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Questions and Answers
The rate of a chemical reaction can be expressed as the:
The rate of a chemical reaction can be expressed as the:
- Total mass of products formed.
- Change in concentration of reactants or products per unit time. (correct)
- Initial concentration of reactants.
- Amount of reactants consumed at equilibrium.
The stoichiometric coefficients of a reaction directly determine the rate law exponents.
The stoichiometric coefficients of a reaction directly determine the rate law exponents.
False (B)
Define the term 'rate constant' in the context of chemical kinetics.
Define the term 'rate constant' in the context of chemical kinetics.
The rate constant (k) is the proportionality constant that relates the rate of a reaction to the concentrations of reactants raised to various powers.
For a reaction, if the rate doubles when the concentration of a reactant doubles, the reaction is said to be ______ order with respect to that reactant.
For a reaction, if the rate doubles when the concentration of a reactant doubles, the reaction is said to be ______ order with respect to that reactant.
Match the rate law with the corresponding reaction order, where [A] and [B] represent reactant concentrations and k is the rate constant:
Match the rate law with the corresponding reaction order, where [A] and [B] represent reactant concentrations and k is the rate constant:
What is the primary purpose of using the method of initial rates in chemical kinetics?
What is the primary purpose of using the method of initial rates in chemical kinetics?
The integrated rate law directly relates the rate of a reaction to the concentrations of reactants.
The integrated rate law directly relates the rate of a reaction to the concentrations of reactants.
Explain how a catalyst affects the activation energy of a chemical reaction.
Explain how a catalyst affects the activation energy of a chemical reaction.
For a first-order reaction, the ______ is constant and independent of the initial concentration of the reactant.
For a first-order reaction, the ______ is constant and independent of the initial concentration of the reactant.
Match each type of reaction order with its corresponding integrated rate law expression:
Match each type of reaction order with its corresponding integrated rate law expression:
How does increasing the temperature generally affect the rate of a chemical reaction?
How does increasing the temperature generally affect the rate of a chemical reaction?
A homogeneous catalyst exists in a different phase from the reactants.
A homogeneous catalyst exists in a different phase from the reactants.
Describe the role of effective collisions in the context of collision theory.
Describe the role of effective collisions in the context of collision theory.
The minimum energy required for a chemical reaction to occur is called the ______ energy.
The minimum energy required for a chemical reaction to occur is called the ______ energy.
Match each statement with the type of catalysis it describes:
Match each statement with the type of catalysis it describes:
According to collision theory, what two factors determine whether a collision between reactant molecules will lead to a reaction?
According to collision theory, what two factors determine whether a collision between reactant molecules will lead to a reaction?
The transition state represents the lowest energy point along the reaction pathway.
The transition state represents the lowest energy point along the reaction pathway.
Describe how a heterogeneous catalyst typically interacts with reactant molecules.
Describe how a heterogeneous catalyst typically interacts with reactant molecules.
The Arrhenius equation, $k = Ae^{-E_a/RT}$, describes the relationship between the rate constant (k), temperature (T), and ______ energy ($E_a$).
The Arrhenius equation, $k = Ae^{-E_a/RT}$, describes the relationship between the rate constant (k), temperature (T), and ______ energy ($E_a$).
Match each term with its corresponding description in the context of chemical kinetics:
Match each term with its corresponding description in the context of chemical kinetics:
In a proposed reaction mechanism, what distinguishes an intermediate from a catalyst?
In a proposed reaction mechanism, what distinguishes an intermediate from a catalyst?
For a multi-step reaction, the rate-determining step is the fastest step in the mechanism.
For a multi-step reaction, the rate-determining step is the fastest step in the mechanism.
Explain the concept of pre-equilibrium in the context of reaction mechanisms.
Explain the concept of pre-equilibrium in the context of reaction mechanisms.
For the reaction $2Fe^{3+}(aq) + Sn^{2+}(aq) \rightarrow 2Fe^{2+}(aq) + Sn^{4+}(aq)$, if the rate of disappearance of $Fe^{3+}$ is $4.0 \times 10^{-4} M/s$, then the rate of appearance of $Sn^{4+}$ is ______ $M/s$.
For the reaction $2Fe^{3+}(aq) + Sn^{2+}(aq) \rightarrow 2Fe^{2+}(aq) + Sn^{4+}(aq)$, if the rate of disappearance of $Fe^{3+}$ is $4.0 \times 10^{-4} M/s$, then the rate of appearance of $Sn^{4+}$ is ______ $M/s$.
Match the rate-determining factors with their effects on reaction rate.
Match the rate-determining factors with their effects on reaction rate.
What is the overall order of a reaction with the rate law $Rate = k[A]^2[B]$?
What is the overall order of a reaction with the rate law $Rate = k[A]^2[B]$?
If a reaction is zero order with respect to a reactant, changing the concentration of that reactant will have no effect on the reaction rate.
If a reaction is zero order with respect to a reactant, changing the concentration of that reactant will have no effect on the reaction rate.
Explain how the method of initial rates is used to determine reaction orders.
Explain how the method of initial rates is used to determine reaction orders.
For a reaction with a rate law of $Rate = k[A][B]^2$, if the concentration of B is doubled and the concentration of A is halved, the reaction rate will be increased by a factor of ______.
For a reaction with a rate law of $Rate = k[A][B]^2$, if the concentration of B is doubled and the concentration of A is halved, the reaction rate will be increased by a factor of ______.
Match the graphical plot with the reaction order that yields a linear relationship:
Match the graphical plot with the reaction order that yields a linear relationship:
How does a catalyst increase the rate of a reaction?
How does a catalyst increase the rate of a reaction?
Enzymes are examples of heterogeneous catalysts.
Enzymes are examples of heterogeneous catalysts.
Describe how temperature affects the rate constant, k, according to the Arrhenius equation.
Describe how temperature affects the rate constant, k, according to the Arrhenius equation.
For a first-order reaction with a half-life of 69.3 seconds, the rate constant, k, is approximately ______ $s^{-1}$.
For a first-order reaction with a half-life of 69.3 seconds, the rate constant, k, is approximately ______ $s^{-1}$.
Match the concepts with their effects on half-life
Match the concepts with their effects on half-life
What is the role of the frequency factor (A) in the Arrhenius equation?
What is the role of the frequency factor (A) in the Arrhenius equation?
In a potential energy diagram, the activated complex exists at the minimum energy point.
In a potential energy diagram, the activated complex exists at the minimum energy point.
Explain how heterogeneous catalysts increase reaction rate at the surface.
Explain how heterogeneous catalysts increase reaction rate at the surface.
If a reaction's rate doubles when the temperature increases from 25°C to 35°C, it indicates a relatively ______ activation energy.
If a reaction's rate doubles when the temperature increases from 25°C to 35°C, it indicates a relatively ______ activation energy.
Match the catalyst with the reaction that it affects:
Match the catalyst with the reaction that it affects:
Flashcards
Chemical Kinetics
Chemical Kinetics
The study of reaction rates and mechanisms.
Reaction Rate
Reaction Rate
The change in concentration of reactants or products per unit time.
Rate Law
Rate Law
An equation that expresses the rate of a reaction in terms of the concentrations of the reactants.
Rate Constant (k)
Rate Constant (k)
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Overall Order of Reaction
Overall Order of Reaction
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Method of Initial Rates
Method of Initial Rates
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Integrated Rate Law
Integrated Rate Law
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Zero-Order Reaction
Zero-Order Reaction
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First-Order Reaction
First-Order Reaction
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Second-Order Reaction
Second-Order Reaction
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Half-Life
Half-Life
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Collision Theory
Collision Theory
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Activation Energy
Activation Energy
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Transition State
Transition State
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Effect of Temperature on Reaction Rates
Effect of Temperature on Reaction Rates
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Arrhenius Equation
Arrhenius Equation
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Catalyst
Catalyst
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Homogeneous Catalysis
Homogeneous Catalysis
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Heterogeneous Catalysis
Heterogeneous Catalysis
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Study Notes
- Chem 26 - Lecture Notes 02 discusses Chemical Kinetics
- Presented by TJ Sotelo from the Institute of Chemistry, College of Science, University of the Philippines Diliman
Learning Outcomes
- Explain the concept of chemical kinetics and reaction rate.
- Explain the effect on concentration of reactants based on the order of reaction.
- Apply the different methods in determining the reaction orders and rate law.
- Assess the effect of temperature on reaction rate.
- Differentiate homogeneous and heterogeneous catalysis.
The Rate of a Chemical Reaction
- Can be expressed in terms of rate of change of concentration of substances in the reaction with time.
- For the equation 2Fe³⁺(aq) + Sn²⁺(aq) → 2Fe²⁺(aq) + Sn⁴⁺(aq), the rate can be expressed as formation of one of the products Fe²⁺(aq) at time t.
- Given t=38.5 s; [Fe²⁺] = 0.0010 M; Δ[Fe²⁺] = (0.0010–0) M
- Rate of formation of Fe²⁺ = Δ[Fe²⁺]/Δt = 0.0010 M / 38.5 s = 2.6 × 10⁻⁵ Ms⁻¹
Rate and Stoichiometry
- Based on the stoichiometry of the reaction,
- 2Fe³⁺(aq) + Sn²⁺(aq) → 2Fe²⁺(aq) + Sn⁴⁺(aq)
- The rates of the appearance of each product and disappearance of each reactant can be written as:
- Δ[Sn⁴⁺]/Δt = ½ Δ[Fe²⁺]/Δt = - ½ Δ[Fe³⁺]/Δt = - Δ[Sn²⁺]/Δt
- As 2 moles of Fe²⁺ is produced per mole of Sn⁴⁺, the rate of appearance of Sn⁴⁺ will be half the rate of appearance of Fe²⁺
General Rule For Rate And Reaction And Stoichiometry
- Generally, for a reaction: aA + bB → gG + hH
- Rate of reaction = negative of rate of disappearance of reactants
-
- 1/a Δ[A]/Δt = - 1/b Δ[B]/Δt
- = rate of appearance of products
- 1/g Δ[G]/Δt = 1/h Δ[H]/Δt
Effect of Reactant Concentration on Reaction Rates: The Rate Law
- For a given reaction, aA + bB… → gG + hH ………, the effect of reactants concentration on rate of reaction can be written as:
- Rate of reaction = k[A]ᵐ[B]ⁿ...
- k: Rate constant
- [A] and [B] : molar concentrations of reactants A and B
- m: order of reaction with respect to reactant A
- n: order of reaction with respect to reactant B
- Overall order of reaction = m + n + …
Effect of Reactant Concentration on Reaction Rates: Order of Reaction
- Note that for the rate law, rate of reaction is not dependent on the stoichiometric coefficient a and b.
- The order of the reaction with respect to each reactant (m, n, ...) are determined experimentally.
- The exponents m, n, ... are usually small whole numbers but more complex reaction may have fractions.
- There will be cases when not all reactants will affect the rate of reaction.
Effect of Reactant Concentration on Reaction Rates: Example
- Consider the reaction: A + 3B + 2C → products
- R = rate of reaction = k[A]¹[B]²[C]⁰
- For above reaction, if m = 1 and n = 2, 0 = 0, rate law will be r= k[A][B]² and the order of the reaction is 3.
- The reaction is said to be first order of reaction with respect to A, and second order of reaction with respect to B.
- As o is zero, this means concentration of C does not affect rate of reaction. [C] does not appear in rate law. The reaction is zero order of reaction with respect to C.
General Effect of Double the Initial Concentration of a Reactant
- The following happens when the other reactant concentrations held constant:
- Zero order in the reactant: there is no effect on the initial rate of reaction.
- First order in the reactant: the initial rate of reaction doubles.
- Second order in the reactant: the initial rate of reaction quadruples.
- Third order in the reactant: the initial rate of reaction increases eightfold.
- R= k[A]¹[B]²[C]⁰
Methods of Determining Reaction Rate, Reaction Constant, and Order of Reaction
- Now that you understand conceptually rate law, following slides will show how to calculate rate of reaction and determine order of reaction given experimental data using below methods:
- Method of Initial Rates or Differential Rate Law
- Integrated Rate Law
Determining Rate Constant via Method of Initial Rate
- The initial rate is used so that the rate of reaction only depends on the forward reaction.
- At t ≈ 0 s, the reverse reaction is insignificant because no products are present yet.
- As the reaction proceeds, the rate slows down due to the presence of products, as shown in the lower slope at t ≈ 1200 s
- For the reaction 2 N₂O₅ (sol’n) → 4 NO₂ (sol’n) + O₂ (g) at 45 °C:
- The rate at [N₂O₅] = 0.90 M is Rate = 5.4 x 10⁻⁴ mol/L.s
- The rate at [N₂O₅] = 0.45 M is Rate = 2.7 x 10⁻⁴ mol/L.s
Method of Initial Rate: Example (1)
- For the reaction: NH₄⁺(aq) + NO₂⁻(aq) → N₂(g) + 2H₂O(l)
- Rate of reaction expression can be written as: Rate = k[NH₄⁺]ᵐ[NO₂⁻]ⁿ
- To determine m, find the experiment where [NO₂⁻] is constant, and [NH₄⁺] varies.
- By holding one reactant constant, the change in rate can be attributed to the reactant that varies.
- Calculate m by taking the ratio of the initial rates for selected Experiments that satisfy condition 1 and equate to the ratio of initial concentration of [NH₄⁺] for the same Experiments.
- DO steps 1 and 2 for n.
Table 1. Summary of initial rates from three experiments for the reaction, NH₄⁺(aq) + NO₂⁻(aq) → N₂(g) + 2H₂O(l)
| Expt no. | [NH₄⁺]₀ | [NO₂⁻]₀ | Initial rate (mol L⁻¹ s⁻¹) |
|---|---|---|---|
| 1 | 0.100 | 5.00 x 10⁻³ | 1.35 x 10⁻⁷ |
| 2 | 0.100 | 1.00 x 10⁻² | 2.70 x 10⁻⁷ |
| 3 | 0.100 | 1.00 x 10⁻² | 5.40 x 10⁻⁷ |
- Using data above, determine m and n, and the reaction order
- Calculate rate constant k
- (rate 3 / rate 2) = (0.200 M / 0.100 M)ᵐ = (5.40 x 10⁻⁷ mol/L.s / 2.70 × 10⁻⁷ mol/L.s)
- 2ᵐ = 2
- m = 1
- rate 2 / rate 1=(1.00 × 10⁻² M / 5.00 × 10⁻³M)ⁿ = (2.70 x 10⁻⁷ mol/L.s / 1.35 × 10⁻⁷ mol/L.s )
- 2ⁿ = 2
- n = 1
- Rate of reaction = k = 1.35 x 10⁻⁷ mol/L.s / (0.100 M)(5.00 × 10⁻³M)
- k = 2.70 × 10⁻⁴M⁻¹s⁻¹
- Note that the unit of rate constant depends on the total order of reaction.
Concentration of Reactants: The Rate Law Expression (1)
- The following rate data were obtained at 25°C for the following reaction.
- What are the rate-law expression and the specific rate-constant for this reaction?
- 3 X(g) + Y(g) → 2 Z(g) | Expt no. | [X]₀ | [Y]₀ | Initial rate of formation of Z (mol L⁻¹ s⁻¹) | | :-------: | :----: | :----: | :---------------------------------------: | | 1 | 0.100 | 0.100 | 2.00 x 10⁻⁴ | | 2 | 0.200 | 0.300 | 4.00 x 10⁻⁴ | | 3 | 0.100 | 0.200 | 2.00 x 10⁻⁴ |
- Solve for the overall order of the reaction and for the reaction constant.
- Rate = k[X]ᵐ[y]ⁿ
- To We want to solve for n but there is something strange with the data. The rate does not change when [Y] is doubled hence n = 0
- (rate 2 / rate 1) = (0.200 M / 0.100 M)ᵐ = (4.00 × 10⁻⁴ mol/L.s / 2.00 × 10⁻⁴ mol/L.s)
- 2ᵐ = 2
- m = 1
- Rate = k[X] and the overall reaction order is 1.
- k = Rate/ [X]
- k = (2.00 × 10⁻⁴M/s) / (0.100 M) = 2.00 × 10⁻³s⁻¹
- Take note of the units, the units of rate constant depends on the total order of reaction.
More Examples
- The following rate data were obtained at 25°C for the following reaction.
- What are the rate law expression and the specific rate-constant for this reaction?
- 2A(g) + B(g) → 3C(g) | Expt no. | [A]₀ | [B]₀ | Initial rate of formation of C (mol L⁻¹ s⁻¹) | | :-------: | :----: | :----: | :-----------------------------------------: | | 1 | 0.100 | 0.100 | 2.00 x 10⁻⁴ | | 2 | 0.100 | 0.200 | 8.00 x 10⁻⁴ | | 3 | 0.200 | 0.100 | 4.00 x 10⁻⁴ |
- The following rate data were obtained at 25°C for the following reaction.
- What are the rate law expression and the specific rate-constant for this reaction?
- 2A(g) + B(g) + 2C(g) → 3D(g) + 2E(g) | Expt no. | [A]₀ | [B]₀ | [C]₀ | Initial rate of formation of D (mol L⁻¹ s⁻¹) | | :-------: | :----: | :----: | :----: | :------------------------------------------: | | 1 | 0.200 | 0.100 | 0.100 | 2.00 x 10⁻⁴ | | 2 | 0.200 | 0.300 | 0.200 | 6.00 x 10⁻⁴ | | 3 | 0.200 | 0.100 | 0.300 | 2.00 x 10⁻⁴ | | 4 | 0.600 | 0.300 | 0.400 | 1.80 x 10⁻³ |
Additional notes on rate constant
| Order of the reaction (x) | Rate constant unit |
|---|---|
| 0 | M s⁻¹ |
| 1 | s⁻¹ |
| 2 | M⁻¹ s⁻¹ |
| 3 | M⁻² s⁻¹ |
- General equation: L⁽ˣ⁻¹⁾ mol⁽¹⁻ˣ⁾s⁻¹
- L is Liters, mol is molecules and s is seconds
Integrated Rate Law
- For this method, the order of reaction, the rate constant, k, can be obtained by plotting graphs.
ZERO-ORDER REACTIONS
- [A] = -kt + [A]₀ , y = mx + b, Plot [A] vs. time
- For Zero-Order Reaction, k equals to the negative slope of the plot of concentration vs. time.
- Rrxn = k[A]⁰
- As rate is independent of [A], calculate slope from initial concentration, [A]₀, at a certain final time.
- Rrxn = (0 - [A]₀) / (tf - 0) = [A]₀ / tf
- k = mol L⁻¹ s⁻¹
FIRST-ORDER REACTIONS
- For first-order reactions, a plot of concentration vs. time, yields a non-linear equation as shown below.
- A linear equation is obtained if natural log of concentration is plotted against time.
- Rate constant, k, is negative
- rate = Δ[A]/Δt = k[A]
- ln [A] = -kt + ln [A]₀ , y = mx + b, Plot In [A] vs. time
EXAMPLE FOR A FIRST ORDER REACTION
- In the graph on the left, rate constant, k, can be calculated from the slope of plot of In[H₂O₂] vs time.
- k = 7.3 × 10⁻⁴ s⁻¹
- Note that sign of rate constant is opposite of the slope = -1.095 / 1500 s = 7.30 × 10⁻⁴s⁻¹
HALF LIFE FOR FIRST ORDER REACTION (1)
- The time taken for one-half of a reactant to be consumed.
- ln ([A]t / [A]₀) = -kt
- ½ [A]₀ : ln ([A]₀ / [A]₀)) = -kt₁/₂
- -ln2 = -kt₁/₂
- t₁/₂= ln2/k = 0.693/k
- Half-life expression for 1st order reactions are not dependent on reactant concentration.
- Used for radioactive decay.
HALF LIFE FOR FIRST ORDER REACTION (2)
- To give you idea of magnitude of half lives and their rate constants, below are some examples of first order reactions. (See table on slide)
- Hydrolysis of sucrose at 15 °C half-life, takes 8.4 hours while dissociation of acetic acid is instantaneous.
HALF LIFE FOR FIRST ORDER REACTION (3)
- The images below depict first-order reaction A → B at various times during the reaction process.
- The black circles represent reactant A, and the red circles represent product B.
- What is the half-life of the reaction?
- What is k for the reaction?
- What happens to k when the initial concentration of A is doubled?
SECOND ORDER REACTIONS
- Rate constant, k, is equal to the slope of plot of 1/[A] vs. time
- Rate = Δ[A] / Δt = k[A]²
- 1/[A] = kt + 1/[A]₀
Rate Law Summary Table
(See Table on slide)
Rate Equations to Determine Rate Order – Example (1)
- Concentration and time data for the thermal decomposition of ethyl bromide: C₂H₅Br(g) → C₂H₄(g) + HBr(g) at 700K. | Time (min) | 0.0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | | :---------: | :---: | :----: | :----: | :----: | :---: | :----: | | [C₂H₅Br] | 1.0 | 0.82 | 0.67 | 0.55 | 0.45 | 0.37 |
- Determine the order of the reaction and the value of the rate constant graphically.
Rate Equations to Determine Rate Order – Example (2)
- Should plot the following and determine the best fit by calculating R².
- Then, determine the rate order and rate constant:
- [C₂H₅Br] vs. time, ln[C₂H₅Br] vs.time, 1/[C₂H₅Br] vs.time | Time (min) | 0.0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | | :-------------: | :---: | :---: | :---: | :---: | :---: | :---: | | [C₂H₅Br] | 1.0 | 0.82 | 0.67 | 0.55 | 0.45 | 0.37 | | ln[C₂H₅Br] | 0.0 | -0.20 | -0.40 | -0.60 | -0.80 | -0.99 | | (1/[C₂H₅Br]) | 1.0 | 1.2 | 1.5 | 1.8 | 2.2 | 2.7 |
Rate Equations to Determine Rate Order – Example (3)
- The plot is generated shown in the slide. Which one is the best model fit?
Rate Equations to Determine Rate Order – Example (4)
- The best fit is the plot of ln [C₂H₅Br] vs. time.
- Therefore, the reaction is first-order with respect to C₂H₅Br.
- Take the slope to get the rate constant for the reaction.
- Two ways to do it: Plotting through linear regression & Point-slope equation.
Rate Equations to Determine Rate Order – Example (5)
| Time (min) | 0.0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 |
|---|---|---|---|---|---|---|
| ln[C₂H₅Br] | 0.0 | -0.20 | -0.40 | -0.60 | -0.80 | -0.99 |
- Plotting through linear regression, the following equation is derived:
- y = -0.1991x - 0.0005
- k ≈ 0.20 /min
- Point-slope equation:
- m = y - y₁ / x - x₁ = 0 + 0.80 / 0 - 4.0 = −0.20
- k = 0.20 /min
Rate Equations to Determine Rate Order – Example 2
- Concentration and time data for the decomposition of nitrogen dioxide: 2NO₂(g) → 2NO + O₂(g) at 500K | Time (min) | 0.0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | | :---------: | :---: | :----: | :----: | :----: | :----: | :----: | | [NO₂] | 1.0 | 0.53 | 0.36 | 0.27 | 0.22 | 0.18 |
- Determine the order of the reaction and the value of the rate constant graphically.
Rate Theories – Collision Theory (1)
- Collision Theory states that for reaction to occur:
- Particles must collide
- Particles must have sufficient energy
- Particles must have right orientation
- Billiards Analogy: sinking of ball in pocket.
- Cue ball needs to collide with a ball at the right orientation and with enough energy.
Rate Theories – Activation Energy
- For a reaction to occur, there must be a redistribution of energy sufficient to break certain bonds in the reacting molecule(s).
- Activation Energy: The minimum energy above the average kinetic energy that molecules must bring to their collisions for a chemical reaction to occur.
Rate Theories – Transition State Theory (1)
- Transition State or Activated Complex: The state where the chemical bonds between reactants are breaking and the chemical bonds of the products are forming.
- For the following reaction: AA(g) + BB(g) → 2AB(g)
- A-A + B-B ⇄ A--A--B---B ⇄ 2A-B
- Transition State
- The energy of the transition state is much higher than the energy of the reactants and the products
Rate Theories – Transition State Theory (2)
- The activation energy, Ea of forward reaction is the difference between the energy of transition state and the energy of the reactant.
- A reaction profile for the reaction N₂O(g) + NO(g) → N₂(g) + NO₂(g)
- To determine the Ea of the reverse reaction, add the Ea of the forward reaction and Heat of enthalpy of reaction.
- Note that Ea is always positive, (Ea,rev = |-139 kJ| + 209 kJ = 348 kJ)
Rate Theories – Effect of Temperature
- Temperature will influence reaction rates.
- Svante Arrhenius conducted several experiments to investigate the relationship of temperature, activation energy, and rate constant.
- As temperature increases, the fraction of molecules with enough energy to surmount the activation energy barrier also increases.
Effect of Temperature on Reaction Rates (1)
- Based on his experimental data, Arrhenius introduced the equation: k = Ae^(-Ea/RT)
- T = Temperature in Kelvin
- R = Ideal gas constant (8.314 J mol⁻¹ K⁻¹)
- A = Arrhenius constant that accounts for collision frequency
- Taking the natural log of each side of the equations yields: lnk = -Ea/RT + lnA
Effect of Temperature on Reaction Rates (2)
- Based on the previous equation, the activation energy, Ea can be obtained from the plot of In K vs. 1/T. The plot is for the reaction: N₂O₅(CCl₄) → N₂O₄(CCl₄) + ½ O₂(g) at -1.2 × 10⁴K.
- Slope = -6.2/0.50 × 10⁻³K⁻¹ = -1.2 × 10⁴K
- Ea = 1.0 × 10² kJ/mol
Effect of Temperature on Reaction Rates (3)
- k = Ae^(-Ea/RT)
- lnk = -E/RT + lnA
- At two different temperatures, ratio of In of k can be expressed as:
- lnk₂ - lnk₁ = - Ea/R * (1/T₂) + lnA - [ - Ea/R * (1/T₁) + lnA]
- ln (k₂ / k₁) = - Ea/R * [1/T₂ - 1/T₁]
Effect of Temperature on Reaction Rates – Example (1)
- (CH₃)₃CBr + OH⁻ → (CH₃)₃COH + Br⁻, in a certain solvent is first order with respect to CBr and zero order with respect to OH⁻.
- In several experiments, the rate constant, k, was determined at different temperatures.
- A plot of Ink vs T⁻¹ was constructed resulting in a straight line with a slope value of -1.10 × 10⁴ K and a y-intercept value of 33.5.
- The rate constant has units of s⁻¹.
- Determine the activation energy for this reaction.
- Determine the value of the frequency factor.
- Calculate the value of k at 25°C
- Calculate value of k at 400 °K using k value obtained for c.
Effect of Temperature on Reaction Rates – Example (2)
The reaction, Cl(g) + H₂(g) → HCl(g) + H(g), was observed under various temperatures. The rate constants at different temperatures are tabulated below.
| T(K) | 90.0 | 100 | 110------- | 122------- |
|---|---|---|---|---|
| k(M⁻¹s⁻¹) | 3.57 x 10⁻³ | 7.73 x 10⁻² | 9.56 x 10⁻¹ | 7.78--- |
- What is the order of the reaction?
- Determine the activation energy for this reaction.
- Determine the value of the frequency factor.
CATALYST
- Gives an alternative reaction pathway of lower energy.
- Homogeneous catalysis - all species in the reaction are in solution.
- Heterogeneous catalysis
- The catalyst is in the solid state.
- Reactants from gas or solution phase are adsorbed.
- Active sites on the catalytic surface are important.
HOMOGENOUS CATALYSIS (1)
- Protonation of hydroxyl O allows easier breakage of bond and supplies H for H₂O
- The acid catalyst accelerated reaction by changing reaction pathway, from one step reaction with large Ea, to 3 steps reaction, with smaller Ea
HOMOGENOUS CATALYSIS (2)
- IMFA hold the substrate in place and form an enzyme-substrate complex
- After the reaction occurs, the products are released from the active site
- Enzymes are highly specific with high rates of reaction
HETEROGENOUS CATALYSIS
- It is usually a metal surface catalyst
- Reactants are adsorbed and products desorbed
- Metal catalyst lowers activation energy by immobilizing and orienting reactants
QUESTION
- A reaction that has a rate only dependent on catalyst will be...
- Zero order reaction
SUMMARY
- An equation that can be used to predict the relationship between the rate of reaction and the concentrations of reactants is called the Rate Law.
- Initial Rates Method and Integrated rate law are two methods used to determine reaction rate constant and order of reaction.
- Collision Theory and Transition State Theory provide theoretical models of chemical kinetics.
- Arrhenius equation show relationship between Ea, temperature and rate constant, k ; k = Ae^(-Ea/RT)
- Catalysts speed up reaction by providing alternative pathways with lower activation energy, Ea.
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