Calculations and
Conversions
LAT Chapter 14
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Chapter 14
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Calculations & Conversions
Chapter 14
• Experimental methodology requires calculation.
 water consumption, record and convert temperatures, determine
the floor area of a cage, detergent solution
• Pharmacology: the science of drugs, their composition,
use, and administration
• The amount of a drug administered to a patient, based on
the species and body weight (usually noted in milligrams
of drug per kilogram body weight or mg/kg) = dosage.
• The dosage is also influenced by an animal’s age, health,
and state of excitement.
Conversions
Chapter 14
• To determine dosages, it is often necessary to convert
weights and volumes from one measuring system to the
other (English to metric).
 For example, a technician might be required to convert kilograms
to pounds, centimeters to inches, or ounces to milliliters.
• You can use tables or a conversion factor by which you
either multiply or divide.
• Generally we use ratios to convert metric to English
systems or to change units of measurement within a
system.
Dose Calculations 1
Chapter 14
2.5% = 2.5 parts/100 parts, or in milligrams, 2.5 mg/100 mg
25 mg =
1 ml
1000 mg
? Ml
25 mg x ? ml = 1000 mg x 1 ml
25 mg x ? ml = 1000 mg x 1 ml
25 mg
25 mg
? ml = 1000 ml
25
? ml = 40 ml
40 ml of dilutant must be added to prepare a 2.5% solution from 1000
mg of anesthetic.
Dose Calculations 1(part 2)
Chapter 14
1000 mg
40 ml
=
300 mg
? ml
1000 mg x ? ml = 300 mg x 40 ml
1000 mg x ? ml
1000 mg
=
300 mg x 40 ml
1000 mg
? ml = 300 x 40 ml
1000
? ml = 12 ml
12 ml of a 2.5% anesthetic solution contains 300 mg of anesthetic.
Dose Calculations 2
Chapter 14
4/100 = 4% = 40 mg/ml
40 mg = 1000 mg
1 ml
? Ml
40 mg x ? ml = 1000 mg x 1 ml
40 mg x ? ml = 1000 mg x 1 ml
40 mg
40 mg
? ml = 1000 ml
40
? ml = 25 ml
25 ml of dilutant must be added to prepare a 4% solution from 1000
mg of anesthetic.
Dose Calculations 2 (part 2)
Chapter 14
18kg x 2.2 lb = 39.6 lb
kg
1 ml = ? Ml
5 lb
39.6 lb
? ml x 5 lb = 1 ml x 39.6 lb
? ml x 5 lb = 1 ml x 39.6 lb
5 lb
5 lb
? ml = 39.6 ml
5
? ml = 7.92 ml
Conversion of % Solutions
Chapter 14
• Solutions are homogeneous mixtures of two or more
constituents.
• A solution can take the form of a gas, a liquid, or a solid.
• Gaseous solutions are made by dissolving one gas in
another.
• Since all gases mix in all proportions, any mixture of two
or more gases is homogeneous and is a solution.
• In solid solutions one component is randomly dispersed
on an atomic or molecular scale throughout another
component.
• Liquid solutions are made by dissolving a gas, liquid, or
solid in a liquid.
 If the liquid is water, the solution is called an aqueous solution.
Solution Components
Chapter 14
• In making up a solution, at least one constituent must be
a solute and one a solvent.
• Substance present in larger amount = solvent.
 Substance present in the smaller amount = solute.
• % of solute may = % by weight or % by volume.
• % by weight = total solution mass of solute.
 % weight in volume (w/v) expresses the no. of grams of solute in
100 milliliters (ml) of solvent.
 % weight in weight (w/w) expresses the no. of grams of solute in
100 grams of solvent.
Solution Components pt.2
Chapter 14
• 5 g of dextrose dissolved in sufficient water to bring the
final volume to 100 ml is a 5 % dextrose solution by
weight in volume (w/v).
• Set up in ratio fashion to translate them into a more
useful expression of mg/g or mg/ml.
5g
=
100 ml
?g
1 ml
100 ml x ? g = 1 ml x 5 g
A simple way to translate %
into mg/ml or mg/g is to move
the decimal point one place to
the right.
For example:
? = 0.05 g/ml
5.0 % = 50 mg/ml
or, since there are 1000 mg/g
2.2 % = 22 mg/ml
? = 50 mg/ml
20.0 % = 200 mg/ml
Percent by Volume
Chapter 14
• % by volume is the percent of the final solution volume
represented by the volume of the solute taken to make
the solution (v/v).
• For example, a 12 % alcohol solution by volume would
be a solution made from 12 ml of alcohol and enough
solvent to bring the total volume up to 100 ml.
Molar Solutions
Chapter 14
• Molecular weight = sum of atomic weights of atoms in a
molecule.
 A 1-molar solution contains the molecular weight (MW) in grams
of that compound per liter of solution.
• To make an aqueous solution of cobalt chloride (CoCl2) it would be
necessary to calculate the MW of CoCl2 from the Periodic Table:
Atomic mass of Co = 58.85 x 1 = 58.85
Atomic mass of Cl = 35.5 x 2 = 71.00
Molecular Weight in g of CoCl2 = 129.85
 1 M solution of CoCl2, 129.85 g of CoCl2 are weighed & dissolved
in water to a total volume of 1000 ml, or 1 L.
 If 2 moles are needed, 129.85 x 2, which equals 259.7 g/L. This
weight of cobalt chloride is added to a 1-liter volumetric flask, &
the flask is filled to the one liter mark with water, giving a final
volume of 1 liter of a 2M solution of CoCl2.
Molality
Chapter 14
• No. of moles of solute per 1000 grams of solvent.
• Therefore, a 1-molar aqueous solution of sucrose,
C12H22Oll, contains 342.2 g of sucrose in 1000 g of water.
• This is calculated by multiplying the atomic mass of each
substance by its respective number of moles.
 C12H22O11
Atomic Mass of C = 12.0 x 12 = 144.0
Atomic Mass of H = 1.01 x 22 = 22.2
Atomic Mass of O = 16.0 x 11 = 176.0
Molecular weight of sucrose in g = 342.2
Statistics, Calculations and Conversions
Chapter 14
Additional Material and Review
Statistics, Calculations and Conversions
Chapter 14
Statistics is a branch of mathematics that deals with the
collection, analysis, interpretation, and presentation
of numerical data.
The collection of the raw data is the most important step
in the use of statistics to make valid conclusions about the
topic being studied.
Statistics are usually used to determine if any differences
exist between treated groups and control groups of animals.
Statistics, Calculations and Conversions
Chapter 14
• Terminology
Validity - conclusions are correctly drawn from the data
Random, Random Selection, Random Number Tables
- members in a given set have an equal probability
of an event occurring
Populations - sets of animals or objects that have some
common characteristic
Samples - subsets of the population
Parameters - measurable characteristics
Bias - tendency to deviate from the truth
Statistics, Calculations and Conversions
Chapter 14
Conversions - change weights or volumes from one
measuring system to another using a conversion factor
1 inch = 2.54 cm
1 gallon = 3.87 liters
1 kilogram = 2.2 pounds
1 mile = 1.6 kilometer
Statistics, Calculations and Conversions
Chapter 14
Dose calculations: Reconstitute 1/2 gram antibiotic powder
to give a 5% solution and give a 25 mg dose to the animal
1/2 gram = 500 mg
1 ml of H2O = 1 gram
5% = 5 parts/100 parts or 5 mg/100 mg or 50 mg/1000 mg =
50mg/ml
50 mg = 500 mg
1 ml
? ml
50 mg(? ml) = 500 mg (1ml)
50 mg (?ml) = 500 mg (1 ml)
= 10
50 mg
50 mg
? ml = 500 mg
50 mg
? ml
Statistics, Calculations and Conversions
Chapter 14
Dose calculations: Reconstitute 1/2 gram antibiotic powder
to give a 5% solution and give a 25 mg dose to the animal
500 mg
10 ml
=
25 mg
? ml
500 mg (? ml)
=
25 mg (10 ml)
? ml
=
25 mg (10 ml)
500
? ml
=
0.5
Statistics, Calculations and Conversions
Chapter 14
Solutions are homogenous mixtures of 2 or more constituents
and can be gas, liquid, or solid.
Liquid solutions are made by dissolving gas, liquid, or solid into
a liquid; if water is used, this is referred to as an aqueous solution.
Statistics, Calculations and Conversions
Chapter 14
Solutions = solute and solvent
Percent by weight = total mass contributed by solute
Percent weight in volume (w/v) = grams of solute/100 mls solvent
Percent weight in weight (w/w) = grams of solute/100 grams solvent
Percent by volume (v/v) = percent of final solution volume made
up by the solute volume
Statistics, Calculations and Conversions
Chapter 14
Mole = quantity of atoms = 6.022 X 1023 = Avagadro’s number
A one molar solution = 1 M = molecular wt in grams/liter solution
Molecular weights are listed in the Periodic Table in the upper right
CCl4
1 Carbon + 4 Chloride = 12g X 1 mole + 35.5 X 4
= 12 + 142 = 154 grams
Statistics, Calculations and Conversions
Chapter 14
Normality = N = the number of equivalents of solute/liter of
solution
The number of equivalents =
actual weight of the substance/equivalent weight
Equivalent weight = Atomic weight/valence
Statistics, Calculations and Conversions
Chapter 14
Valence (Net positive valence) = (Valence of + element) X (its subscript)
NaCl
1X1=1
K2CO3
1X2=2
CaSO4
2X1=2
AlCl3
3X1=3
Fe2(SO4) 3
3X2=6
Equivalent wt = Molecular weight/Net positive valence
58.5/1
138/2
136/2
133.5/3
400/6
Statistics, Calculations and Conversions
Chapter 14
58.5/1
58.5
138/2
136/2
133.5/3
400/6
69
68
44.5
66.6
The number of equivalents = actual weight of the substance/equivalent
weight.
Normality = N = the number of equivalents of solute/liter of solution.
Normality = molarity X net positive valence.
Therefore, normality will always be equal to or greater than molarity.
Chapter 14
THE END