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Simple Explanation:
Introduction to Reaction Rates
Instantaneous Reaction Rate: Measures the rate of a reaction at a specific moment in time. Think of it as a frame of how fast the reaction is happening at a given point.
Average Reaction Rate: Measures the average rate of a reaction over a period of time.
Formula: Rate = Δ[A]/Δt (Slope Formula)
Δ (capital Delta sign) represents change. So, it's the average change in concentration of reactant A divided by the change in time (t) over the period.
Demonstration of Reaction Rate Relationships
Relationships between reaction rates depend on stoichiometry. According to the coefficients of 2H₂O₂ → 2H₂O + O₂:
The rate of O₂ is half that of H₂O, because for every O₂ molecule produced, 2 H₂O molecules are produced.
H₂O is being created at the same rate as H₂O₂ decomposing, as both compounds have a coefficient of 2.
In kinetics, we only determine rates based on experimental data. This also means that no calculations are theoretical.
Differential Rate Law
This law represents how the rate of a reaction changes with the concentration of reactants over a particular time period.
Here is the formula for the differential rate law:
Rate = k[A]ˣ[B]ʸ[C]ᶻ
[A], [B], [C]: Concentration of reactants A, B, and C.
x, y, z: Reaction orders, indicating how the rate of the reaction is affected by the concentration of each reactant.
k: Rate constant, proportional to the concentration and rate of a reaction. Therefore, it has a specific and unique value for each reaction.
Zero-Order: Unit of k is M/s
First-Order: Unit of k is s⁻¹
Second-Order: Unit of k is M⁻¹s⁻¹
M stands for molarity, s stands for second(s).
Example of Writing Rate Laws:
NO + O₂ → 2NO₂, given that: reaction order of NO is 1, reaction order of O₂ is 2.
Rate = k[NO][O₂]²
2H₂ + O₂ → 2H₂O, given that: reaction order for H₂ is 1, reaction order for O₂ is 2.
Rate = k[H₂][O₂]²
NOTE: For questions using the differential rate law, the values of initial rates of reactions and molarity of substances must be given.
Solving Differential Rate Law Questions:
We run two trials of the reaction A + B → C.
If doubling [A] makes the rate stay the same: [A] is zero-order.
If doubling [A] doubles the rate: [A] is first-order.
If doubling [A] quadruples the rate: [A] is second-order.
Exponents on the differential rate laws add up to determine the overall reaction order.
For example, Rate = k[A][B] is second-order since 1 + 1 = 2, Rate = k[A][B]² is third-order since 1 + 2 = 3)
Integrated Rate Laws
These laws describe how the concentration of reactants changes over time for different orders of reactions.
Key:
t: time
k: Rate constant, proportional to the concentration and rate of a reaction.
[A]: Concentration of Reactant A.
When plotted on a concentration versus time graph with the concentration labeled according to the appropriate reaction order, the reactions can display linear relationships.
These concentrations could be measured with various methods, such as:
Spectrophotometry: Measures the absorption of light in a solution during a reaction that changes color. These measurements could indicate the concentration of a substance at any given time, as light absorption is directly correlated with concentration (based on the Beer-Lambert Law).
Characteristics of Reaction Orders (With Graph Visualizations)
Zero-Order Reactions
The rate is constant and only determined by the value of 𝑘, independent of the concentration of the reactant.
Rate Law: Rate = k
Integrated Rate Law: [A]ₜ - [A]₀ = -kt
Graph: Negatively linear when concentration is measured in [A].
Slope = -k
First-Order Reactions
The rate is proportional to the concentration of one reactant and is determined by 𝑘 times the concentration.
Rate Law: Rate = k[A]
Integrated Rate Law: ln[A]ₜ - ln[A]₀ = -kt
Graph: Negatively linear when concentration is measured in ln[A].
Slope = -k
Second-Order Reactions
The rate is determined by 𝑘 times the concentration squared.
Rate Law: Rate = k[A]² (or Rate = k[A][B] if two reactants contribute)
Integrated Rate Law: 1/[A]ₜ - 1/[A]₀ = -kt
Graph: Positively linear when concentration is measured in 1/[A] (aka [A]⁻¹).
Slope = k
To summarize, differential rate laws show how reaction rates depend on concentrations, while integrated rate laws show how concentrations change over time.
Half Life for First-Order Reactions:
We can calculate the half-life of a first-order reaction by:
Formula: t½ = 0.693/k
t with subscript ½ means half-life time.
k: Rate constant.
To solve for how much time it takes a sample to decay into a certain mass, use the half-life formula to solve for k and then use the integrated rate law for first-order reactions (ln[A]ₜ - ln[A]₀ = -kt) to solve for t.
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