Pharmaceutical Calculations (5)

1
Pharmaceutical Calculations (5)
Dilutions
Phil Rowe Liverpool School of Pharmacy
2
Dilutions
When we dilute a solution, we can inter-relate 4
things C1 The initial concentration (i.e. prior
to dilution)C2 The final concentration (i.e.
after dilution) V1 The initial volume of
solution which is to be dilutedV2 The final
volume of solution after dilution The equation
linking these is C1.V1 C2.V2
3
Dilution factor
When we use the equation, it is usually
re-arranged with one term on the left and three
on the right. Two of the terms on the right hand
side will form a dilution factor. e.g. If we
want to calculate C2, knowing that 10mL of a
20mg/mL solution has been diluted to 200mL, we
would re-arrange the equation to C2 C1 x V1
V2 C2 20mg/mL x 10mL
200mL C2 20mg/mL x 0.05
1mg/mL The ratio of the two volumes on the right
hand side indicates the extent of dilution. In
this case it is 10200, indicating a 20 fold
dilution. As they have to form a ratio, it is
essential that the two volumes are in the same
units. There is no restriction on the units of
C1.
Dilution factor of 1/20 0.05
4
Re-arrangements of C1.V1 C2.V2
This equation can be re-arranged to allow us to
calculate any one of the terms, so long as we
know the values for the other three.
C1 C2 x V2
V1 C2 C1 x V1
V2 V1 V2 x C2
C1 V2
V1 x C1 C2
Dilution factors. Units of the two volumes or
concentrations must match.
5
C1 C2 x V2 / V1
Example question that would require equation
above What concentration of stock solution
should we prepare, so that we can take 10mL of
that stock and dilute it to 2.5L and the result
will be a 200mg/L solution? Note that we are
provided with values for all the terms on the
right hand side (C2 ,V2 V1) and so we can
calculate an appropriate initial concentration
(C1)
C1 C2 x V2 / V1 200mg/L x 2.5L / 10ml
(Use mL as common unit for dilution)
200mg/L x 2,500mL / 10mL 200mg/L x 250
50,000mg/L 50g/L
6
C2 C1 x V1 / V2
Example question that would require equation
above If we diluted 50ml of 0.45M phenol to a
final volume of 15L, what would be the resultant
concentration?
C2 C1 x V1 / V2 0.45M x 50ml / 15L
(Use mL as common unit for dilution) 0.45M
x 50mL / 15,000mL 0.45M x 0.00333
0.0015M 1.5mM
7
V1 V2 x C2 / C1
Example question that would require equation
above If we want to dilute a solution of sodium
dodecyl sulphate (5g/L) to produce 2L of a
50mg/100mL solution, what volume of the original
solution should we use?
V1 V2 x C2 / C1 2L x 50mg/100mL / 5g/L
(Use mg/L as common unit for dilution) 2L
x 500mg/L / 5,000mg/L 2L x 0.1
0.2L 200mL
8
V2 V1 x C1 / C2
Example question that would require equation
above If we are starting with 50ml of a solution
contaminated with 12ppm of aluminium, to what
volume would we need to dilute it, to reduce the
aluminium concentration to 0.1ppm? (Assume the
diluent is aluminium free.)
V2 V1 x C1 / C2 50ml x 12ppm / 0.1ppm
(Both parts of dilution 50mL x 120
already in same units)
6,000ml 6L
9
Caution!!!What exactly is V2?
Some dilution questions can be deceptive. For
example If we diluted 1L of sulphuric acid (1M)
with 5L of water, what is the resultant
concentration? C2 is the unknown and It is all
too easy to think that we know the values of the
other 3 parameters to be
C1 1MV1 1LV2 5L
No!!!
V2 Is supposed to be the total final volume. 5L
is the volume of diluent, but the total final
volume is 6L and this is the true value of V2
10
Assumption that volumes are additive
In order to be able to calculate the
concentration in the previous slide, we would
have to assume that mixing 1L of dilute sulphuric
acid and 5L of water will result in a total
volume of 6L. This assumption does not
necessarily hold for all liquids, but if all the
materials are reasonably dilute aqueous
solutions, there will be no significant error.
11
Being aware that the volume of diluent, is NOT V2
(Example 1)
What concentration will arise if we mix together
the following- 250ml carbamazepine solution
(1g/L)750ml phosphate buffer (pH 7.4)
C1 1g/LV1 50mlV2 250ml 750ml
1,000ml C2 C1 x V1 / V2 1g/L x 250ml /
1,000ml 1g/L x 0.25 0.25g/L
12
Being aware that the volume of diluent, is NOT V2
(Example 2)
We start with 2L of 0.2M sodium carbonate and we
need to dilute it to 0.01M. How much water
should we add?
C1 0.2MC2 0.01MV1 2L V2 V1 x C1 / C2
2L x 0.2M / 0.01M 2L x 20 40L
Beware The figure of 40L is the final volume
required. That does not mean that we should
dilute with 40L of water. What we should do is
to add 38L of water to bring the final total
volume up to 40L
13
Examples of dilution calculations
Question 1 What concentration would arise if
350ml of potassium chloride solution (1.8g/100ml)
was diluted to a volume of 7L?
14
Examples of dilution calculations
Question 2 We want to be able to take 500ml of a
stock solution of hydrochloric acid and dilute it
by the addition of 3L of water, producing a final
concentration of 0.1M. What should be the
strength of the stock solution?
15
Examples of dilution calculations
Question 3 What volume of a 400ppm solution of
fluoride should be diluted to 200L to produce a
0.8ppm solution?
16
Examples of dilution calculations
Question 4 If we start with 100ml of a 5mM
solution of human serum albumin and need to
dilute this to 12.5microM, to what volume should
it be diluted?
17
Examples of dilution calculations
Question 5 How much water should we add to 2ml of
theophylline solution (60mg per 5ml) to produce a
concentration of 2mg/ml?
18
Examples of dilution calculations
Question 6 We want to be able to take
200microlitres of ethanol solution and dilute it
to 4ml thereby achieving a concentration of
0.5(v/v). What should be the strength of the
original solution?
19
Examples of dilution calculations
Answer 1 What concentration would arise if 350ml
of potassium chloride solution (1.8g/100ml) was
diluted to a volume of 7L? (Answer in units of
g/L) C2 C1 x V1 / V2 1.8g/100ml x
350ml / 7L (Use mL as common units
1.8g/100ml x 350ml / 7,000mL for
dilution) 1.8g/100mL x 0.05 0.9g/L
20
Examples of dilution calculations
Answer 2 We want to be able to take 500ml of a
stock solution of hydrochloric acid and dilute it
by the addition of 3L of water, producing a final
concentration of 0.1M. What should be the
strength of the stock solution? Caution Final
volume produced (V2) is 3.5L (Not 3L). C1 C2 X
V2 / V1 0.1M x 3.5L / 500ml (Use L as
common units for dilution) 0.1M x 3.5L /
0.5L 0.1M x 7 0.7M
21
Examples of dilution calculations
Answer 3 What volume of a 400ppm solution of
fluoride should be diluted to 200L to produce a
0.8ppm solution? V1 V2 x C2 / C1 200L x
0.8ppm / 400ppm (Both concs already in same
units) 200L x 0.002 0.4L
400mL
22
Examples of dilution calculations
Answer 4 If we start with 100ml of a 5mM solution
of human serum albumin and need to dilute this to
12.5 microM, to what volume should it be
diluted? V2 V1 x C1 / C2 100ml x 5mM /
12.5microM (Concentration units need to match)
100ml x 5,000microM/12.5microM 100mL
x 400 40,000ml 40L
23
Examples of dilution calculations
Answer 5 How much water should we add to 2mL of
theophylline solution (60mg per 5mL) to produce a
concentration of 2mg/mL? V2 V1 x C1 / C2
2mL x 60mg/5mL / 2mg/mL (Use mg/mL as common
units) 2mL x 12mg/mL / 2mg/mL
2ml x 6 12mL BUT this is the final volume and
we were asked for the volume of diluent. Diluent
vol 12ml 2ml 10ml
24
Examples of dilution calculations
Answer 6 We want to be able to take
200microlitres of ethanol solution and dilute it
to 4ml thereby achieving a concentration of
0.5(v/v). What should be the strength of the
original solution? C1 C2 X V2 / V1 0.5
x 4ml / 200microlitres(Use mL as common units for
dilution) 0.5 x 4mL / 0.2mL 0.5 x
20 10(v/v)
25
What you should be able to do

• Calculate
• An initial concentration (C1), so that when a
  volume (V1) is diluted to a volume (V2) it will
  yield a concentration (C2).
• A volume (V1) of solution of concentration (C1)
  that when diluted to volume (V2) will yield
  concentration (C2).
• The concentration (C2) that will arise if
  volume (V1) of a solution of concentration (C1)
  is diluted to volume (V2).
• The volume (V2) to which volume (V1) of a
  solution of concentration (C1) must be diluted in
  order to yield concentration (C2)
• Deal properly with those cases that either
  provide, or ask you to calculate, the volume
  of diluent rather than the final total volume
  (V2).