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Questions and Answers
What is the expression for the rate constant k in terms of the concentrations [Ao], [At], and time t for a first-order reaction?
How is the half-life of a first-order reaction defined?
If the initial concentration [Ao] is doubled, how does this affect the half-life of a first-order reaction?
Which equation relates the concentrations of reactants at different times for a first-order reaction?
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What does k represent in the context of a first-order reaction?
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For a first order reaction, what is the relationship between the rate constant (k) and the half-life (t1/2)?
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Which of the following best describes a zero order reaction?
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What type of graph would you use to illustrate the relationship between log [A]t and time for a first order reaction?
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How is the rate of reaction affected at double the initial concentration ([A]0) for a first order reaction?
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In the integrated rate law for a first order reaction, what is the significance of the slope in the graph of log [A]0 versus time?
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Study Notes
First Order Reaction
- Rate Law: Rate = k[A]
- Integrated Rate Law: ln[A]t - ln[A]o = -kt
- Half-life: t1/2 = 0.693/k
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Graphical Representation:
- Rate vs Initial Concentration: Linear graph with slope = k
- Concentration vs Time: Exponential decay curve
- Log[A]o vs Time: Linear graph with slope = k/2.303
- Log[A]t vs Time: Linear graph with slope = -k/2.303
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Examples:
- 2H2O2(l) → 2H2O(l) + O2(g)
- 2N2O5(g) →4NO2(g) + O2(g)
- Gaseous Phase Reaction: k = 2.303/t * log10(Pi / (2Pi - P))
Zero Order Reaction
- Rate Law: Rate = k
- Integrated Rate Law: kt = [A]o - [A]t
- Half-life: t1/2 = [A]o / 2k
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Graphical Representation:
- [A]t vs Time: Linear graph with slope = -k
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Examples:
- Decomposition of ammonia (NH3) on Platinum metal surface: 2NH3(g) → N2(g) + 3H2(g)
- Decomposition of Nitrous oxide in the presence of Platinum(Pt) catalyst: 2N2O(g) → 2N2(g) + O2(g)
Pseudo-First Order Reaction
- A reaction that follows first order kinetics despite having two or more reactants.
- Occurs when one reactant is present in significant excess, rendering its concentration essentially constant.
- Example: CH3COOCH3 (aq) + H2O(l) → CH3COOH(aq) + CH3OH(aq)
Units of Rate Constants
- General Formula: Unit = (mol/L)1-n s-1, where n = order of reaction
- Zero Order: mol/L * s
- First Order: s-1
- Second Order: L/mol * s
- Third Order: L2/mol2 * s
Collision Theory of Bimolecular Reactions
- Collision is necessary for reaction: Rate of Reaction = Rate of Collision
- Activation Energy (Ea): Minimum kinetic energy for reaction to occur
- Proper Orientation: Reactant molecules must be aligned correctly for a successful reaction.
- Activated Complex: Transient species formed when reactant molecules collide with sufficient energy and orientation.
Arrhenius Equation
- k = A * exp(-Ea/RT): Relationship between rate constant, temperature, and activation energy
- A: Frequency factor
- Ea: Activation Energy
- R: Gas constant
- T: Temperature (in Kelvin)
Graphical Determination of Activation Energy
- ln(k) vs 1/T: Linear graph with slope = -Ea/R
- log10(k) vs 1/T: Linear graph with slope = -Ea/2.303R
- Activation Energy can be calculated from the slope of the graph: Ea = -slope * 2.303 * R
Effect of Temperature on Reaction Rate
- Higher temperature: Increased kinetic energy, greater fraction of molecules exceed activation energy, faster reaction rate
- Lower temperature: Decreased kinetic energy, smaller fraction of molecules exceed activation energy, slower reaction rate
Summary
- Reaction order: Describes how the rate of a reaction changes with concentration.
- Integrated rate laws: Describe the relationship between reactant concentration and time.
- Half-life: Time taken for the concentration of a reactant to decrease to half its initial value.
- Collision theory: Explains the relationships between reactant concentration and reaction rate.
- Arrhenius Equation: Predicts the effect of temperature on reaction rate.
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