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Chemical Kinetics and Drug Stability
Apparent-Order: If a reaction is second or higher order, but the concentration of one of the
reactants does not change much (like what happens to this ester drug when placed in a buffer), it will
appear to be first order, and is referred to as an apparent first-Order reaction (pseudo first order).
The decomposition of an ester drug above is an example of a second order degradation. If this reaction
was carried out in a buffer, the concentration would essentially be constant, behaving as though it was
first order.
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Complex Reactions: There are three types of complex reactions
1. Opposing or reversible reactions
at equilibrium the rate of forward and backward reaction is the same. Kc is the ratio of the forward rate
constant over the reverse rate constant.
2. Parallel or simultaneous reactions: The drug is being converted to several decomposition products
simultaneously.
3. Consecutive reactions: Drug A is first converted to an intermediate drug B, and finally to C.
The decomposition products are inactive, only the original drug A is pharmacologically active.
Question:
Ina biological setting, say a drug in the GI tract, A would represent the initial concentration of the drug,
B would be the concentration of the drug in the blood, and C would be the rate at which the drug is
being eliminated.
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Rate-Limiting Step: slowest step in a reaction; determines overall rate.
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Factors Affecting Reaction Rate
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Catalyst: is a substance that alters the rate of a reaction but is not consumed in the
reaction. It provides a different pathway for the reaction to occur; this different pathway has a
lower energy requirement, lower activation energy.
pH:Hydronium or hydroxyl ion concentration
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Hydronium ions – if a reaction is catalyzed by the presence of H+ ions, it is referred to as
specific acid catalysis.
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Hydroxyl ions: if a reaction is catalyzed by the presence of OH-, it is referred to as specific
base catalysis.
How do we know that a reaction is catalyzed by a specific pH(H+ or OH- ions).? We can determine it by
the construction of a pH rate profile. This is a graph of log of k value vs pH. If the slope of the line in
this graph is -1, it implies that a specific acid catalysis is occurring. If the slope of the line is +1, a
specific base catalysis is occurring. To find k we can graph concentration vs time in the case of a zero
order, and natural log of concentration vs time in 1st order reactions. The slope of these lines is then the
rate constant k.
The second pH rate profile is the plot for one compound at different temperatures. Acid catalyzed
decomposition appears to be taking place below pH 4. Between pH 4 and 8, base catalysis is occuring.
Above pH 8 it appears that pH has no influence, the reaction is solvent catalyzed. The drug exhibits
optimum stability at around pH 4 where the k value is the smallest, indicating the slowest rate of
decomposition. So this drug would be prepared in a formulation with a buffer around pH 4.
Sigmoidal shapes (like the one on the graph below at around pH 8) in pH rate profiles indicate the point
at which a drug changes from ionized to unionized or vice versa, and one form or the other becomes
dominant after that point. The inflection point of the graph is most often where the pKa of the compound
occurs.
The compound with the pH rate profile in the above graph has two pKa and the different components are
being degraded at different pHs. It has more than one functional group that can donate and accept
protons.
If both specific acid and specific base catalysis is occurring, the pH rate profile assumes a V shape. The
standard V shape maybe shifted to one side or the other of the pH. The minimum value in the pH rate
profile maybe more in the acidic range, in this case the relative base catalysis would be fairly strong.
However if the V shape is shifted more to higher pH, then the relative acid catalysis is stronger.
In the following graph it appears that the relative acid catalysis is fairly strong, because the rate of the
reaction increases at lower pH. It is also a an apparent first order reaction because the graph is a semi log
and the points on the y-axis are not the same distance apart. (When the points are not the same distance
apart, it is like graphing the log of the concentration)
The graph below is of Moricizine in two different buffers, the total concentration of buffer components
is increasing along the X-axis. We can keep a constant pH but change the total concentration of buffer
components if we keep the ratio of the acid and base components constant. This data shows what is
known as general acid or base catalysis. In specific acid catalysis hydronium ions catalyze the reaction,
in general acid catalysis any acid other than hydronium ions does the catalysis. From this graph we can
not tell if there is
Question: Solution of an ester at pH 10 buffer was found to contain 3mg/ml one hour after preparation.
Two hours after preparation it contained 2.45 mg/ml. Assuming apparent first-Order degradation,
calculate the rate constant. When would the concentration equal 1.5 mg/ml?
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Other acids/bases: these might come from the excipients
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Any other acid: general acid catalysis
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Any other base: general base catalysis
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Temperature:generally increases the rate of a reaction by increasing the K.E of molecules
 Arrhenius Relationship: this is an empirically developed equation. It relates rate
constant, temperature and activation energy.
The equation on the right is the logarithmically modified version of the one on the left.
In the graph above the plot with the greatest slope takes place at the highest temperature (60%). We can
calculate the k values at each temperature from the slope of the lines.
We can use the data we get from the graph to predict the rate constant at some other temperature such as
the optimum storage temperature. We can also estimate the shelf life. (time required for 10%
decomposition to occur using t = 0.105/k, because this is a first order reaction).
Other forms of the Arrhenius equation:
 Energy of Activation: is the energy barrier that must be overcome for a reaction to
occur.
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Solubility: The concentration of a drug in solution in a saturated solution.
Suspension: is a type of dosage form that contains solid drug particles suspended or dispersed in a
solution. Some drug particles are dissolved; there are undissolved drug particles as well. The drug in
solution is in equilibrium and undissolved drug particles, We make the assumption that the drug in
solution is the one undergoing decomposition. If we are not given the order of the reaction, but we are
told that its a drug in suspension, then we can assume that its degrading by apparent zero order
decomposition.
If we were to draw a graph for the decomposition of a suspension, it would look something like this. It
would look like a zero order reaction upto the point where all the solid drug particles dissolve. When we
no longer have solid drug particles (indicated by the arrow on the graph below), it would resemble a first
order reaction, because it is a solution after this point.
We are trying to get the penicillin out of solution, because we make the assumption that decomposition
occurs from the drug in solution. Therefore by adding a common ion we make the penicillin less soluble,
essentially increasing its shelf life.
Note: A suspension is more stable than a solution, because it has some drug in solid form (remember
that its drug in solution that undergoes decomposition.)
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Light
Degradation Pathways
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Hydrolysis
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Oxidation
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Isomerization/Racemization
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Photolysis
We usually allow patients to take a drug if at least 90% of the labeled amount of a drug is present.(only
less than 10% decomposition is allowed).