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Kinetics. Ways to Express Rates. Relative Average Instantaneous. More commonly, rates are expressed by a rate law or rate expression – two methods: Differential – expresses how rate depends on initial concentration Integrated – expresses how concentration depends on time.
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Ways to Express Rates • Relative • Average • Instantaneous • More commonly, rates are expressed by a rate law or rate expression– two methods: • Differential – expresses how rate depends on initial concentration • Integrated – expresses how concentration depends on time
Initial rxn rate = k[A]om[B]on k = rate constant [A] = initial concentration of reactant A [B] = initial concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B
Exponents (orders) can be zero, whole numbers, or fractions -- AND MUST BE DETERMINED BY EXPERIMENTATION!!
THE RATE CONSTANT, k Is temperature dependent & must be evaluated by experiment. The units of k depend on the rate law and the units in which the data was collected
Differential • Experiment and rate change
Zero order • The change in concentration of reactant has no effect on the rate. • These are not very common. • General form of rate equation: Rate = k[A]0 = k
First order • Rate is directly proportional to the reactants concentration; doubling [rxt], doubles rate. These are very common! Nuclear decay reactions usually fit into this category. • General form of rate equation: Rate = k [A]1 = k[A]
Second order • Rate is quadrupled when [rxt] is doubled and increases by a factor of 9 when [rxt] is tripled, etc. These are common, particularly in gas-phase reactions. • General form of rate equation: Rate = k [A]2
12.4 INTEGRATED RATE LAW -CONCENTRATION/TIME RELATIONSHIPS When we wish to know how longa reaction must proceed to reach a predetermined concentration of some reagent, we can construct curves or derive an equation that relates concentration and time.
Graphical methods fordistinguishing FIRST, SECOND and ZERO order reactions First order: ln[A] = -kt + ln[A]o (y = ax + b) ln[reactant] vs. time straight line for first order in that reactant & since a = -k the slope of the line is negative. ln[A] t
Second order: 1/[A] = kt + 1/[A]o (y = ax + b) 1/[reactant] vs. time straight line for second order in that reactant since a = k the slope is positive. 1 [A] t
Zero order: [A] = -kt + [A]o (y = ax + b) [A] vs. time straight line for zero order in that reactant & since a = -k the slope of the line is negative [A] t
Half-life and reaction rate for FIRST-ORDER REACTIONS, t1/2 rate = k[A]1 integrated rate law is: ln[A] = -kt + ln[A]o k = ln2 t ½ = .693 t ½ k
Mechanisms • Rate determining step is the slowest step • It will reflect the rate law
2 H2(g) + 2 NO(g) N2(g) + 2H2O(g) Possible mechanism 2 NO(g) N2O2(g) N2O2(g) + H2(g) N2O(g) + H2O(g) N2O(g) + H2(g) N2(g) + H2O(g)
H2O2 + Br-1 BrO-1 + H2O H2O+ BrO-1 Br-1 + H2O+ O2 Overall reaction? Catalysts? Intermediates?