Numbers and Units

Chemical Quantities

Chemistry is a quantitative science. Amounts of substances and energies must always be expressed in numbers and units. (in order to make some sense of what you are talking about) You should also develop a sensation about quantities every time you encounter them; you should be familiar with the name, prefix, and symbol used for various quantities.

However, due to the many different units we use, expression of quantities is rather complicated. We will deal with the number part of quantities on this page, using SI Units.

Expressing Numbers

Usually, base-ten numbers are used for chemical quantities. Be prepared to read the numbers in words. Here are some cardinal numbers and their prefixes that will help you appreciate quantities throughout your study. You will benefit from remembering them:

Throughout this document, exponents of 10XXX are expressed by eXXX or EXXX.

```
Words          Number               Prefix  Symbol Exponent
-----         --------------------- ------  ------ -of 10--
Quindrillion  1,000,000,000,000,000                  e15
Trillion          1,000,000,000,000 Tera-    T       e12
Billion               1,000,000,000 Giga-    G       e9
Million                   1,000,000 Mega-    M       e6
Thousand                      1,000 Kilo-    k       e3
Hundred                         100
Ten                              10
One                               1
Tenth                           0.1 Deci-    d
Hundredth                      0.01 Centi-   c
Thousandth                    0.001 Milli-   m       e-3
Millionth                  0.000001 Micro-   u (mu)  e-6
Billionth               0.000000001 Nano-    n       e-9
Trillionth           0.000000000001 Pico-    p       e-12
-----         --------------------- ------  ------ -------
```
By now, you probably realized that every time the number increases by a factor of a thousand, we give a new name, a new prefix, and a new symbol in its expression.

After you are familiar with the words associated with these numbers, you should be able to communicate numbers with ease. Consider the following number:

123,456,789,101,234,567

In words, this 18-digit number takes up a few lines:

One hundred twenty three quindrillions, four hundred fifty six trillions, seven hundred eighty nine billions, one hundred and one millions, two hundred and thirty four thousands, five hundred and sixty seven.

If a quantity makes use of this number, the quantity has been measured precisely. Most quantities do not have a precise measurement to warrant so many significant figures. The above number may often be expressed as 123e15 or read as one hundred twenty three quindrillions.

Exercises

1. Express the numbers 456e12, 789e9 in words.
2. Give the numerical expression for "Nine hundred eighty seven million" and "Fifty six millionth".

Skills acquired

1. Read numbers as a part of a quantity - don't just count the digits. For this, you have to realize a simple order: Quindrillion, Trillion, Billion, Million, Thousand.
2. Impose a sensation to the numbers associated with a quantity - recognize and appreciate the meaning of the digits.
3. For numbers greater than a quindrillion or smaller than a trillionth, you have to consult other sources, but the range given here is adequate for most occasions.

Seven Basic Quantities and Their Units

There are seven basic quantities in science, and these quantities, their symbols, names of their units, and unit symbols are listed below:
```      == Basic Quantity ==  ==== Unit =====
Name    Symbol  Symbol Name
============= ======  ====== ========
Length    l       m   meter
Mass    m      kg   Kilogram
Time    t       s   Second
Electric current    I       A   Ampere (C/s)
Temperature    T       K   Kelvin
Amount of substance    n     mol   Mole
Luminous intensity    Iv     cd   Candela
============= ======  ====== ========
```
*The unit ampere, A, is equal to Coulombs per second, (A = C/s).

The Seven Basic SI Units

Length
Length is a basic quantity measured by comparison to a standard length. Its SI unit is the meter (or metre).
One meter (1 m) is defined as 1 650 763.73 times the wavelength of radiation from the 86K isotope from the state 2p10 to the state 5d5. Note that these are energy levels of the nuclide, not of the electrons in the K atom. The definition involves a nuclear phenomenon.

Other common units are:
kilometer (1 km =1000 m),
centimeter (1 cm = 0.01 m),
decimeter (1 dm = 0.1 m),
millimeter (1 mm = 0.001 m),
nanometer (1 nm = 1e-9 m),
picometer (1 pm = 1e-12 m)

Mass
Mass is a quantity measured by comparison. The SI unit for mass is kilogram, and 1 kg is a standard block of material adopted by the international community. In chemistry, the most commonly used unit is the gram, symbol g.

1 kg = 1000 g
1 milligram (mg) = 1/1000 g

Electric Current
The unit Ampere for current was originally defined as the unvarying current which when passed through a solution of silver nitrate, deposits silver at the rate of 0.00111800 g of silver per second. This definition is related to chemistry due to the electrochemical reaction:
Ag+ + e = Ag(s)
It was redefined in 1948 from a physical point of view, but you should realize that the current definition also defines the unit Coulomb (C) for charge, because the current of 1 A is equivalent to the flow of 1 C per second on a conductor.

Temperature
Temperature is an intensive property, and the common units include Kelvin (K) and Celsius (oC). To convert temperature from to Celsius to T K, use the relationship T K = 273.15 + toC

Amount of Substance
The amount of a substance is related to the number of atoms or molecules it contains - different from mass. A mass equal to the atomic or molecular weight in grams is called one mole. Thus, the number of moles of a pure substance is its mass m divided by its molar mass M: n = m / M

Luminous intensity
Intensity of illumination,Iv, is measured in Candela (cd). Since this quantity is not used extensively, we will not elaborate on it here.

Exercises

1. The atomic weight of silver, Ag, is 107.9. How many moles is 0.001118 g of silver?

Solution
The number of moles n is calculated by:

n = 0.001119 / 107.9 = 1.036e-5 mol
or 0.1036 micro-mole.

2. How long would it take to deposit 1 mole of silver if the current is 1 A?

Solution
The time t required is

t = 107.9/0.001119 = 96425 s. In other words, one mole of electrons has a charge of 96425 C from the definition given earlier. Today, the accepted Faraday constant is 96485.309 C/mol.
3. How many electrons will have a charge of 1 C?

Solution
To evaluate the number of electrons having a charge of 1 C, we need to know the charge per electron, 1.6oe-19 C/e, which was determined by R. Millikan between 1908 and 1917. Using this data,

The number of electrons per Coulomb = 1 C/(1.60e-19 C/e) = 6.25e18.

Let us go a step further to find the the number of electrons in one mole

NA = 96425*6.25e18
= 6.027e23, number / mol.

Of course, this is the Avogadro's number, and the updated value is 6.022e23.

Skills acquired

1. Be able to tell anyone what the seven basic quantities are, including their symbols used in formulations, their units, and the symbols of their units.
2. Be able to correlate various quantities, and recognize what quantities are required in order to derive one from another.
3. Be able to explain the amount of a substance as a quantity in the unit mole, mili-mole, or micro-mole.