Chemical Kinetics and Drug Stability

In terms of drug stability, we do not want:

1. Chemical degradation of the active ingredient (result in lowering the quantity of therapeutic agent in the dosage form, dangerous for drugs with a narrow therapeutic index) 2. Degradation of the drug is not extensive but the degradation product is very toxic 3. Deterioration in the physical appearance of a dosage form (these do not result in loss of therapeutic efficacy, but patient confidence may be lost)

Reaction rates are affected by

1. Concentration of reactants 2. Concentration of products (Decomposition product, as soon as it is formed the product goes faster/slower) 3. Concentration of other chemical species (excipients) 4. Temperature (Increasing temperature by 10 degrees C will cause rate to double -- storing at room temp is ideal) 5. The solvent used 6. Pressure

Time for 10% of drug degradation (t10%)

10% degradation represents upper limit of drug degradation t10% = (0.1 x Co)/k

After the third 1/2 life

12.5% of the initial amount remains

Degradation of drug is not extensive, but the degradation product is toxic: Examples

200 mg API degrades by 1 mg over time 1. Degradation of tetracycline to epianhydrotetracycline = toxic 2. p-aminosalcilic acid to m-aminophenol = toxic

If drug concentration does not change

(dC/dt = 0) = good thing, because is not degrading

Zero order

-dC/dt = k

Rate equation for first order reaction

-dC/dt = kC Therefore, as there is a progressive decrease in C, the value of dC/dt will also change progressively, since k is constant slope = -dC/dt

First order

-dC/dt = kC k = 2.303/t x log (Co/Ct) Units of k = 1/h for first order reaction

How much degradation can be tolerated in a dosage form

90 to 110% actual amount of API Will usually be less than 1%, between 0.1 to 0.05% For decomposition of more than 0.1%, FDA will ask questions about what the decomposition products are

Graphic representation of zero-order reactions

Ct = Co - kt Ct = -kt + Co Equation is in form of y = -mx + b Independent variable (x) = time Dependent variable (y) = concentration at time t (Ct) Slope = k y intercept = concentration at time 0 (Co)

The concentration time plot of a zero order reaction resulted in a slope of -0.2 mol L-1 h-1, and a y-intercept of 1.0 mol L-1. The half life of this reaction is:

Ct = Co - kt k = slope y intercept = Co half life = Co/2k 1 mol/L/(2 x 0.2 mol/(L x hr)) = 2.5 hours

Half life for first order process

does not depend on concentration

First order reactions go ______ at higher temperatures

faster

Rate constant (k) tells you

how fast/slow the reaction will be Want low k value

Remember that the reaction velocity only approaches zero and reaches zero only at

infinite time

The reaction order (order of reaction) provides measure of

influence of concentration of reactants on reaction rate

Why is the concentration (on the log scale)--time plot linear for first order reaction?

log Ct = log Co - (kt)/2.303 Equation is in form y = -mx + b A plot of Ct (on the log scale) vs time will be linear Intercept on y-axis = Co Slope = -k/2.303 So by plotting concentration (on the log scale) vs time, the value of k can be obtained from the slope

First order kinetics are usually plotted in

log scale

As time elapses, there is a

progressive decrease in reaction velocity

Kinetics refers to

rate process We are concerned with the rate of a chemical decomposition during the shelf-life of a pharmaceutical product

As concentration approaches zero,

the reaction velocity approaches zero

Half-life of zero order reaction

time required for 1/2 of material to disappear t1/2 = Co/2k Increase initial concentration = increased half life Increase k = decrease half life

In a zero order reaction, the reaction rate is

Independent of the concentration of reactants -dC/dt = k Where dC is the change in concentration for a given time interval of dt, and k is the zero order rate constant

For all the drug to undergo decomposition

Infinite time would be required = will never have complete decomposition

Lidocaine HCl injection

Is a local anesthetic If pH is 4-5.5, there is pain at the site of administration Raising the pH with sodium bicarbonate reduces the pain (pH 7.2 causes adequate stability for 19 days; 12% loss in 27 days)

When the initial concentration of a drug that undergoes zero-order decomposition is halved, the half life of the reaction:

Is halved

Powders have a....

Limited shelf life once reconstituted (example Amoxicillin once reconstituted has a 10 day shelf life)

Solids have a...

Long shelf life

Units of k

One can arrive at untis of k from 2 equations k = -dC/dt = (mol/L)/h = mol/L x h Ct = Co - kt k = (Co - Ct)/t (mol/L)/h = mol/L x h

If a drug undergoes first-order decomposition...

Plot of concentration (logarithmic scale) versus time will be linear

If a drug undergoes second order decomposition...

Plot of inverse concentration vs time will be linear

Freeze-dried powders have no...

Shelf life once reconstituted

What will affect reaction rate of zero order reaction

Temperature----increase of 10 degrees causes doubling of reaction rate Light intensity (why we use amber vial containers)

As k value goes up

The decomposition is faster

It is important to slow down/decelerate

The drug decomposition rate

The driving force (reaction rate) of a chemical reaction is proportional to

The molar concentration of the reacting substances each raised to a power of the number of molecules of the substance participating in the reaction mA + nB = products

In first order reactions

The reaction rate is directly proportional to the first power of the concentration of one reactant -dC/dt is directly proportional to C^1 C is the concentration of drug remaining undecomposed at time t (Co to Ct)

Significance of half life of a drug for first order reaction

Time for decomposition of half of the initial drug is independent of drug concentration

True or false: In a drug undergoing zero-order decomposition, a plot of the concentration of drug remaining versus time will be linear.

True

Labeled versus actual amount of API in a dosage form

USP allows within 10% (90 to 110%) Most companies have between 99 and 101% of actual amount of API compared to labeled For most part, labeled API is very close to actual amount

After the second 1/2 life

25% of the initial amount remains

After the first 1/2 life

50% of the initial amount remains

Kinetics is the

Acceptable stability during the shelf-life of a pharmaceutical product. We are looking for stability during a defined time

Chemical degradation of API example: Digoxin

Digoxin - a cardiotonic drug used in the treatment of congestive heart failure This drug has a narrow therapeutic index. Therapeutic concentration may be 60% of toxic dose. Under such conditions, the dosage form must contain an exactly known amount of the drug.

Answer the following question as True (T) or False (F). There is a new pain relief medication, Painzapper. Two different liquid formulations are available: (a) an adult liquid pain reliever (500 mg in 1 tablespoonful; 1 tablespoon = 15 mL) (b) drops for infants (50 mg/mL) The drug undergoes zero-order decomposition and the value of the zero-order rate constant, k, is the same for the two formulations. These two products WILL have the same half-life (t1/2)?

False

True or false: The units of zero-order decomposition rate constat are: (concentration)-1 (time) -1

False

For first order reactions, the reaction will proceed with

Greatest velocity at the beginning

A drug solution loses 10% of its potency in 24 hours at 25°C. If the reaction is first-order:

Half life: 0.693/k k = 2.303/t x log (Co/Ct) k = 2.303/24 hours x log (100/90) = 4.39 x 10^-3 0.693/4.39 x 10^-3 = 157.8 hours The half-life is about 158 hours and the shelf life is independent of the initial drug concentration

Half life for zero order process

depends on concentration