Dandamun, Benbellah Ali Y.

BSCHE-5 Engr. Elaine G. Mission

KINETICS OF DRUGS

1

KINETICS OF DRUGS

Contents Introduction ...................................................................................................................................... 2

Drug kinetics ..................................................................................................................................... 2

Rate, Order, and Molecularity .................................................................................................. 2

Zero-Order, First-Order, and Second-Order Reactions and Their Rate Equations, Half-

Life and Shelf-Life ......................................................................................................................... 3

Zero-Order Reaction ................................................................................................................ 4

First-Order Reaction ................................................................................................................. 7

Second-Order Reactions ...................................................................................................... 10

Special Cases ......................................................................................................................... 13

Sample Problems ....................................................................................................................... 13

Solutions to Problems ................................................................................................................ 15

References ...................................................................................................................................... 17

2

KINETICS OF DRUGS

KINETICS OF DRUGS

Introduction For us to be able to predict the shelf-life of a dosage, it is essential to determine the

kinetics of the breakdown of the drug under carefully controlled conditions. Drug kinetics

is essential because it determines the following:

Stability of Drugs (Half-life or t1/2)

Shelf Life (t0.90)

It is even used in the determination of the drug’s expiration date. But the discussion will

only focus on the basic principles of Drug Kinetics.

Drug kinetics Drug kinetics is simply defined as how drug changes with time. Many drugs are not

chemically stable and the principles of chemical kinetics are used to predict the time

span for which a drug (pure or formulation) will maintain its therapeutic effectiveness or

efficacy at a specified temperature.

Rate, Order, and Molecularity The underlying principle on which all of the science of kinetics is built is the law of mass

action (Cairns, 2008). The law of mass action states that, the rate of a reaction is

proportional to the molar concentrations of the reactants each raised to power equal to

the number of molecules undergoing reaction.

𝑎𝐴 + 𝑏𝐵 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠

𝑅𝑎𝑡𝑒 = −𝑘 [𝐴]𝑎[𝐵]𝑏

The Rate of a chemical reaction is the speed of the reaction or simply, how fast the

reaction occurs. It is, in a dilute solution, proportional to the concentrations of the various

reactants each raised to the power of the number of moles of the reactant in the

balanced chemical equation.

Reactions are classified according to number of reacting species whose concentration

determines the rate at which the reaction occurs (Florence and Attwood, 2006). The

Order of the reaction (Overall Order) is the sum of the powers to which these

concentrations are raised. The individual order of the reactant is simply the exponent of

the reactant.

𝑂𝑟𝑑𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 𝑆𝑢𝑚 𝑜𝑓 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡𝑠

3

KINETICS OF DRUGS

𝑂𝑟𝑑𝑒𝑟 𝑜𝑓 𝐴 = 𝑎

𝑂𝑟𝑑𝑒𝑟 𝑜𝑓 𝐵 = 𝑏

𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝑂𝑟𝑑𝑒𝑟 = 𝑎 + 𝑏

In practice, the rate of a chemical reaction depends only on a small number of

concentration terms, and the sum of the powers to which these concentrations are raised.

This is because chemical reactions occur in a number of steps, or stages (called a

mechanism) and the rate of the overall reaction is often governed by the rate of the

slowest step (called, not surprisingly, the rate-determining step). Even if every other stage

of a chemical reaction occurs essentially instantaneously, the rate of the reaction as a

whole cannot exceed that of the slowest stage. (Cairns, 2008)

The order of a chemical reaction cannot be predicted from the chemical equation, even

if it has been balanced. The order of a reaction is determined experimentally from

accurate measurements of the rate under different conditions (Cairns, 2008). Typically,

drugs react in the zero, first, and second order. There are also rare cases wherein the

drugs undergo a third order reaction, or even a fractional order of reaction.

The Molecularity is the total number of molecules taking part in the slowest of the

elementary reaction steps. In most chemical reactions, two molecules collide and react;

the molecularity is 2 and the reaction is said to be bimolecular.

e.g.: 𝐴 + 𝐵 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠

Reactions in which only one molecule is involved (unimolecular) are known, but usually

occur in the gas phase.

e.g.: 𝐴 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠

Reactions with a molecularity higher than 2 are very rare, since this would require three

or more reactants all encountering each other at the same time.

Zero-Order, First-Order, and Second-Order Reactions and

Their Rate Equations, Half-Life and Shelf-Life Taking an example of a reaction:

𝐴 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡

𝑅𝑎𝑡𝑒 = −𝑘 [𝐴]

Rate can be rewritten as:

𝑑𝑥

𝑑𝑡= −𝑘[𝐴]

Differential rate equations like these are not much use to the practicing chemist, so it is

usual to integrate the differential form of the rate equation, shown above, to obtain more

4

KINETICS OF DRUGS

useful expressions (Cairn, 2008). The next discussion will be all about the derivation of the

rate reactions for zero, first, and second order reactions. For the following derivations, we

let:

𝑪𝒂 = 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝐴

𝑪𝒂𝒐= 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝐴 (@𝑡 = 0)

𝑘 = 𝑅𝑎𝑡𝑒 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡

𝑡 = 𝑡𝑖𝑚𝑒

𝑡1/2 = 𝐻𝑎𝑙𝑓 − 𝑙𝑖𝑓𝑒

𝑡0.9 = 𝑆ℎ𝑒𝑙𝑓 − 𝑙𝑖𝑓𝑒

The shelf life of a pharmaceutical product is the length of time the product may safely

be stored on the dispensary shelf before significant decomposition occurs. This is

important since, at best, drugs may decompose to inactive products; in the worst case

the decomposition may yield toxic compounds. The shelf-life is often taken to be the time

for decomposition of 10% of the active drug to occur, leaving 90% of the activity.

The unit for the rate constant (k) can be determined using the formula:

(𝑡𝑖𝑚𝑒)−1(𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛)1−𝑛

Zero-Order Reaction There are some reactions in which the rate of the reaction is independent of the

concentration of the reactants but does depend on some other factor, such as the

amount of catalyst present. These reactions are termed zero-order reactions, and rate

equations can be derived as follows:

𝑑[𝐴]

𝑑𝑡= −𝑘[𝐴]0

∫ 𝑑[𝐴] = − ∫ 𝑘 𝑑𝑡

∫ 𝑑[𝐴]𝑪𝒂

𝑪𝒂𝒐

= −𝑘 ∫ 𝑑𝑡𝑡

0

𝑪𝒂 − 𝑪𝒂𝒐= −𝒌𝒕 or 𝑪𝒂𝒐

− 𝑪𝒂 = 𝒌𝒕

We can also rewrite the equation in terms of the mole fraction of A (Xa).

𝑪𝒂𝒐 𝑿𝒂 = 𝒌𝒕

5

KINETICS OF DRUGS

Zero-order process takes place at a constant rate independent of the existing

concentration or initial concentration.

Example:

A patient was given 100 mg drug A orally. Assume that the drug absorption follows zero-

order kinetics at a rate of 10 mg/min.

In the example, 10 mg of drug will undergo absorption for every minute. It does not matter

even if the initial concentration administered to the patient is higher or lower than 100

mg. The same rate (10 mg/min) will be followed. Eventually, the process will come to an

end when the amount of drug administered is absorbed by the body completely (for the

example, the process ends in 10 minutes.)

In zero-order reactions the amount of product formed varies with time so that the amount

of product formed after 20 minutes will be twice that formed after 10 minutes. Reactions

that follow zero-order kinetics are quite rare, but they do occur in solid-phase reactions

such as release of drug from a pharmaceutical suspension.

A plot of the amount remaining (as ordinate) against time (as abscissa) is linear with a

slope of k0. Many decomposition reactions in the solid phase or in suspensions apparently

follow zero-order kinetics. (Florence and Attwood, 2006)

FIGURE 1 PLOT OF T VS CA

FIGURE 2 HYDROLYSIS OF A SUSPENSION OF

ACETYLSALICYLIC ACID AT 34°C.

6

KINETICS OF DRUGS

Drugs that follow Zero-order kinetics

Phenytoin

Phenylbutazone

Warfarin

Heparin

Ethanol

Aspirin

Theophylline

Tolbutamide

Salicylates

Half-life for a Zero-Order Reaction

The half-life of a reaction can be derived by letting 𝐶𝑎=0.5𝐶𝑎𝑜 and 𝑡 = 𝑡1/2.

𝐶𝑎𝑜− 𝐶𝑎 = 𝑘𝑡

𝐶𝑎𝑜− 0.5𝐶𝑎𝑜

= 𝑘𝑡1/2

0.5𝐶𝑎𝑜= 𝑘𝑡1/2

𝒕𝟏/𝟐 =𝟎. 𝟓𝑪𝒂𝒐

𝒌

Note that for the half-life of a zero-order reaction, rate constant (k) and half-life (t1/2)

depend on the initial concentration of the reactant (𝐶𝑎𝑜).

FIGURE 3 SAMPLE PLOT FOR THE HALF-LIFE OF A ZERO-ORDER REACTION

7

KINETICS OF DRUGS

Shelf-life for a Zero-Order Reaction

The shelf-life of a reaction can be derived by letting 𝐶𝑎=0.9𝐶𝑎𝑜 and 𝑡 = 𝑡0.90.

𝐶𝑎𝑜− 𝐶𝑎 = 𝑘𝑡

𝐶𝑎𝑜− 0.9𝐶𝑎𝑜

= 𝑘𝑡0.90

0.1𝐶𝑎𝑜= 𝑘𝑡0.90

𝒕𝟎.𝟗𝟎 =𝟎. 𝟏𝑪𝒂𝒐

𝒌

Same as the half-life, rate constant (k) and shelf-life (t0.90) depend on the initial

concentration of the reactant (𝐶𝑎𝑜).

First-Order Reaction This type is the most common in the pharmaceutical industry (e.g.: drug absorption and

drug degradation). The rate of first-order reactions is determined by one concentration

term and may be derived as follows:

𝑑[𝐴]

𝑑𝑡= −𝑘[𝐴]

∫𝑑[𝐴]

[𝐴]= − ∫ 𝑘𝑑𝑡

∫𝑑[𝐴]

[𝐴]

𝐶𝑎

𝐶𝑎𝑜

= −𝑘 ∫ 𝑑𝑡𝑡

0

ln 𝐶𝑎 − ln 𝐶𝑎𝑜= −𝑘𝑡

− 𝐥𝐧𝑪𝒂

𝑪𝒂𝒐

= 𝒌𝒕

In terms of the mole fraction of A (Xa), the equation becomes:

− 𝐥𝐧(𝟏 − 𝑿𝒂) = 𝒌𝒕

First-order process takes place at a constant proportion of the drug concentration

available at that time so the process is depending on the initial concentration.

Example:

A patient was given 100 mg of drug B orally and it was assumed to be following first-order

kinetics, a proportion of 10% per minute of the existing concentration at that time.

For this example, the dose given to the patient is again 100 mg but the proportion being

absorbed is 10% per minute. This means that in the first minute, 10% of the initial drug will

be absorbed (10 mg in the example). For the second minute, again 10% of the drug that

remained for absorption will be absorbed (10% of 90 mg = 9 mg, meaning, after the

8

KINETICS OF DRUGS

second minute, only 81 mg of the reactant will remain). And this process goes on. This

means that the first-order process never comes to an end.

If a plot of equation is made, with t on the horizontal axis and −ln𝐶𝑎

𝐶𝑎𝑜

on the vertical axis,

a straight line passing through the origin will be obtained for a reaction obeying first-order

kinetics. The slope of this straight line will be equal to k, the rate constant for the reaction.

FIGURE 4 PLOT OF T VS LN(CA/CAO)

FIGURE 5 FIRST-ORDER PLOT FOR HYDROLYSIS OF HOMATROPINE IN

HYDROCHLORIC ACID (0.226 MOL DM-03) AT 90°C.

9

KINETICS OF DRUGS

As can be seen in the figure, the main difference between a first-order and a zero-order

reaction is that in zero-order reaction, the process will end eventually while in a first-order

reaction, the process does not end.

Half-life for a First-Order Reaction

The half-life of a reaction can be derived by letting 𝐶𝑎=0.5𝐶𝑎𝑜 and 𝑡 = 𝑡1/2.

− ln𝐶𝑎

𝐶𝑎𝑜

= 𝑘𝑡

− ln0.5𝐶𝑎𝑜

𝐶𝑎𝑜

= 𝑘𝑡1/2

− ln 0.5 = 𝑘𝑡1/2

𝒕𝟏/𝟐 = −𝐥𝐧 𝟎. 𝟓

𝒌

Note that for the half-life of a first-order reaction, rate constant (k) and half-life (t1/2) does

not depend on the initial concentration of the reactant (𝐶𝑎𝑜).

FIGURE 6 GRAPHS SHOWING THE DIFFERENCE OF FIRST AND ZERO-ORDER KINETICS IN TERMS

OF ELIMINATION OF DRUGS

10

KINETICS OF DRUGS

Shelf-life for a First-Order Reaction

The shelf-life of a reaction can be derived by letting 𝐶𝑎=0.9𝐶𝑎𝑜 and 𝑡 = 𝑡0.90.

− ln𝐶𝑎

𝐶𝑎𝑜

= 𝑘𝑡

− ln0.9𝐶𝑎𝑜

𝐶𝑎𝑜

= 𝑘𝑡0.90

− ln 0.9 = 𝑘𝑡0.90

𝑡0.90 = −ln 0.9

𝑘

Same as the half-life, rate constant (k) and shelf-life (t0.90) does not depend on the initial

concentration of the reactant (𝐶𝑎𝑜).

Second-Order Reactions For reactions of the type:

2𝐴 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 or 𝐴 + 𝐵 → 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠

The rate of the reaction will be first order with respect to each reactant and hence

second order overall. The rate of a second-order reaction is determined by the

concentrations of two reacting species. The rate equation for a second-order reaction is

derived as follows:

FIGURE 7 SAMPLE PLOT FOR THE HALF-LIFE OF A FIRST-ORDER REACTION

11

KINETICS OF DRUGS

𝑑[𝐴]

𝑑𝑡= −𝑘[𝐴]2

∫𝑑[𝐴]

[𝐴]2= − ∫ 𝑘𝑑𝑡

∫𝑑[𝐴]

[𝐴]2

𝐶𝑎

𝐶𝑎𝑜

= −𝑘 ∫ 𝑑𝑡𝑡

0

𝟏

𝑪𝒂−

𝟏

𝑪𝒂𝒐

= 𝒌𝒕

In terms of the mole fraction of A (Xa), the equation becomes:

𝟏

𝑪𝒂𝒐

𝑿𝒂

𝟏 − 𝑿𝒂= 𝒌𝒕

The equations derived are only valid for second-order reactions in which the

concentrations of the reactants are equal. In most cases it is possible to arrange for the

concentrations of the reactants to be equal and the equations may be used.

The equation derived is a straight line of the type y = mx + b, so that a plot of 1/Ca against

t yields a straight line of slope k, with an intercept on the vertical axis of 1/Cao.

Half-life for a Second-Order Reaction

The half-life of a reaction can be derived by letting 𝐶𝑎=0.5𝐶𝑎𝑜 and 𝑡 = 𝑡1/2.

1

𝐶𝑎−

1

𝐶𝑎𝑜

= 𝑘𝑡

1

0.5𝐶𝑎𝑜

−1

𝐶𝑎𝑜

= 𝑘𝑡1/2

𝐶𝑎𝑜− 0.5𝐶𝑎𝑜

0.5𝐶𝑎𝑜2 = 𝑘𝑡1/2

FIGURE 8 PLOT OF T VS 1/CA

12

KINETICS OF DRUGS

1

𝐶𝑎𝑜

= 𝑘𝑡1/2

𝒕𝟏/𝟐 =𝟏

𝑪𝒂𝒐𝒌

The half-life for a second-order reaction is inversely proportional to the initial

concentration.

Shelf-life for a Second-Order Reaction

The shelf-life of a reaction can be derived by letting 𝐶𝑎=0.9𝐶𝑎𝑜 and 𝑡 = 𝑡0.90.

1

𝐶𝑎−

1

𝐶𝑎𝑜

= 𝑘𝑡

1

0.9𝐶𝑎𝑜

−1

𝐶𝑎𝑜

= 𝑘𝑡0.90

𝐶𝑎𝑜− 0.9𝐶𝑎𝑜

0.9𝐶𝑎𝑜2 = 𝑘𝑡0.90

FIGURE 9 SAMPLE PLOT FOR THE HALF-LIFE OF A SECOND-ORDER REACTION

13

KINETICS OF DRUGS

0.1

0.9𝐶𝑎𝑜

= 𝑘𝑡0.90

𝒕0.90 =𝟎. 𝟏

𝟎. 𝟗𝑪𝒂𝒐𝒌

The shelf-life for a second-order reaction is inversely proportional to the initial

concentration.

Special Cases

Apparent Zero-Order of Reaction

In aqueous suspensions of drugs, as the dissolved drug decomposes more drug dissolve

to maintain drug concentration i.e. drug concentration kept constant, once all

undissolved drug is dissolved, rate becomes first order.

Pseudo First-Order

In some second-order reactions the concentration of one of the reactants is many times

more than the concentration of the other, too large in fact as to be considered constant

throughout the reaction. In these cases, the reaction appears to follow first-order kinetics,

even though, strictly speaking, it is still a second-order process.

The majority of decomposition reactions involving drugs fall into this category, either

because the species reacting with the drug is maintained constant by buffering or

because, as in the case of uncatalysed hydrolysis reactions, the water is in such large

excess that any change in its concentration is negligible.

Example:

In a Hydrolysis Reaction catalyzed by [𝐻+]:

𝑑[𝐴]

𝑑𝑡= 𝑘[𝐴][𝐻+]

When the solution is buffered at constant pH, [𝐻+] is constant and we can write the

equation as:

𝑑[𝐴]

𝑑𝑡= 𝑘[𝐴]

Sample Problems 1. A solution of a drug was freshly prepared at a concentration of 300 mg/ml, after

30 days, the drug concentration in the solution was 75 mg/ml.

a. Assuming First-order kinetics. What is the rate constant? When will the drug decline

to one-half of the original concentration?

b. Assuming Zero-order kinetics. What is the rate constant? When will the drug decline

to one-half of the original concentration?

14

KINETICS OF DRUGS

c. Assuming Second-order kinetics. What is the rate constant? When will the drug

decline to one-half of the original concentration?

2. If the half-life for decomposition of a drug is 12 hr., how long will it take for 125 mg

of the drug to decompose 30%? Assume First-order kinetics and constant

temperature.

3. A pharmacist dissolved a few milligrams of a new antibiotic drug into exactly 100

ml of distilled water and placed the solution in a refrigerator (5 C°). At various time

intervals, the pharmacist removed a 10 ml aliquot from the solution and measured

the amount of drug contained in each aliquot.

a. What is the order of the decomposition process of this antibiotic?

b. What is the rate of decomposition of this antibiotic?

c. How many milligrams of antibiotic were in the original solution prepared by the

pharmacist?

4. Determine the first-order rate constant for the hydrolysis of acetyl-β-methylcholine

at 85˚C from the information given below.

5. Hydrogen peroxide solutions are normally stable, but when metal ions are added,

hydrogen peroxide decomposes:

15

KINETICS OF DRUGS

2𝐻2𝑂2 → 2𝐻2𝑂 + 𝑂2

In a solution containing FeCl3, the concentration of H2O2 varied as follows:

Using these data, determine the order of the reaction with respect to peroxide, and the

value of the rate constant (include appropriate units).

Solutions to Problems 1. 𝐶𝑎 = 75 𝑚𝑔/𝑚𝑙

𝐶𝑎𝑜= 300 𝑚𝑔/𝑚𝑙

𝑡 = 30 𝑑𝑎𝑦𝑠

a. − 𝑙𝑛𝐶𝑎

𝐶𝑎𝑜

= 𝑘𝑡

− 𝑙𝑛75

300= 𝑘(30 𝑑𝑎𝑦𝑠)

𝒌 = 𝟒. 𝟔𝟐 × 𝟏𝟎−𝟐 /𝒅𝒂𝒚

𝑡1/2 = −𝑙𝑛 0.5

𝑘

𝑡1/2 = −𝑙𝑛 0.5

4.62 × 10−2/𝑑𝑎𝑦

𝒕𝟏/𝟐 = 𝟏𝟓 𝒅𝒂𝒚𝒔

b. 𝐶𝑎 − 𝐶𝑎𝑜= −𝑘𝑡

(75 − 300)𝑚𝑔/𝑚𝑙 = −𝑘(30 𝑑𝑎𝑦𝑠)

𝒌 = 𝟕. 𝟓 𝒎𝒈/(𝒎𝒍 ∙ 𝒅𝒂𝒚)

𝑡1/2 =0.5𝐶𝑎𝑜

𝑘

𝑡1/2 =0.5(300

𝑚𝑔𝑚𝑙

)

7.5 𝑚𝑔/(𝑚𝑙 ∙ 𝑑𝑎𝑦)

𝒕𝟏/𝟐 = 𝟐𝟎 𝒅𝒂𝒚𝒔

c. 1

𝐶𝑎−

1

𝐶𝑎𝑜

= 𝑘𝑡

16

KINETICS OF DRUGS

1

75𝑚𝑔𝑚𝑙

−1

300𝑚𝑔𝑚𝑙

= 𝑘(30 𝑑𝑎𝑦𝑠)

𝒌 = 𝟑. 𝟑𝟑 × 𝟏𝟎−𝟒 (𝒅𝒂𝒚)−𝟏 (𝒎𝒈

𝒎𝒍)

−𝟏

𝑡1/2 =1

𝐶𝑎𝑜𝑘

𝑡1/2 =1

300𝑚𝑔𝑚𝑙

(3.33 × 10−4 (𝑑𝑎𝑦)−1 (𝑚𝑔𝑚𝑙

)−1

𝒕𝟏/𝟐 = 𝟏𝟎 𝒅𝒂𝒚𝒔

2. 𝑡1/2 = 12 ℎ𝑟𝑠

𝑡1/2 = −𝑙𝑛 0.5

𝑘

12 ℎ𝑟𝑠 = −𝑙𝑛 0.5

𝑘

𝒌 = 𝟎. 𝟎𝟔/𝒉𝒓

− 𝑙𝑛(1 − 𝑋𝑎) = 𝑘𝑡

− 𝑙𝑛(1 − 0.30) =0.06

ℎ𝑟𝑡

𝒕 = 𝟔. 𝟏𝟕 𝒉𝒓𝒔

3. a. The plot of t vs Ca formed a straight line, therefore the reaction is at zero-

order.

b. The slope of the graph (-k) is -6.55. Therefore, rate constant (k) = 6.55 (mg/ml)

hr

c. The intercept of the graph is 87.30. Therefore, Cao= 87.30 mg/ml

4. The slope (k) of the graph is 0.35. Therefore, rate constant (k) = 0.35/day

5. The plot of t vs ln(Ca/Cao) formed a straight line, therefore the reaction order is

first-order. The slope (k) of the graph is 3.99 x 10-3. The rate constant (k) is 3.99 x

10-3.

17

KINETICS OF DRUGS

References Attwood, D. and Florence, A. (2006). Physicochemical Principles of Pharmacy, 4th ed.

Retrieved from: http://www.scribd.com

Cairns, D. (2008). Essentials of Pharmaceutical Chemistry, 3rd ed. Retrieved from:

http://www.4shared.com/office/_wd4P3B4/Essentials_of_Pharmaceutical_C.htm

Differences between Zero-order kinetics and First-order kinetics. Retrieved from:

http://www.pharmainfo.net/og/rcp/downloads

Drug Stability and Kinetics. Retrieved from: http://www.scribd.com

Drugs following zero order pharmacokinetics.

http://www.lifehugger.com/moc/84/Drugs_following_zero_order_pharmacokinetics

First and zero order kinetics. Retrieved from:

https://sites.google.com/site/pharmacologyinonesemester/2-drug-distribution-

metabolism-and-elimination/2-5-blood-levels/2-5-3-first-and-zero-order-kinetics

Half-lives. Retrieved from:

http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Reaction_Rates/Half-

lives_and_Pharmacokinetics

Levenspiel, O. Chemical Reaction Engineering, 3rd ed. Retrieved from:

http://www.scribd.com