Chapter 12: Chemical Kinematics
- Three fundamental questions related to chemical reactions:
o What happens? – balanced chemical equation.
o To what extent does it happen? – chemical equilibrium.
o How fast does it happen? – chemical kinetics.
- How does concentration and temperature affect rates of reactions?
- How is a mechanism proposed using rate data?
12.1 – Reaction Rates
- Reaction rate is determined by Δ[reactant/product]/Δ time.
- Δ  with time can be determined by the Δ pressure as gas molecules are produced.
- Reaction rate is either an increase in [product] or a decrease in [reactant] measure in mol/Ls.
o Rate of formation = Δ*Product+/Δt.
o Molar coefficients show the rate in respect to that of another reactant or product.
o Rate is always positive, therefore the rate of decomposition = -Δ*Reactant+/Δt.
- The general rate of reaction is the rate of one reactant or product, divided by the coefficients of
the other reactants/products.
o Eg) For 2N2O 5(g)4NO 2(g) O 2(g),O 2/Δt = -(1/2)(Δ*N 2 5/Δt) = (1/4)(Δ*NO ]2Δt+
- Rate changes as reaction proceeds.
- Depend on [reactions] and decreases as reactants are used up.
- Instantaneous rate is over a specific time t rather than an interval.
12.2 – Rate Laws and Reaction Order
- Rate law represents the dependence of rate on .
- If the reaction is aA+bB products, then Rate = -Δ*A+/Δt = - Δ*B+/Δt = k[A] [B] (because 
o k = rate constant.
o m and n show how sensitive the rate is the Δ*reactants+.
in this case, m and n are unrelated to the coefficients.
o If m or n is one, the rate depends linearly on [reactant].
Eg) if m=1 and [A] doubles, then the rate doubles as well.
Eg) if m=2 and [A] doubles, then the [A] is quadrupled and the rate increases by
a factor of 4.
o Rate is proportional to [A] or [B] .
- m and n give the respective reaction orders.
- m+n gives the overall reaction order.
- m+n must be determined experimentally.
12.3 – Experimental Determination of Rate Law
- Method of initial rates: used to determine rate law exponents through a series of experiments. - The rate law exponents can be determined by comparing the changes in  for each reactant and
the rates of their reactions.
- As products build up, the rates for the reverse reaction increase.
o When the forward and reverse reactions are comparable, then rate depends on the
[reactants and products].
o Initial rates works because there are no products at the beginning of a reaction.
o Therefore rate law only includes reactants.
- k depends on temperature but not the [reactants].
o Can be determined by substituting experimental values into rate law equation.
o Units of k depend on the  terms and their rate law exponents.
12.4 – Integrated Rate Law for a First Order Reaction
- Integrated rate laws shows how [reactants and products] vary over time.
- First-order reaction is one whose rate depends on the [one reactant] raised to an exponent 1.
o i.e., Rate = -Δ[A]/Δt = k[A]
- integrated rate law of a first-order reaction: ln[A] /tA] =0-kt
o [A]t/[A]0is the fraction of A that remains at a given time.
o Can be written as: ln[A] =t-kt + ln[A] ,0therefore k = -slope
- The plot of [A] vs time gives an exponential decay; ln[A] vs time gives linear decay for first order.
12.5 – Half-Life of a First Order Reaction
- Half-life (1/2 is the time required for half the [initial] to remain.
- When t= t ,1/2] /[t] = 0. Therefore t 1/2for a first-order reaction is = 0.693/k.
o Half-life of first-order reaction is constant because it only depends on k.
i.e., each half-life is an equal amount of time from each other.
 decreases by a factor of 2 each time.
12.6 – Second-Order Reactions
- Rate can depend on one reactant with an exponent of 2 or two reactants with exponent of 1.
- Integrated rate law: (1/[A] )t= kt + (1/[A] 0.
- The plot of [A] vs time gives an exponential decay; 1/[A] vs time gives linear growth for second
- k = slope