Intro to Pharmacology and Toxicology
Topics
Kinetics is the study of the properties of chemical reactions, i.e. the rate, time course and dependence upon reactants concentration. The simplest chemical reaction is one in which a reactant R is converted to a product P:
R 
P
If we measure the appearance of product, then the rate or velocity of reaction v equals the rate of appearance of product:
v = d[P] / dt = - d[R] / DT
When observing the rate of appearance of product, v is positive. If the disappearance of reactant is observed, then v is negative.
For uncatalyzed chemical reactions, v is proportional to reactant concentration:
v µ [R] Þ v = k[R]
The proportionality constant k includes such factors as the energy required to carry out the reaction, and is dependent upon temperature and other conditions in which the reaction is carried out.
The equation above describes a first order reaction, since the exponent of the [R] term is 1, and the sum of the exponents of all terms in the equation is 1. This means that k is a first order rate constant with units of 1/time:
v = d[P] / DT = k[P]
Þ k[R] = d[R] / DT
Þ k(concentration) = concentration / time
Þ k = 1 / time
The same principles apply to a reaction where two reactants, A and B, combine to form product P:
A + B
P
v = d[P] / DT = - d[A] / DT = - d[B] / DT
v µ [A][B] Þ v = k[A][B]
In this case, the reaction rate is proportional to the product of the reactant concentrations. In other words, the reaction depends upon a molecule of A colliding with a molecule of B. How frequently such a collision results in the formation of P is expressed by the rate constant k.
The reaction above is first order in A, first order in B, but second order overall. Therefore, k is a second order rate constant with units of 1/(concentration)(time):
v = d[P] / DT = k[A][B]
Þ k[A][B] = d[P] / DT
Þ k(concentration)(concentration) = concentration / time
Þ k = 1 / (concentration)(time)
The following equation describes both the first and second order reactions:
qA + rB
P
v = k[A]^q[B]^r
(^=exponent) where q is the reaction order in A, r is the reaction order in B and q+r is the overall reaction order. This generic equation can be expressed in logarithmic form, which can be rearranged to conform the equation of a straight line if one of the concentrations is held constant:
ln v = ln k + q ln [A] + r ln [B]
ln v = q ln[A] + (ln k + r ln[B])
y = m x + b
Note that the slope will be the order in one of the reactant concentrations (the one held constant).
A series of experiments may be developed to measure v and the reaction order by holding [B] at a fixed high concentration and measuring v (or changes in [P] ?) at different [A], then repeating the measurements holding [A] constant and varying [B]. Such a procedure will yield the data required to calculate the average v, q and r.
The previous reactions were irreversible and uncatalyzed, thus requiring only one rate constant k. Reversible reactions involve two rate constants:
k1
A + B 
P
k-1
where k1 is the rate constant for the forward reaction (formation of product) and k-1 is the rate constant for the reverse reaction (degradation product).
A reversible reaction, rather than going to completion, will go to equilibrium, a point at which the forward reaction equals the reverse reaction. At equilibrium, the concentrations of reactants and products no longer change and the observed velocity is determined by the difference between the forward and reverse velocities:
vf = k1[A][B] ; vr = k-1[P]
Þ v = VF - vr = k1[A][B] - k-1[P]
This equation presents experimental difficulties. Concentrations of A, B and P must be known at the time velocity is determined in order to calculate a ratio of k1 and k-1. To avoid the complication, this type of reactions is often analyzed at equilibrium, when v = 0.
0 = k1[A][B] - k-1[P]
Þ k-1[P] = k1[A][B]
Þ k-1 / k1 = [A][B] / [P]
The ratio k-1 / k1 is defined as the dissociation or equilibrium constant Kd for this reaction. The reciprocal would be the association constant Ka for this reaction.
Continue to "Absorption
and Elimination" or take a quiz: [Q1] [Q2] [Q3] [Q4].
Need more practice? Answer the review questions below (after sponsor).
1- What is kinetics?
The study of the properties of chemical reactions.
2- List 3 properties of a chemical
reaction.
rate or velocity
time course
dependence upon reactant concentrations
3- Mathematically define velocity
for an irreversible uncatalyzed reaction with one reactant.
v = d[P] / DT = -d[R] / DT = k[R], where k includes such factors as the energy
of reaction and is dependent upon temperature and other conditions in which
the reaction is carries out.
4- What is a first order reaction?
The sum of all the exponents in the equation is 1.
5- What are the units of a first
order rate constant?
1 / time
6- Mathematically define velocity
for an irreversible uncatalyzed reaction with two reactant.
v = d[P] / DT = -d[A] / DT = -d[B] / DT = k[A][B]
where k describes how frequently a molecule of A and one of B collide with each
other resulting in the formation of P.
7- What is a second order reaction?
The sum of all the exponents in the equation is 2.
8- What are the units of a second
order rate constant?
1 / (concentration)(time)
9- Mathematically define velocity for ANY irreversible uncatalyzed reaction.
10- How is the equation v = k [A]^q [B]^r used experimentally?
11- Describe an experiment to measure v and the reaction order.
12- What is equilibrium?
13- Mathematically define velocity for a reversible uncatalyzed reaction with two reactant.
Hey! DON'T PEEK!!! Finish the questions fist!
1- What is kinetics?
2- List 3 properties of a chemical reaction.
3- Mathematically define velocity for an irreversible uncatalyzed reaction with one reactant.
4- What is a first order reaction?
5- What are the units of a first order rate constant?
6- Mathematically define velocity for an irreversible uncatalyzed reaction with two reactant.
7- What is a second order reaction?
8- What are the units of a second
order rate constant?
1 / (concentration)(time)
9- Mathematically define velocity
for ANY irreversible uncatalyzed reaction.
v = k [A]^q [B]^r
were q is the reaction order in A, r is the reaction order in B and q+r is the
overall reaction order
10- How is the equation v = k
[A]^q [B]^r used experimentally?
It is expressed in logarithmic form, rearranged to yield a linear equation with
slope equal to the order in
the reactant held constant.
11- Describe an experiment to
measure v and the reaction order.
working...
12- What is equilibrium?
working...
13- Mathematically define velocity
for a reversible uncatalyzed reaction with two reactant.
Kd = [A][B] / [P]
where Kd is the dissociation or equilibrium constant equal
to the rate of the reverse reaction divided by the rate for the forward reaction
(k-1/k1), and its reciprocal is
the association constant Ka.