Differential Rate Law
Related Examples and Practice Problems
Additional Worked Out Examples/ Practice
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Separation techniques: Selected and explaining limitation of appropriate separation
Relating Properties to Composition: Predicting classification based on descriptive properties
Topic Summary & Highlights
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Core Concept
The differential rate law expresses the reaction rate as a function of the concentrations of reactants.
General Form: ${Rate} = k[\text{A}]^m[\text{B}]^n$
k: Rate constant.
[A] and [B]: Concentrations of reactants.
m and n: Reaction orders with respect to A and B.
m+n: Overall order of the reaction.
Practice Tips
Memorize Units: Know the units of k for different reaction orders.
Confusing reaction order with stoichiometric coefficients: Reaction order is determined experimentally and does not always match the coefficients in the balanced chemical equation.
Neglecting units of k: Always confirm the units of k match the reaction order.
Assuming all reactions follow simple rate laws: Complex reactions may involve mixed or fractional orders.
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LABORATORY
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Reaction Orders and Their Meanings
Zero-Order Reaction:
Rate Law: Rate=k
Dependence: Reaction rate is independent of reactant concentration.
Example: Decomposition of a reactant on a saturated catalyst surface.
First-Order Reaction:
Rate Law: Rate = k[A]
Dependence: Reaction rate is directly proportional to the concentration of the reactant.
Example: Radioactive decay or unimolecular reactions.
Second-Order Reaction:
Rate Law: $\text{Rate} = k[\text{A}]^2$ -or- $\text{Rate} = k[\text{A}][\text{B}]$
Dependence: Reaction rate is proportional to the square of one reactant's concentration or the product of two reactants' concentrations.
Example: Bimolecular reactions in solutions.
3. Determining the Rate Law
Method 1: Initial Rates Method
Steps:
Perform experiments by varying initial concentrations of reactants.
Measure the initial rate of the reaction for each experiment.
Compare how the rate changes with changes in concentration to determine reaction orders mmm and nnn.
Example Calculation: If doubling [A] doubles the rate, m=1 (first order with respect to A). If doubling [B] quadruples the rate, n=2 (second order with respect to B).
Determining the Rate Law
Method 1: Initial Rates Method
Steps:
Perform experiments by varying initial concentrations of reactants.
Measure the initial rate of the reaction for each experiment.
Compare how the rate changes with changes in concentration to determine reaction orders mmm and nnn.
Example Calculation: If doubling [A] doubles the rate, m=1 (first order with respect to A). If doubling [B] quadruples the rate, n=2 (second order with respect to B).
