Zero Order (0)
First Order (1st)
Second Order (2nd)
Final Concentration [A]t
Initial Concentration [A]0
Rate Constant (k)
Time (t)
Result:
Understanding Integrated Rate Laws
In chemical kinetics, the rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. However, to determine how the concentration changes over a specific period, we use Integrated Rate Laws. These mathematical expressions allow chemists to calculate the amount of reactant remaining after a certain time, or the time required for a reaction to reach a specific concentration.
Types of Reaction Orders
The behavior of a reaction depends on its order, which is determined experimentally:
Zero-Order Reactions: The rate is independent of the reactant concentration. Doubling the concentration has no effect on the speed of the reaction.
First-Order Reactions: The rate is directly proportional to the concentration of one reactant. These are common in radioactive decay and many biological processes.
Second-Order Reactions: The rate is proportional to the square of the concentration of one reactant, or the product of two different reactants.
The Mathematical Formulas
Order
Integrated Law Formula
Linear Plot
Zero
[A]ₜ = -kt + [A]₀
[A] vs. t
First
ln[A]ₜ = -kt + ln[A]₀
ln[A] vs. t
Second
1/[A]ₜ = kt + 1/[A]₀
1/[A] vs. t
Example Calculation
Scenario: A first-order reaction has a rate constant (k) of 0.025 min⁻¹. If the initial concentration [A]₀ is 0.80 M, what is the concentration after 30 minutes?
Solution:
Using the first-order formula: ln[A]ₜ = -kt + ln[A]₀
ln[A]ₜ = -(0.025)(30) + ln(0.80)
ln[A]ₜ = -0.75 + (-0.2231) = -0.9731
[A]ₜ = e^(-0.9731) ≈ 0.378 M
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if (order === 0) {
// [A]t = -kt + [A]0
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label = "Rate Constant (k)";
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// ln[A]t = -kt + ln[A]0
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label = "Initial Concentration [A]₀ (M)";
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label = "Rate Constant (k)";
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label = "Final Concentration [A]ₜ (M)";
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label = "Initial Concentration [A]₀ (M)";
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