Lecture 12 - Chemical kinetics and stability of dosage forms 2

Question 1

When we talk about second order reactions we are talking about what type of reactions?

Answer 1

biomolecular.

Question 2

What is a biomolecular reaction?

Answer 2

Two molecules come together to from a product.

Question 3

Two possibilities for biomolecular reactions. Which one are we focusing on?

Answer 3

1. two reactants with equal concentrations. This is what we are focusing on.
   A+B –> C
   2A –> B
2. Two reactants with different concentrations.
   A + B –> C Rate is proportional to two different concentrations.

Question 4

Rate equation for A + B –> C second order reaction where concentration of reactants are the same.

Answer 4

Question 5

Rate equation for 2A –> B second order reaction where concentration of reactants are the same.

Answer 5

Question 6

Overall rate equation for second order.

Answer 6

Question 7

How can we work out rate constant for second order reactions?

Answer 7

We can calculate the rate constant by plotting 1/[A] versus time. Graph will be a straight line with a positive gradient. The gradient of this graph is K

Question 8

K equation second order reaction.

Answer 8

Question 9

What is the relationship between
and half life for second order reactions and initial concentration of the drug.

Answer 9

Half life is inversely proportional to the initial concentration of the drug.

Question 10

Give the equation for half life of a second order reaction.

Answer 10

Question 11

Describe the relationship between shelf life and initial concentration in second order reaction

Answer 11

shelf life is dependent upon the initial concentration - also inversely proportional to the concentration of the drug

Question 11

Equation of half life to shelf life ratio

Answer 11

Question 12

Give equation for shelf life in second order reactions.

Answer 12

Question 13

There are different methods of determining reaction order. Name the three.

Answer 13

substitution method, shelf life method, graphical method

Question 14

Describe substitution method to determining order of reaction

Answer 14

Substitution method: substitute degradation data into the rate equations to see which they fit with. If K remains constant it is zero, if K and concentration are directly proportional, it is first order.

Question 15

Describe the shelf-life method for determining reaction order

Answer 15

for zero order, increasing initial concentration will increase shelf life. For first order, there is no relationship between initial concentration and shelf life. For second order increasing initial concentration decreases the shelf life.

Question 16

Describe graphical method for determining reaction order.

Answer 16

draw a graph for natural log against time. Zero order is curved, first order is straight down, and second order is curved below the first order line.

Question 17

Factors affecting reaction rate

Answer 17

• Temperature
• pH
• pressure
• catalysts
• solvent
• ionic strength
• relative humidity
• excipients
• light.

Question 18

Describe the effect of ionic strength on reaction rate.

Answer 18

• electrolytes are often added to drug solutions
• non reacting or inert ionic species can affect the rate of drug degradation- the salt effect
• rate can also be affected by the concentrations of ions such as H+ and OH-

Question 19

What is the effect of pH on reaction rate? How can we protect drugs from the effects?

Answer 19

• pH has a significant effect on the apparent rate constant for many reactions
• hydrolysis is often catalysed by H+ or OH- ions (specific acid and specific base catalysis)
• rate of hydrolysis increases at low and high pH compared to neutral pH
• buffering may protect drugs from specific acid or base catalysis
• As buffer concentration changes so does K

Question 20

For a reaction to occur what must happen?

Answer 20

Molecules must come in contact with each other.
Collisions don’t necessarily cause reactions- frequency of collisions is not responsible for changing rection rate. Only molecules with energy of activation will react

Question 21

What does the Arrhenius equation describe?

Answer 21

the relationship between temperature, reaction rate and activation energy.

Question 22

What is the Arrhenius equation? Label it.

Answer 22

K= rate constant
A = Arrhenius factor
Ea = activation energy
R = gas constant 8.314 Jmol-1k-1
T = absolute temperature, K

Question 23

What does the pre-exponential / frequency factor tell us?

Answer 23

tells us the number of molecules which collide in the right orientation with sufficient energy.
The frequency of collisions that could yield a reaction

Question 24

What is activation energy?

Answer 24

The minimum amount of energy needed for a chemical reaction to occur

Question 25

Effect of temperature in relation to activation energy.

Answer 25

• By increasing temperature, you increase the number of molecules with sufficient energy to react.
  Only a small fraction of molecules at T1 have sufficient energy to undergo a chemical reaction. A large proportion of molecules at T2 have sufficient energy to undergo a chemical reaction.

Question 26

Accelerated stability testing is good. Why?

Answer 26

• can reject unsatisfactory formulations early in development
• Rapid detection of deterioration.
• Prediction of shelf life.
• Rapid quality control.

Question 26

In the past, pharmaceutical companies used to observe stability over the entire shelf life of a product. This was not great. Why? What do we do now?

Answer 26

time consuming and uneconomical.
Now, we do accelerated stability testing

Question 27

Stability testing protocols need to cover…?

Answer 27

the temperature and humidity of storage, storage time before sampling, number of batches to be samples, number of replicates with each batch, suitable light challenge, details of assay.

Question 28

How does accelerated stability testing link to the Arrhenius equation?

Answer 28

• For drugs that degrade slowly, accelerated stability testing can be used: raise temperature and determine k values then extrapolate Arrhenius plot to determine k at room temperature.

Question 29

log form of Arrhenius equation

Answer 29

Question 30

We can plot a graph for lnk against 1/T. From this graph how can we find activation energy?

Answer 30

-Ea/R = the gradient  from this we can work out the activation energy/Ea
(multiply gradient by R and change the sign to get + Ea)

Question 31

Ball park that activation energy should be in

Answer 31

50 and 100

Question 32

We can plot a graph for lnk against 1/T. From this graph how can we find A?

Answer 32

lnA is the y intercept. We extrapolate data to find lnA and then from that, A.

Question 33

Two ways to extrapolate to find lnA

Answer 33

1. extend our line on the graph so it hits the y axis. This y intercept is lnA). A = e^lnA
2. We know that the y intercept = lnA. If we know Ea, we therefore know the gradient of the line (-Ea/R). Gradient is also equal to (change in y)/(change in x)….

y1 = lnA
x1 = 0

(y2-y1)/(x2-x1) = gradient
(y2- lnA)/(x2-0) = gradient
lnA= y2- (gradient × (x2-0))

Question 34

We can also work out A using the Arrhenius equation and not by extrapolating just using experimental data. Give equation

Answer 34

Question 35

How could we find shelf life and half life of a drug at room temperature, 20 degrees, using the Arrhenius equation (if the temperatures on the graph are all high temps because of accelerated stability testing)

Answer 35

1. We have temperature, so we can calculate 1/T.
2. Take two random plots on the line- these are x1 and y1
3. Make the 1/T for 20 degrees Celsius x2
4. y2 = lnk
5. gradient = (lnk – y1)/(x2-x1)
6. to find lnk… lnk= y1-(gradient ×difference in x)
7. K is the antilog of lnk
8. Input K into equations for half-life and shelf life (for the specific order of reaction)

Question 36

limitations to accelerated stability testing

Answer 36

• Temperature increase may need to be very large.
• Assumes reaction mechanism is constant over experimental range and extrapolation.