Units And Unit Conversion Page 2

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Exponentiation, Scientific Notation, Logarithms, and pH
page 2
the solvent. For example, a solution consisting of 30 grams of sodium chloride and 70 grams of water would be
30% sodium chloride by mass: [(30 g NaCl)/(30 g NaCl + 70 g water)] * 100% = 30%.
To avoid confusion whether a solution is percent by weight or percent by volume (see below), the symbol "w/w"
(for weight to weight) is often used after the concentration such as "10% potassium iodide solution in water (w/w)".
Percent by volume
Also called volume percent, this is typically used for mixtures of liquids, = (solute volume)/(total volume)*100.
Example: if 30 mL of ethanol is added to 70 mL of water, the percent ethanol by volume is 30%. To differentiate
from percent by mass, the term v/v (volume to volume) can be added after the concentration term.
Parts per million (ppm)/billion (ppb) /trillion (ppt)
These units are frequently encountered in the public media, less so in scientific papers. It is a variation on percent
by mass, and may apply to any substance in any medium, and is a simple method to express very small
concentrations. A 1 ppm of a substance contains 1 gram of that substance for every milion grams of the solution.
Unit
Base Formula
Multiplication Factor
Equivalences
parts per million (ppm)
one million
1 ppm = 1 mg/kg = 1 mg/L in water
⎛
⎞
substance mass
⎟ *
=
parts per billion (ppb)
one billion
1 ppb = 1 µg/kg = 1 µg/L in water
⎜
total sample mass
⎝
⎠
parts per trillion (ppt)
one trillion
1 ppt = 1 ng/kg = 1 ng/L in water
Molarity
Molarity is the number of moles of a solute dissolved per litre of solution. For example, if we have 90 g of iron (II)
sulphate monohydrate (molar mass = 169.92 g/mol) in 1 L of water, this is a 90/169.92 = 0.53 molar solution. (0.53
M). This form of concentration unit is often used when creating solutions for experimental work.
Converting Units
When performing math calculations it is a good idea to carry the units through with the calculation. This helps to
confirm that the math was done correctly (sort of a double-check), and confirm the new unit of the answer (if it is
uncertain or unknown). Here are some examples:
1. Express 231 L in cubic metres.
3
3
3
231 L = 231 L * (1 m
/1x10
L) = 0.231 m
2. What is the speed of a vehicle in km/hr that travels 30 m in 1 second?
30 m/s = [30 m*1 km/1000 m]/[1 s*1 min/60 s*1 hr/60 min] = 0.03 km/(1/3600) hr = 108 km/hr
3. What is the concentration in ppm of Pb in a lake of volume 1,567,340 m3 where a railway car spilled 4,692
kg of Pb into the water?
ppm = mg/L for water.
First, the lake volume: there are 1000 L in 1 m3, so
3
6
3
3
9
1,567,340 m
= 1.567340x10
m
(1000 L/1 m
) = 1.56734x10
L
3
6
9
Next, the amount of lead: 4,692 kg = 4.692x10
kg * (1x10
mg/1 kg) = 4.692x10
mg
9
9
Finally, the concentration calculation: 4.692x10
mg Pb/1.56734x10
L = 2.994 mg/L = 2.994 ppm
Some common conversions:
1 pound (lb) = 0.4536 kg
Length
Volume
1 long ton (UK) = 1.016 t
3
1000 m in 1 km
1 cc = 1 cm
= 1 mL
3
100 cm in 1 m
1000 L in 1 m
Concentration
1000 mm in 1 m
1000 mL in 1 L
1 ppm = 1 mg/kg = 1 mg/L in water
3
1 inch = exactly 2.54 cm
1 cu foot = 0.0283 m
1 ppb = 1 µg/kg = 1 µg/L in water
1 mile ≃ 1.61 km
1 fluid ounce (imperial) = 28.412 mL
1 ppt = 1 ng/kg = 1 ng/L in water
1 gallon (imperial) = 4.546 L
Area
Velocity
1 gallon (US) = 3.7854 L
2
2
1 m
= 10000 cm
1 knot - 0.514 m/s
2
1 hectare (ha) = 10000 m
1 mile/hr = 0.447 m/s
Mass
2
1 km
= 100 ha
1000 mg in 1 g
Temperature
2
1000 g in 1 kg
1 sq foot = 0.0929 m
C = (F-32)*5/9
2
1000 kg in 1 tonne (t)
1 acre = 4047 m
2
1 ounce (oz) = 28.35 g
1 sq mile = 2.59 km
Robert Loney, Environmental and Resource Studies Program, Trent University
rev. 2010-August

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