Transcript Measures of mass (1) grams

Pharmaceutical
Calculations (2)
Re-expressing simple
mass/volume concentrations
Phil Rowe Liverpool School of Pharmacy
Re-expressing concentrations
- the plan of the next 3 presentations
We will tackle the problem of
re-expressing concentrations
in three stages. These are
shown on the next 3 slides:-
Pharmaceutical calculations 2
Molarity
%(w/v)
ppm
Ratio
Mass/volume
Molarity
%(w/v)
ppm
Ratio
Current presentation ‘Pharmaceutical
Calculations (2)’ deals only with interconversions within this category.
i.e. one mass/volume into another.
Pharmaceutical calculations 3
Molarity
%(w/v)
ppm
Ratio
Mass/volume
Molarity
%(w/v)
ppm
Ratio
The next presentation ‘Pharmaceutical Calculations
(3)’ will deal with interconversions EITHER from
mass/volume to another system OR from another
system to mass/volume
Pharmaceutical calculations 4
Molarity
%(w/v)
ppm
Ratio
Mass/volume
Molarity
%(w/v)
ppm
Ratio
Then ‘Pharmaceutical Calculations (4)’ will deal
with inter-conversions from any system to any
other, using mass/volume as an intermediate
step where necessary.
Inter-converting
concentrations expressed as
mass/volume
Tips
Tip (1)
Take it easy – Do one step at a time.
Example:
You need to convert 25mg per 5ml to units of g/L. If you
are very confident you could do it in a single step,
changing both the volume and the mass units. However,
at this stage, you are probably better tackling one thing at
a time.
It would be possible to change either the volume first and
then the mass or vice versa. Either is OK. In the example
calculation that follows, volume is tackled first.
Tip (1)
Take it easy – Do one step at a time.
Example:
You need to convert 25mg per 5ml to units of g/L.
First convert the volume to litres
25mg per 5ml = 5mg/ml
= 5,000mg/L
Then convert the mass to grams
5,000mg/L = 5g/L
Tip (2)
When converting from one unit to another,
jump one level at a time.
Example:
You need to convert 0.0025g/L to units of microgram/100ml.
When tackling the mass units, don’t try to jump directly from
g to micrograms; go via milligrams.
Convert grams to micrograms via mg
0.0025g/L = 2.5mg/L
= 2,500microgram/L
Convert the volume to 100ml
2,500microgram/L = 250microgram/100ml
Tip (3)
The “Increase/decrease both units” rule
When a conversion involves either:
• Increasing both the mass and volume units by one level or
• Decreasing both the mass and volume units by one level
there is no effective change of units and the number stays
the same.
15mg/ml = 15g/L (mg goes up to g. ml goes up to L.)
200mg/L = 200microgram/ml (mg goes down to microgram.
L goes down to ml.)
0.75ng/ml = 0.75microgram/L (ng goes up to microgram.
ml goes up to L.)
Tip (4)
Avoid intermediate calculations with
excessively small or large numbers
Example:
A solution contains 1.5 microgram per 0.1ml. Re-express as
g/L.
You could proceed as below (But I wouldn’t recommend it!)
Convert micrograms to grams via mg
1.5microgram/0.1ml = 0.0015mg/0.1ml
= 0.0000015g/0.1ml
Convert the volume to litres
0.0000015g/0.1ml = 0.000015g/ml
= 0.015g/L
Profusion of zeros
makes arithmetic
errors very likely!
Tip (4)
Avoid intermediate calculations with
excessively small or large numbers
A better approach is:
A solution contains 1.5 microgram per 0.1ml. Re-express as
g/L.
Convert 0.1ml to 1ml
1.5microgram/0.1ml = 15microgram/ml
Convert microgram to mg
15microgram/ml = 0.015mg/ml
Use the “increase/decrease both units” rule
0.015mg/ml = 0.015g/L
Examples of inter-converting
mass/volume concentrations
Question 1 (of 12)
Re-express 0.75mg/100ml in units of
microgram/100ml
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 2 (of 12)
Re-express 2.5mg per 5ml in units of mg/L
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 3 (of 12)
Re-express 655mg/L in units of microgram/ml
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 4 (of 12)
Re-express 800mg/L in units of g/100ml
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 5 (of 12)
Re-express 40mg per 5ml in units of g/L
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 6 (of 12)
Re-express 35mg/L in units of g/L
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 7 (of 12)
Re-express 50mg/ml in units of g/L
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 8 (of 12)
Re-express 150microgram/ml in units of mg per 5ml
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 9 (of 12)
Re-express 0.035g/100ml in units of mg/L
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 10 (of 12)
Re-express 7,500pg/ml in units of microgram/ml
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 11 (of 12)
Re-express 60microgram per 5ml in units of mg
per 5ml
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Question 12 (of 12)
Re-express 0.004mg/ml in units of ng/ml
Answers are provided after all the questions.
Examples of inter-converting
mass/volume concentrations
Answer 1
Re-express 0.75mg/100ml in units of
microgram/100ml
[Only mass units change]
0.75mg/100ml = 750microgram/100ml
Examples of inter-converting
mass/volume concentrations
Answer 2
Re-express 2.5mg per 5ml in units of mg/L
2.5mg per 5ml = 5mg/10ml
= 500mg/L
Examples of inter-converting
mass/volume concentrations
Answer 3
Re-express 655mg/L in units of microgram/ml
[Use “Increase/decrease both units” rule]
655mg/L = 655microgram/ml
Examples of inter-converting
mass/volume concentrations
Answer 4
Re-express 800mg/L in units of g/100ml
800mg/L = 0.8g/L
= 0.08g/100ml
Examples of inter-converting
mass/volume concentrations
Answer 5
Re-express 40mg per 5ml in units of g/L
40mg per 5ml = 8mg/ml
[Use “Increase/decrease both units” rule]
8mg/ml = 8g/L
Examples of inter-converting
mass/volume concentrations
Answer 6
Re-express 35mg/L in units of g/L
[Only mass units change]
35mg/L = 0.035g/L
Examples of inter-converting
mass/volume concentrations
Answer 7
Re-express 50mg/ml in units of g/L
[Use “Increase/decrease both units” rule]
50mg/ml = 50g/L
Examples of inter-converting
mass/volume concentrations
Answer 8
Re-express 150microgram/ml in units of mg per
5ml
150microgram/ml = 0.15mg/ml
= 0.75mg per 5ml
Examples of inter-converting
mass/volume concentrations
Answer 9
Re-express 0.035g/100ml in units of mg/L
0.035g/100ml = 35mg/100ml
= 350mg/L
Examples of inter-converting
mass/volume concentrations
Answer 10
Re-express 7,500pg/ml in units of microgram/ml
[Mass units change two levels - go via ng]
7,500pg/ml = 7.5ng/ml
= 0.0075microgram/ml
Examples of inter-converting
mass/volume concentrations
Answer 11
Re-express 60microgram per 5ml in units of mg
per 5ml
[Only mass units change]
60microgram per 5ml = 0.06mg per 5ml
Examples of inter-converting
mass/volume concentrations
Answer 12
Re-express 0.004mg/ml in units of ng/ml
[Mass units change two levels - go via microgram]
0.004mg/ml = 4microgram/ml
= 4,000ng/ml
What you should be able to do
• Re-express a concentration quoted in
units of mass/volume in any other units of
mass/volume