PHAR 6718 Chemical Kinetics and Drug Stability

kt =

1/(a-x) - 1/(a-0) (a-x) change in concentration at time t (a - 0) = initial concentration kt = 1/Ct - 1/Co k = 1/at(x/(a-x) a = initial concentration x = concentration at time t

Second order plot/graph

1/Ct = kt + 1/Co slope = k y intercept = 1/Co Slide 63 Chemical Kinetics

Units of k for first order

1/time 1/hour

Time for 10% of drug degradation (t10%)

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

After the 3rd 1/2 life

12.5% of initial amount remains, and so on

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

Slope of the line of logarithmic Arrhenius equation is

-Ea/2.303R

Zero order

-dC/dt = k

Example: Photochemcial reactions in which the reaction rate is determined by light intensity

-dC/dt = k -dC = kdt dC = -kdt The rate equation is integrated between time t = 0 when concentration = Co and time = t when concentration = Ct Ct = Co - kt------zero order reaction As k value goes up, decomposition is faster

If drug in solution (of suspension) undergoes first order decomposition, then

-dC/dt = kC As son as drug concentration decreases, drug becomes dissolved in solution to keep saturation solubility---gets converted to zero order process

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 Slide 48 Chemical Kinetics

First order

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

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)

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

t 1/2 for first order process

0.693/k

In terms of drug stability, do not want:

1) Chemical degradation of the API 2) Degradation of drug is not expensive, but the degradation product is very toxic 3) Deterioration in the physical appearance of a dosage form

Reaction rates are affected by:

1) Concentration of reactants Dose, amount in formulation. If liquid, will be higher concentration for pediatric than adult---less chance to spit it all out 2) Concentration of products Decomposition product, as soon as it is formed the product goes faster/slower 3) Concentration of other chemical species Excipients can influence stability---can change excipient to keep product stable or not increase degradation 4) Temperature Related to storage. 10 degreees C ideally, need to make drug stable at range of temperatures if possible---storing at room temp is ideal 5) Solvent used 6) Pressure, etc 1) and 4) will be investigated in detail

Deterioration in the physical appearance of a dosage form: Examples

Creaming of emulsions Settling of suspended particles These do not result in loss of therapeutic efficacy, however patient confidence may be lost.

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) Example Graph Slide 34 Chemical Kinetics

Kinetics is the

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

Preceding condition is known as

apparent zero order. The zero order condition exists only because of the suspended drug that acts as a reservoir. After the dissolution of all the suspended drug, the behavior of system would be first order Slide 56 Chemical Kinetics for graph

Pharmacists want to keep k

as low as possible = longer shelf life

The reaction starts

as soon as drug product (formulation) has been prepared

The decomposition of drug in solution (of suspension) is accompanied by

dissolution of the suspended drug so that the drug concentration in solution is maintained constant. If C is maintained constant then: kC = k0 = zero order process -dC/dt = k0 Slide 56 Chemical

Half life for first order process

does not depend on concentration

It is important to slow down/decelerate

drug decomposition rate

Pharmacist

expert on drugs

First order reactions go ___________ at higher temperatures

faster

Suspension is a

finely divided insoluble drug dispersed in liquid medium

For first order reaction, the reaction proceeds with

greatest velocity at the beginning

When compounding a product =

higher risk of decomposition

The potential instability of all pharmaceutical products the pharmacist handles is

his/her responsibility. He/she needs to be aware of any instability when the product is dispensed.

Rate constant (k) tells you

how fast/slow the reaction will be

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

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

infinite time

For all the drug to undergo decomposition

infinite time would be required = will never have complete decomposition

The reaction order (order of reaction) provides measure of

influence of concentration of reactants on reaction rate

In a suspension, solid is referred to as being

insoluble----some drug dissolved in solution

Arrhenius equation

k = Ae^(-Ea/(RT)) k = specific reaction rate constant A = constant called frequency factor Ea = energy of activation (cal/mol or J/mol) R = gas constant (1.987 cal/(K x mol) or 8.314 J/(K x mol)) T = Temp in K

Want low values of

k for pharmacy

Therefore, -dC/dt =

k0, where k0 = zero order rate constant

Powders have a

limited shelf life once reconstituted---powder has much longer shelf life

The plot of log k against 1/T will be

linear of logarithmic Arrhenius equation

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

Logarithmic form of Arrhenius equation

log k = log A - Ea/(2.303RT) Slide 67 Chemical Kinetics for graphs of zero, 1st, 2nd orders

If reaction rate is determined at 2 temperatures, T1 and T2:

log k2/k1 = Ea/2.303R (T2 - T1)/(T1 x T2)

In a suspension, the concentration of drug in solution is

maintained constant

Driving force 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 Ex: mA + nB = products Reaction rate = (A)^m x (B)^n = k(A)^m x (B)^n where k = rate constant

In extemporaneously prepared pharmaceutical formulations, it is unusual to tolerate

more than 10% degradation of API. So the time required for 10% of drug to degrade is important from point of view of dosage form design & development

First order kinetics are usually

plotted in log scale

As time elapses, there is a

progressive decrease in reaction velocity

Chemical kinetics is the study of the

rate of a chemical reaction

In second order reaction: Rate of decomposition of A is equal to the

rate of decomposition of B and is given as: -dA/dt = -dB/dt = k(A)^1 x (B)^1 Where k is second order constant

Kinetics refers to

rate process

Concentration in solution =

saturation solubility with a suspension

Suspensions have

shorter shelf life than solutions

First order rate constant can be determined by

slope of decomposition lines (slide 72 Chemical Kinetics) slope = -k/2.303

Conventional evaluation of stability

storage for a time period corresponding to the shelf-life of product Time consuming and expensive

Half life for second order reaction

t 1/2 = 1/(Co x k)

We know that k = 0.693/t 1/2

t 10% = 0.105/(0.693/(t 1/2)) = 0.152 x t/12

t 10% for first order

t 10% = 2.303/k x log (100/90) 0.105/k

Like t 1/2 for first order,

t 10% is also concentration independent

With a suspension, the concentration is

the equilibrium solubility of the drug

As concentration approaches zero,

the reaction velocity approaches zero

In a suspension, if the drug in solution decomposes

the suspended drug particles dissolve----suspended drug acts as a reservoir

Commercially products stored properly =

very good stability

If a and b are the initial concentrations of A and B respectively in second order reaction,

x = decrease in concentration of A and B at time t dx/dt = k(a-x)(b-x) (a-x) = concentration of A remaining at time t (b-x) = concentration of B remaining at time t dx/dt = reaction rate Change in concentration of both is going to be the same Value of x increases as time increases Rate of reaction will increase over time If concentrations of A and B were the same, then a = b

Units of k for second order reaction

L/(mol x hr)

Containers

Light intensity can change reaction rate Do not want light exposure to pharmaceuticals if can help it Reasons would not use kinds of containers on slide 26 Chemical Kinetics: 1) Need to used manufacturer's container, 2) Patient has bad eyesight and is on multiple medications----use clear bottle but store in a dark place

Lidocaine Hydrochloride injection

Local anesthetic pH of 0.5% w/v aqueous lidocaine solution = 4 to 5.5, causes pain at the site of admin at this pH Raising the pH with sodium bicarbonate reduces pain pH 6.8 = no lidocaine loss in 27 days pH 7.2 = adequate stability for 19 days, 12% loss in 27 days pH 7.4 = 23% loss in 5 days----significant drug decomp at this pH Need to find a pH where pain is reduced for the patient, and shelf life/stability is adequate for duration of use

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

Formation of ethyl acetate again

Rf = -d(CH3COOH)/dt = -d(C2H5OH)/dt = k(CH3COOH) x (C2H5OH)-------one molecule of each Earlier, the reaction order had been defined as the number of molecules of the reactants whose concentration influences the reaction rate. Exponent of (CH3COOH) and (C2H5OH) is 1 for each. So overall reaction order is 1 + 1 = 2

Kinetics example:

Say 100 mg of drug has been dissolved in 100 mL of water After 1 hour, 10 mg of the drug in solution has degraded, therefore only 90 mg of drug remains After one more hour, some more drug has degraded So, as time progresses, more and more of the drug degrades (from 100 mg to 0 mg)

Graphic representation of first order reaction: Not on log scale

Slide 45 Chemical Kinetics

Graphical representation of first order reaction: On semi-log scale to have constant slope

Slide 46 Chemical Kinetics

What will affect reaction rate of zero order reaction

Temperature----increase of 10 degrees causes doubling of reaction rate Light intensity

Significance of half life of a drug: first order reaction

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

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 more part, labeled API is very close to actual amount

Graphical representation of data

Use all the data points to draw your conclusion Don't just use on set of x/y values Take the data and do a best fit line

Kinetics example continued:

What is the initial concentration? 100 mg of drug dissolved in 100 mL of water Concentration is 1 mg/mL Concentration at 1 hour 90 mg of drug in 100 mL of water Concentration is 0.9 mg/mL What is the change in drug concentration with respect to time? 0.9 mg/mL - 1 mg/mL/(1 hour - 0 hour) = -0.1 mg/mL x hour = dC/dt

Solids have

a long shelf life

After the 2nd 1/2 life

25% of initial amount remains

After the first 1/2 life,

50% of initial amount remains

Reaction order example: Acetic acid and ethyl alcohol to form ethyl acetate

CH3COOH + C2H5OH ------ CH3COOC2H5 + H2O Rate of forward reaction (Rf) measures the decrease in concentration of acetic acid and ethanol as a function of time. Since equivalent amounts of acetic acid and ethanol react: Rf = - d(CH3COOH)/dt = -d(C2H5OH)/dt = change in concentration over time

Units of k for zero order

Concentration/time mol/(L x hr)

If a tablet formulation has to be compounded into a suspension, what are the concerns?

Want to decrease solubility of drug so it does not decompose----can do this by adjusting the pH If have good solubility, but not good stability---taste will become apparent Some tablets do not dissolve fully into solution and will look cloudy

Chemical degradation of API example: Digoxin

Digoxin: cardiotonic drug used in the treatment of congestive heart failure Drug has narrow therapeutic index. Maintenance dose is 250 to 740 micrograms/day----0.25 mg API in 100 mg tablet Effective (therapeutic) plasma concentration is greater than 0.8 nanograms/mL Manifestation of toxicity is approximately equal to 1.8 nanograms/mL Therapeutic concentration may be 60% of toxic dose Under such conditions, the dosage form must contain an exactly known amount of drug

Accelerated stability studies

Drug solutions of known concentrations are stored at various elevated temps Concentration of drug remaining undecomposed in solution is determined as a function of time For a drug undergoing first order decomp, a plot of concentration (log scale) against time would be linear Slide 72 Chemical kinetics for decomp at different temps

Effect of Temperature on Reaction Rates

Each 10 degree rise in temp increases speed of reaction 2 to 3 times Variation of temp of reaction rate constant is given by Arrhenius equation

Half-life of zero order reaction

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

Second order reactions: Consider reaction A + B ------- products

If reaction rate is directly proportional to the first power of the concentration of both A and B----is a second order reaction

Solution is preferred dosage form over the suspension

because do not have to shake it to keep it well dispersed----already is with a solution

Chemical degradation of API

can result in substantial lowering of the quantity of therapeutic agent in dosage form In case of potent drugs with a narrow therapeutic index, this can lead to serious problems

Kinetics is the rate of

chemical decomposition, during the shelf-life of a pharmaceutical product

There is drug decomposition, but

concentration in solution is maintained constant

The reaction is occuring

continuously

Change in drug concentration with respect to time

dC/dt C = concentration t = time Concentration is decreasing as a function of time: expressed as -dC/dt Change in concentration: Concentration remaining after 1 hour (Ct) - initial concnetration (Co) = 0.9 - 1 = - 0.1 mg/mL This change in concentration came about in 1 hour The process started at time "zero" and went on for 1 hour (t - 0) Therefore dC/dt = -0.1mg/mL/1 hr or -dC/dt = 0.1 mg/(mL x hr)

Every chemical reaction occurs at a

definite rate

Half life for zero order process

depends on concentration