s concentration changes but the other reactant’s concentration stays constant

Rate = k[B] !

x2

(proportional increase with [B])

No change

x2

constant

x2

constant

(the numbers represent growth factors)

Differential

Integrated

Concentration vs time

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Graph to see which is linear!

Graph

• The amount of product increases as the reaction proceeds
• The amount of reactant decreases as the reaction proceeds

Graphs

• Look at the slopes of graphs to determine what the reaction order is.

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• 2 main types of graphs used:
• Concentration vs. time
• Straight line plots.

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Concentration vs Time

• 0th order: straight line
• 1st order: curved line
• 2nd order: sharply curved line

0th 1st 2nd

Straight Line Plot

0th 1st 2nd

Often a table with [A] over time is given.

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1. Convert each [A] given into ln[A] or 1/[A]
2. Plot ln[A] or 1/[A] over time.
3. If the slope is straight for that new graph, that means it’s that order of reaction

Helpful summary table!!!!!!

Practice!

Rate Law Practice Question

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Rate Law Practice Question

Write the rate law expression for the reaction

-1 Δ[N₂O₅] 1 Δ[O₂]

2 Δt 1 Δt

=

-½ Δ[N2O5]/Δt = 2.4

Δ[N2O5]/Δt= 4.8

(rate of disappearance is positive rate, so remove negative sign)

Stoichiometry Relationship Problems

-1 Δ[A₃] 1 Δ[A₂]

2 Δt 3 Δt

=

-½ (5*10^-5-1*10^-4) / (30-20) = ⅓ Δ[A₂]/Δt

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Δ[A₂]/Δt= 7.5*10^-6

Rate of reaction includes 1/coefficient!

Collision Theory

Collision Theory

Collision theory states that for a reaction to occur, reactant particles must collide with:

1. Sufficient energy (at least the activation energy) to break bonds
2. Proper orientation so that new bonds can form

If both conditions are met, a successful collision leads to the formation of products. If not, the reactants simply bounce off each other without reacting.

This theory explains why factors like temperature, concentration, and catalyst affect reaction rates by influencing the frequency and effectiveness of collisions.

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Practice!

Collision Theory Practice Question

Which one of the following is more likely to create the product given on the right side?

1. ​

B.

^ successful collision

Collision Theory Practice Question

Factors for Rate of Reaction

Factors that affect the rate of the reaction

• Concentration
• ↑ [ ] → ↑ frequency of collision → ↑ probability of successful collision → ↑ rate of reaction
• Temperature
• ↑ temperature → ↑ Kinetic energy
• Presence of catalyst
• Lowers the activation energy
• Minimum amount of energy required for chemical reaction to occur
• Surface area
• ↑ surface area → ↑ collision → rate of reaction ↑

Energy Diagram

• △E = E_final - E_initial
• If △E<0, exothermic
• If △E>0, endothermic
• Activation Energy
• energy required for reactants to reach the transition state
• Difference between reactant and transition state
• Transition state
• the point where there is a maximum value of energy
• where old bonds are partially broken and new bonds are formed

Graph with catalyst and without

Practice!

3, 1, 2

The experiment that has a greater concentration and has more surface area reacts the fastest

Factors for Rate of Reaction Practice Question

Factors for Rate of Reaction Practice Question

Explain why the rate of disappearance of NO and the rate of formation of N2 are not the same in the reaction, 2CO(g) + 2NO(g) → 2CO2(g) + N2(g).

Reaction Mechanisms

Reaction Mechanism

Shows an overall chemical reaction broken up into individual reactions (elementary steps), which each have their own rate law

Rules

1. The sum of the elementary steps must equal the overall balanced equation
2. The slow step (aka rate-determining step) must equal the rate law of the entire reaction

Rate-Determining Step (=slow step)

Slow step rate law:

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Rate= k[A][B]

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Therefore, overall reaction rate law is Rate= k[A][B]

Intermediates

• Formed in one step of a reaction mechanism and consumed in a later step
• Do not appear in the overall balanced chemical equation or in the overall rate law

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EXAMPLE:

H₂O, HOCl, HOBr, and OH^-

would be the intermediates

Finding overall equation

• Can flip around equations
• Can multiply entire equation by a factor
• Cancel out all intermediates!!!

Molecularity

Rate= k[A]

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Rate = k[A]² Rate = k[A][B]

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Rate= k[A]²[B] Rate=k[A][B][C]

Conditions to be met

• Unimolecular
• Needs enough energy to split it apart
• Bimolecular
• Needs enough energy & correct orientation
• Termolecular
• Needs enough energy & correct energy & simultaneously →rare

Practice!

Reaction Mechanisms Practice Question

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Reaction Mechanism Practice Question