# Enduring Understanding 4.A: Reaction Rates

• Chemical reactions vary widely in the speed at which they occur.
• The reaction rate is defined as the change in concentration of a substance divided by the time interval:
• Rate = Δ concentration / Δ time

• Reactions can be examined experimentally to determine their rate. If a reactant or product is colored, it can be followed by spectrometry using Beers Law.
• Factors that influence a rate of reaction include:
• Concentration of reactants (except in zero order processes)
• Pressure (for reactions involving gases)
• Surface area (for a solid)
• Temperature (increased temperature = faster reaction)
• Presence of a catalyst.

• Example: A reaction in a closed container, A→2B, is monitored for 60 seconds, giving the following results. What concentrations of A and B are present at 90 seconds?
• Time, seconds [A], mol/L [B], mol/L
0 2.00 0
30 1.00 2.00
60 0.50 3.00
90 ? ?
• Every 30 seconds, the concentration of A drops by half and the concentration of B increases by twice the drop in A.
• Therefore, after 90 seconds, [A] will be 0.25 mol/L and [B] will be 3.50 mol/L.
• The rate of a chemical reaction can be expressed mathematically by a rate law. For the reaction:
• A + B → C

• The rate law for this reaction would take the form rate = k[A]x[B]y
• k is the specific rate constant, the rate when [A] and [B] are 1.
• The exponents, x and y, are the order of the reaction with respect to that reactant. The sum of the exponents, x + y, is the overall order of the reaction.
• If x = 0, doubling [A] has no effect on the rate (zero order)
• If x = 1, doubling [A] doubles the rate (first order)
• If x = 2, doubling [A] increases the rate by 22 or four times (second order).
• Example: For the reaction:
• O2 + 2NO → NO2
• The rate equation is k[O2][NO]2
• If the concentration of O2 doubles, the rate doubles.
• If the concentration of NO doubles, the rate increases by 22, or quadruples.
• The overall order of the reaction is 3.
• Rate laws cannot be determined from the chemical equation; they must be determined experimentally.
• Sample Question: Give the following data, what is the rate law for the reaction:
• A + B + C → D

[A][B][C]Initial Rate (mol/s)
0.100.100.105.0
0.200.100.1020.0
0.200.200.1040.0
0.200.200.2040.0
• Doubling [A] quadruples the rate, so the order of A is 2.
• Doubling [B] doubles the rate, so the order of B is 1.
• Doubling [C] has no effect on the rate, so the order of C is zero.
• The rate law must therefore be k[A]2[B]

• Radioactive decay is an example of a first-order process. The time taken for half of a sample of a radioactive isotope to decay is called the half-life.
• The amount of a sample remaining after n half-lives is given by the equation:
• Amount remaining = (1/2n) x original amount

 Related Links: Chemistry Chemistry Quizzes AP Chemistry Notes Redox Reactions

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