PHYSICAL PHARMACEUTICS-2 UNIT 5TH

DRUG STABILITY

Most Important Question

Drug Stability

• It is the ability of a drug to maintain its quality, potency and safety over time without degradation, when stored under specified conditions.

Reaction Kinetics

• It includes the study of the speed or rate of chemical process that occurs during chemical reactions.

  A (Reactant) $\rightarrow$ B (product)

• Rate of reactions, is the speed at which chemical reactions take place depends on concentration and time.

  $$Rate of reactions = \pm \frac{dc}{dt} = \frac{\text{change in concentration}}{\text{change in time}}$$

ZERO ORDER REACTIONS

• These are those reactions, in which rate of reaction is independent of the concentration of the reactant.

• In this, reaction rate remains constant because of zero order reaction.

  • Let,

A $\rightarrow$ B $$Rate = k[A]^x$$ At this, $x=0$ so, $Rate = k$

• Rate of reaction $= \frac{-dA}{dt}$
• So, $\frac{-dA}{dt} = k$

• Where,

  $\frac{-dA}{dt} =$ change in concentration with respect to time

  $k =$ specific rate constant for zero order.

Derivation :

• The rate of zero order $= \frac{-dA}{dt} = k$ or

  $-dA = k \times dt$

• On integrating both sides,

  $$\int dA = k \int dt$$

  $$-[A]_{A_0}^{A_t} = k[t]_0^t$$

$$-[A_t - A_0] = k(t - 0)$$

$$A_0 - A_t = kt$$

$$k = \frac{A_0 - A_t}{t}$$

Where
$k =$ rate constant
$A_0 =$ starting concn of reactant at $t=0$
$A_t =$ concn of reaction (final) after time $t=time$

Half Life : It is the time required to reduce half amount of Initial concentration of reactant.

Initial $conc^n = A_0$
Final $conc^n = \frac{A_0}{2}$ at half time $t_{1/2}$

• By putting these value in main equation -
  $$k = \frac{A_0 - A_0/2}{t_{1/2}}$$
  $$k(t_{1/2}) = \frac{A_0}{2}$$
  $$t_{1/2} = \frac{A_0}{2k}$$

• Half life is directly proportional to the initial concn of reactant.

Shelf Life : It is the time required to reduces the reactant concentration up to 90% from the initial concentration.

• Initial $conc^n = A_0$
• Final $conc^n = A = 0.9(A_0)$

• Putting these value into main eq

  $$k = \frac{A_0 - A}{t} = \frac{A_0 - 0.9 A_0}{t_{0.9}}$$
  $$t_{0.9} = \frac{0.1 A_0}{k}$$

• Shelf life for zero order reactions

FIRST ORDER REACTIONS

• It is, when rate of reaction depend on the concentration of reactant.

  A $\rightarrow$ B (product)
  $$Rate = k[A]^1$$
  $$Rate = \frac{-d(A)}{dt}$$

• Equate both

  $$k[A] = \frac{-d(A)}{dt}$$

or $$k \cdot dt = \frac{-d(A)}{[A]}$$

Integration on Both Sides

$$k \int dt = -\int \frac{dA}{A}$$
$$k[t]_0^t = -[\log A]_{A_0}^{A_t}$$
$$kt = -[\log A_t - \log A_0]$$
$$kt = -\left[\log \frac{A_t}{A_0}\right] \quad \text{Or} \quad kt = 2.303 \log_{10} \left[\frac{A_0}{A_t}\right]$$
$$k = \frac{2.303}{t} \log \left[\frac{A_0}{A_t}\right]$$

For half life

$$k \cdot t_{1/2} = 2.303 \log \left[\frac{A_0}{A_0/2}\right]$$
$$t_{1/2} = \frac{2.303 \log(2)}{k}$$
$$t_{1/2} = \frac{0.693}{k}$$

• Hint: $A_t = A_0 e^{-kt}$ in exponential form

  

• For shelf life (t_{0.9}$) $\rightarrow $$A_t = 0.9 A_0$$
  $$t_{0.9} = \frac{2.303}{k} \log \left[\frac{A_0}{0.9 A_0}\right]$$
  $$t_{0.9} = \frac{2.303}{k} \log [10/9]$$
  $$t_{0.9} = \frac{2.303}{k} \log [1.11]$$
  $$t_{0.9} = \frac{0.105}{k}$$

Accelerated Stability Testing

• Stability of drug product is the ability of drugs to maintain its quality (retains its properties).

Expiry Date

• It is the time period, at which drug is safe but after this time drug is not considered for use.

• Now, expiration date of drug is selected on the basis of its shelf life and its accelerated stability testing.

Shelf Life

• It is defined as the time required for concn of the reactant to reduce 90% of its Initial / original concn.
• Is the period of time at which food/drug maintain its safety and quality.

Accelerated Stability Testing

• In this test, the rate of decomposition of drug is accelerated or increases by providing high temp, high humidity & light conditions.
• Because, high temperature increase instability or decomposition of drug products.
• From this, we get idea regarding decomposition of drug when it stored for long period of time.

• In this we rise the temp for storage.
• 25°C product
• 45°C product
• 40°C
• 60°C
• Relative humidity also increases

• It is based on Arrhenius equation. $$k = A e^{-E_a/RT}$$
• According to Arrhenius, for every 10°C rise in temp, speed of reaction increases upto 2-3 times.

• Product stored at diff-diff temperatures.

• After all this, Calculate its shelf life which is safe for the use of the products.

Degradation : It is the process of decreasing the quality of products.

Factor Affecting

• Temperature
• Light
• Moisture/humidity
• Degradation depends on $\rightarrow$ pH, solvent, excipients, buffer.

Photolytic Degradation :

• It is the process of decreasing the quality of product through sunlight/light.
• Photon + lytic $\rightarrow$ light breakdown its prevent $\rightarrow$ Chem dy