Transcript Introduction to Environmental Geochemistry

Units Used in Measurement
GLY 4241 - Lecture 4
Fall, 2014
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The “Metric System”
• Metric system was actually two systems
 MKS, or Meter-Kilogram-Second system
 CGS, or Centimeter-Gram-Second system
 To resolve differences between the system, the
10th General Conference on Weights and Measures
adopted the International System of Units in 1954
 This system is abbreviated SI, for the French
Système International d’Unitès.
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Basic Units in the SI System
• There are seven basic units in the SI system, from which
other units are derived, shown in the following table
Physical Quantity
Name
Symbol
Length
Meter
m
Mass
Kilogram
kg
Time
Second
s
Temperature
Kelvin
K
Amount of Substance
Mole
mol
Electric Current
Ampere
A
Luminous Intensity
Candela
cd
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Derived Units
Physical Quantity
Name
Symbol
SI Base Units
Electric charge
Coulomb
C
As
Electric
Conductance
Siemens
S
m-2 kg-1 s3 A2
Electric Potential
Difference
Volt
V
m2 kg s-3 A-1
Energy (work, heat)
Joule
J
m2 kg s-2
Force
Newton
N
m kg s-2
Frequency
Hertz
Hz
s-1
Power
Watt
W
m2 kg s-3
Pressure (stress)
Pascal
Pa
m-1 kg s-2
Volume
Liter
L or l
10-3 m3
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Temperature
• The SI unit is the Kelvin, K, not ̊K, often mistakenly seen
in the literature
• The Kelvin scale is an absolute temperature scale, where
0K is absolute zero
 At absolute zero, molecules have no thermal energy, neither
rotational, translational, nor vibrational
• The Kelvin is defined as 1/273.16 of the triple point of
water
• On the Celsius scale, the triple point of water is 0.01̊C
• The ice point (point at which water melts at 1 atmosphere)
is 0̊C, or 273.15K
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Kelvin-Celsius Relationship
• Thus, the Kelvin and Celsius scales are
related by
T ( K)  t (  C)  27315
.
• In thermodynamics, all temperatures must
be expressed in Kelvin
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Prefixes
Submultiple Prefix
Symbol
Multiple
Prefix
Symbol
10-1
deci
d
10
deca
da
10-2
centi
c
102
hecto
h
10-3
milli
m
103
kilo
k
10-6
micro
μ
106
mega
M
10-9
nano
n
109
giga
G
10-12
pico
p
1012
tera
T
10-15
femto
f
1015
peta
P
10-18
atto
a
1018
exa
E
10-21
zepto
z
1021
zetta
Z
10-24
yocto
y
1024
yotto
Y
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Extensive and Intensive Units
• A quantity whose magnitude is additive for
subsystems is called extensive.
 Examples include mass m, volume V, Gibbs energy G.
• A quantity whose magnitude is independent of the
extent of the system is called intensive;
 Examples include temperature T, pressure p, density ρ,
and chemical potential (partial molar Gibbs energy) µ
 The latter two are examples of quantities made
intensive by dividing one extensive variable by another.
(i.e. ρ = m/V)
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Modifying Units
• The adjective specific before the name of an
extensive quantity is often used to mean divided
by mass.
• When the symbol for the extensive quantity is a
capital letter, the symbol used for the specific
quantity is often the corresponding lower case
letter.
 Example: Heat capacity at constant pressure, Cp
 Specific heat capacity at constant pressure, cp = Cp/m
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Solutes and Solvents
• Many units involve concentration of solutes in a solution
• The solution may be a liquid, a gas, or a fluid above the
critical point.
• There are a number of ways of expressing concentration.
 Each may be useful in certain situations, and less useful or
inappropriate in others
 As scientists, it is our job to choose units carefully so as to convey
maximum information and not, however inadvertently, deceive the
reader.
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Concentration in Liquid Solution
• Mass Concentrations
 Parts per million (ppm)
 Milligrams per liter (mg/L)
 Equivalent weights per liter (Eq/L)
• Molar Concentrations
 Molarity (M)
 Molality (m)
 Mole Fraction (X)
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Parts per million
ppm = Mass of solute in mg / Mass of solution in kg
• Parts per million really means parts by million by
mass
• There is another unit, ppm (V) which means parts
per million by volume
• When expressed as ppm, parts per million by mass
is understood
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Milligrams per liter
mg/L = Mass of solute in mg / volume of solution in liters
• The density of a solution, denoted ρ, expressed as g/mL or
kg/L, may be used to relate ppm and mg/l measurements:
concentration of solute ( g / L)
Concentration( ppm) 
 ( g / mL)
• For dilute solutions near 25̊C the density of the solution is
very close to pure water, which has ρ = 1.00 kg/L, so there is
little difference between ppm and mg/L
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Units Related to ppm
• There are several quantities related to parts
per million
• These include the familiar percent (%), and
the less familiar per mille (‰) which means
parts per thousand
• Also ppb, meaning parts per billion, and
ppt, meaning parts per trillion.
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Equivalents per liter (Eq/L)
N = equivalent weight of solute in g / volume of solution in L
• N stands for normality
• Context should avoid confusion with the
Newton, also denoted N
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Uses of Normality
• Acid-base chemistry - either hydrogen ion
(H+) or hydroxide ions (OH-1) in a solution
• Redox reactions - # of electrons that an
oxidizing or reducing agent can accept or
donate
• Precipitation reactions - number of ions
which will precipitate
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Possible Confusion
• A solution of MgCl2 that is 1N with respect
to Mg2+ ions is 2N with respect to Cl-1 ions
• Both IUPAC and NIST discourage the use
of normality
• For both acid/base and redox chemistry, the
concept has value
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The Mole
• The mole is the amount of substance of a system
which contains as many elementary entities as
there are atoms in 0.012 kilogram of 12C
• When the mole is used, the elementary entities
must be specified and may be atoms, molecules,
ions, electrons, other particles, or specified groups
of such particles (IUPAC definition)
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Use of “Mole”
• 1 mol of H2 contains about 6.022×1023 H2 molecules, or
12.044×1023 H atoms
• 1 mol of HgCl has a mass of 236.04 g
• 1 mol of Hg2Cl2 has a mass of 472.08 g
• 1 mol of Hg2+ has a mass of 401.18 g and a charge of
192.97 kC
• 1 mol of Fe0.91S has a mass of 82.88 g
• 1 mol of e-1 has a mass of 548.60 µg and a charge of
-96.49 kC
• 1 mol of photons whose frequency is 5×1014 Hz has energy
of about 199.5 kJ
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Molar (M)
= Moles of solute/ volume of solution in liters
• Molarity is dependent on the volume of solution
• Volume varies as a function of temperature, so
molarity depends on these quantities as well
• The advantage of molarity is the ease of
measurement of the volume of a liquid, rather than
its weight, in many situations
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Molality and Mole Fraction
Molality (m) = Moles of solute/ mass of solvent in kg
Mole fraction (X) = moles of solute/ total moles of
solution
• Both molality and mole fraction are independent of
the temperature and pressure
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Concentration in a Gas
• Two common methods are used to express
concentration in gas
• One involves a certain number of particles
per unit volume
• The second method is to express the mass
per unit volume
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Particles Per Unit Volume
• ppmv, or parts per million by volume, is
one example
• Similar expressions are ppbv, or parts per
billion by volume, and pptv, or parts per
trillion by volume
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Mass Per Unit Volume
• A typical example if mg/m3
• It is possible to convert from one method to the
other – at 1 atmosphere pressure:
(0.08205  T )
ppmv  mg / m 
M
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Where T = temperature in Kelvin
and M = molecular mass of the substance in question
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Conversion to Mass Per Unit
Volume
• To convert from ppmv to mg/m3:
M
mg / m  ppmv 
(0.08205 T )
3
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Dry vs. Wet Atmosphere
• One problem with gaseous atmospheric
measurements is the variable amount of
water that air may contain
• It is common to give concentrations in “dry
air”, or air which has no water at all
• Environmentally, this is entirely unrealistic
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Conversion to “Dry Basis”
• It is possible to convert measurements made in air
containing water to a “dry basis” using the
following formula
CDry basis 
CWet basis
1 w
where C = concentration of the substance in question
and w = fraction of the gas sample which is water
vapor
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Example Calculation
• A wet basis concentration of 52.3 ppmv in a
gas having 3.43 volume percent water vapor
would have a dry basis concentration of:
52.3
CDry basis 
 54.2 ppmv
1  0.0343
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