1. Units Used in Measurement
GLY Lecture 4
Fall, 2018
Geochemical measurements are expressed in a variety of ways. All scientific measurements are based on the “metric system.”

2. 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.
The MKS (Meter-kilogram-second) system derived from the system introduced in France in 1791
The CGS (centimeter-gram-second) system adopted by the British Association for the Advance of Science in 1874

3. 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
Table 4-1 in lecture notes
Many other units can be derived from the seven basic SI units. Some examples of these are shown on the next slide.

4. Derived Units Table 4-2 in lecture notes
Note that some derived units may be expressed in term of other derived units.
A joule, the unit for energy, heat, or work, is a Nm. Pressure, in pascals, is Nm-2.
The Pascal unit is often inconvenient in geology, where many measurements are done at 1 atmosphere ambient pressure. The atmosphere equals 101,325 pascals. A more convenient unit is the bar, which equals 100,000 Pascals. Since 1 bar = atm, the difference is often ignored.
Another derived unit is the megapascal, equal to 106 Pascals, or 10 bars.
A unit still very much in use is the calorie, which comes from the older CGS system. A calorie is defined as the quantity of heat necessary to raise 1 gram of water from 14.5̊C to 15.5̊C, is equal to J. One food calorie, sometimes called a large calorie, is 1000 calories or 4184 joules.

5. 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/ 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 K

6. Kelvin-Celsius Relationship
Thus, the Kelvin and Celsius scales are related by
In thermodynamics, all temperatures must be expressed in Kelvin
Equation 4-1 in lecture notes

7. Prefixes Table 4-3 in lecture notes
Both the SI base units and derived units may be modified by prefixes. These are used to signify decimal multiples and submultiples of SI units.

8. 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)

9. 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
In addition to the use of prefixes, some terms may be used to modify units

10. 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.

11. 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)

12. 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

13. 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:
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
Equation 4-2 in lecture notes

14. 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

15. 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

16. 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
Acid-base chemistry: Used to express the concentration of either hydrogen ion (H+) or hydroxide ions (OH-1) in a solution. Each solution can produce one or more equivalents of reactive species when dissolved. For example, hydrochloric acid (HCl) produces one mole of hydrogen ion per mole of hydrochloric acid, whereas sulfuric acid (H2SO4) produces two moles of hydrogen ion per mole of sulfuric acid.
Redox reactions: The equivalence factor describes the number of electrons that an oxidizing or reducing agent can accept or donate
Precipitation reactions: The equivalence factor measures the number of ions which will precipitate in a given reaction.

17. 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
IUPAC = International Union of Pure and Applied Chemistry
NIST = National Institute of Standards and Technology, formerly the National Bureau of Standards, or NBS

18. The Mole
The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 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)

19. Use of “Mole”
1 mol of H2 contains about 6.022×1023 H2 molecules, or ×1023 H atoms
1 mol of HgCl has a mass of g
1 mol of Hg2Cl2 has a mass of g
1 mol of Hg2+ has a mass of g and a charge of kC
1 mol of Fe0.91S has a mass of g
1 mol of e-1 has a mass of µg and a charge of kC
1 mol of photons whose frequency is 5×1014 Hz has energy of about kJ
From IUPAC, The international system of units (SI), section 1.4, 2002

20. 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 temperature as well
The advantage of molarity is the ease of measurement of the volume of a liquid, rather than its weight, in many situations

21. 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

22. 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

23. 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

24. Mass Per Unit Volume A typical example is mg/m3
It is possible to convert from one method to the other – at 1 atmosphere pressure:
Where T = temperature in Kelvin
and M = molecular mass of the substance in question
Equation 4-3 in lecture notes

25. Conversion to Mass Per Unit Volume
To convert from ppmv to mg/m3:

26. 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

27. Conversion to “Dry Basis”
It is possible to convert measurements made in air containing water to a “dry basis” using the following formula
where C = concentration of the substance in question and w = fraction of the gas sample which is water vapor

28. 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: