# AP Chemistry Unit 5.3 Concentration Changes Over Time

First-Order Rate Law

• Order = 1 → changing the reactant concentration has an identical effect on the reaction rate (same factor)
• Rate Law =
• If a plot of ln[A] versus time is a straight line → reaction is first order
• Integrated First Order rate law: (on reference sheet)
• Subzero = initial molarity
• Sub t = molarity after some time has gone by
• Y = mx + b
• Rate constant = slope of line; y-int = initial value of molarity

Half-Life of a First-Order Reaction

• Half life: the time required for a reactant to reach half its original concentration (on RFS)
• The half-life of a 1st-order reaction is only dependent on K (NOT on concentration)
• A constant time is required to reduce the concentration of the reactant by half, and then by half again
• All type of radioactive decay is first-order

Second-Order Reaction

• Order = 2 → changing reactant concentration will affect the reaction rate to the square of the change in the reactant
• Rate Law: Rate =
• Integrated Rate Law: (on ref. sheet)
• If a plot of 1/[A] versus time is a straight line → reaction is second order

Half-Life of a Second Order Reaction

• (not on RFS)
• The half-life of a second-order reaction depends on both K and the initial concentration [A]₀
• Finding half-life of 2nd order reaction → Pick any value for initial, plug in value for final answer that is half of initial value
• To find half-life must be given value of k

Zero-Order Rate Law

• Order = 0 → a change in reactant concentration has no effect on the rate
• Reactant will not appear in the overall rate law for the equation
• Rate Law: Rate = k
• Integrated rate law is :
• If a plot of [reactant] versus time is a straight line → reaction is zero-order
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