Lecture 12 - Chemical kinetics and stability of dosage forms 2 Flashcards
When we talk about second order reactions we are talking about what type of reactions?
biomolecular.
What is a biomolecular reaction?
Two molecules come together to from a product.
Two possibilities for biomolecular reactions. Which one are we focusing on?
- two reactants with equal concentrations. This is what we are focusing on.
A+B –> C
2A –> B - Two reactants with different concentrations.
A + B –> C Rate is proportional to two different concentrations.
Rate equation for A + B –> C second order reaction where concentration of reactants are the same.
Rate equation for 2A –> B second order reaction where concentration of reactants are the same.
Overall rate equation for second order.
How can we work out rate constant for second order reactions?
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
K equation second order reaction.
What is the relationship between
and half life for second order reactions and initial concentration of the drug.
Half life is inversely proportional to the initial concentration of the drug.
Give the equation for half life of a second order reaction.
Describe the relationship between shelf life and initial concentration in second order reaction
shelf life is dependent upon the initial concentration - also inversely proportional to the concentration of the drug
Equation of half life to shelf life ratio
Give equation for shelf life in second order reactions.
There are different methods of determining reaction order. Name the three.
substitution method, shelf life method, graphical method
Describe substitution method to determining order of reaction
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.
Describe the shelf-life method for determining reaction order
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.
Describe graphical method for determining reaction order.
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.
Factors affecting reaction rate
- Temperature
- pH
- pressure
- catalysts
- solvent
- ionic strength
- relative humidity
- excipients
- light.
Describe the effect of ionic strength on reaction rate.
- 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-
What is the effect of pH on reaction rate? How can we protect drugs from the effects?
- 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
For a reaction to occur what must happen?
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
What does the Arrhenius equation describe?
the relationship between temperature, reaction rate and activation energy.
What is the Arrhenius equation? Label it.
K= rate constant
A = Arrhenius factor
Ea = activation energy
R = gas constant 8.314 Jmol-1k-1
T = absolute temperature, K
What does the pre-exponential / frequency factor tell us?
tells us the number of molecules which collide in the right orientation with sufficient energy.
The frequency of collisions that could yield a reaction
What is activation energy?
The minimum amount of energy needed for a chemical reaction to occur
Effect of temperature in relation to activation energy.
- 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.
Accelerated stability testing is good. Why?
- can reject unsatisfactory formulations early in development
- Rapid detection of deterioration.
- Prediction of shelf life.
- Rapid quality control.
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?
time consuming and uneconomical.
Now, we do accelerated stability testing
Stability testing protocols need to cover…?
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.
How does accelerated stability testing link to the Arrhenius equation?
- 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.
log form of Arrhenius equation
We can plot a graph for lnk against 1/T. From this graph how can we find activation energy?
-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)
Ball park that activation energy should be in
50 and 100
We can plot a graph for lnk against 1/T. From this graph how can we find A?
lnA is the y intercept. We extrapolate data to find lnA and then from that, A.
Two ways to extrapolate to find lnA
- extend our line on the graph so it hits the y axis. This y intercept is lnA). A = e^lnA
- 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))
We can also work out A using the Arrhenius equation and not by extrapolating just using experimental data. Give equation
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)
- We have temperature, so we can calculate 1/T.
- Take two random plots on the line- these are x1 and y1
- Make the 1/T for 20 degrees Celsius x2
- y2 = lnk
- gradient = (lnk – y1)/(x2-x1)
- to find lnk… lnk= y1-(gradient ×difference in x)
- K is the antilog of lnk
- Input K into equations for half-life and shelf life (for the specific order of reaction)
limitations to accelerated stability testing
- Temperature increase may need to be very large.
- Assumes reaction mechanism is constant over experimental range and extrapolation.
