Symbols and Units.
Many properties of matter such as length area volume etc are quantitative in nature. Any quantitative observation or measurement is represented by a number followed by units in which it is measured.
A physical quantity is expressed in terms of a number and a unit, e.g.,
Length of a rod = 2.8 metres
Time taken to reach a place=230 seconds
The two different systems of measurement ie the English system and the Metric system were being used in different parts of the world. The metric system which is originated in France In late 18th century was more convenient as it was based on the decimal system. The need of a common standard system was being felt by the scientific community. Such a system was established in 1960 and is discussed below in detail.
The International System of Units (SI)
The International System of Units (abbreviated as SI) was established by the 11th General Conference on Weights and Measures (CGPM) The CGPM is an inter governmental treaty organization created by a diplomatic treaty known as Metre Convention which was signed in Paris in 1875.
The SI system has seven base units and they are listed in Table below.
Table-Basic Physical Quantities and Units
| Basic physical quantity | Symbol for quantity | Units | Symbol of Unit |
| Length | l | Metre | m |
| Mass | m | Kilogram | kg |
| Time | t | Second | s |
| Electric current | I | Ampere | A |
| Temperature | T | Kelvin | K |
| Luminous intensity | Iv | Candela | cd |
| Amount of substance | n | mole | mo |
These units pertain to the seven fundamental scientific quantities. The other physical quantities such as speed, volume, density etc. can be derived from these quantities.
The definitions of the SI base units are given below.
a) Unit of length is metre.
Metre is the length of the path travelled by light in vacuum during the time interval of 1/299792458 of a second.
b) Unit of mass is kilogram.
Kilogram is the unit of mass which is equal to international prototype of the kilogram.
c) Unit of time is second.
One second is the time that elapses during 9,192,631,770 (or 9.192631770 x 109 in decimal forms) cycles of the radiation produced by the transition between two levels of the cesium-133 atom.
d) Unit of electric current is ampere.
The current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section and placed 1 metre apart in vacuum, will produce between them a force equal to 210-7newton per metre length. The ampere is realized in practice by measuring the force between current carrying coils of measured dimensions.
e) Unit of thermodynamic temperature.
It is the fraction of 1/273.16 of the thermodynamic temperature of the triple point of water. It si denoted by ‘T’ and the unit is Kelvin (symbol ‘K’).
Celsius temperature ( °C) t = T – T0. Where T0 = 273.15
Note: Triple point of a substance is the temperature and pressure at which three phases (gas, liquid, and solid) of that substance may coexist in thermodynamic equilibrium.
Note: One degree Celsius is equal to one degree Kelvin for calculations. It means difference in both scales is same.
f) Unit of amount of substance.
Mole is the amount of substance which contains same number of elementary entities (like atoms, molecules, ions, electrons etc) as they are present in 0.012kilogram of carbon-12. Its symbol is ‘mol’.
g) Unit of luminous intensity.
Candela is the unit. Defined as the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and has a radiant intensity in that same direction of 1/683 watt per steradian (unit solid angle).
Derived SI Units
SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.
The meter per second (distance), mole per cubic meter (concentration of a material), and specific volume are examples of derived units (cubic meter per kilogram).
Radian (rad) Unit of plane angle.
The angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius.
Steradian (sr) Unit of solid angle.
The solid angle which, having its vertex in the centre of a sphere, cuts off an area of the surface of the sphere equal to that of a square having sides of length equal to the radius of the sphere.
Degree Celsius (°C) Customary unit of temperature.
The zero of this scale is the temperature of the ice point (273.15 K). The units of Celsius and kelvin temperature interval are identical.
Hertz (Hz) Unit of frequency.
The number of repetitions of regular occurrence in one second.
Newton (N) Unit of force.
That force which, applied to a mass of 1 kilogram, gives it an acceleration of 1 metre per second per second.
Pascal (Pa) Unit of pressure.
The pressure produced by a force of 1 newton applied, uniformly distributed, over an area of 1 square metre. (This unit is mostly used in France and is not internationally accepted.)
Joule (J) Unit of energy, including work and quantity of heat.
The work done when the point of application of force of 1 newton is displaced through a distance of 1 metre in the direction of the force.
Watt (W) Unit of power.
The watt is equal to 1 joule per second.
Coulomb (C) Unit of electric charge. The coulomb is the quantity of electricity transported in 1 second by 1 ampere.
Volt (V) Unit of electric potential.
The difference of electric potential between two points of a conducting wire carrying a constant current of 1 ampere, when the power dissipated between these is equal to 1 watt (IX CGPM, 1948).
Ohm (Ω) Unit of electric resistance.
The resistance between two points of a conductor when a constant difference of potential of 1 volt, applied between these two points, produces in this conductor a current of 1 ampere, the conductor not being the source of any electromotive force.
Farad (F) Unit of electric capacitance.
The capacitance of a capacitor between the plates of which there appears a difference of potential of 1 volt when it is charged by 1 coulomb of electricity.
Note: Faraday – a unit of charge
1 faraday = F x 1 mol = 96485. 33212… C. Conversely, the Faraday constant F equals 1 faraday per mole. The faraday is not to be confused with the farad, an unrelated unit of capacitance (1 farad = 1 coulomb/1 volt).
Weber (Wb) Unit of magnetic flux.
The magnetic flux which, linking circuit of one turn, produces in it an electromotive force of 1 volt as it reduced to zero at a uniform rate in 1 second.
Henry (H) Unit of electrical inductance.
The inductance of a closed circuit in which an electromotive force of 1 volt is produced when the electric current in the circuit varies uniformly at the rate of 1 ampere second.
Tesla (T) Unit of magnetic flux density.
The tesla is equal to 1 we per square metre of circuit area.
Lumen (lm) Unit of luminous flux.
The flux emitted within unit angle of 1 steradian by a point source having a uniform intensity candela.
Lux (lx) Unit of illumination.
An illumination of 1 lumen pers metre.
Roentgen (R)
One roentgen is that quantity of X- or y-radiation such that the associated corpuscular emission per 0.001293 g of air produces in air, ions carrying 1esu of quantity of electricity of either sign.
Curie (C).
One curie of any radioactive substance is an amount such that exactly 3.71010 atoms disintegrate per second.
The SI system allows the use of prefixes to indicate the multiples or submultiples of a unit. These prefixes are listed in Table below.
| Multiple | 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 | zeta | Z |
| 10-24 | yocto | y | 1024 | yotta | Y |
Table – Special Names and Symbols for Certain SI Derived Units
| Physical quantity |
Symbol for
quantity |
Units | Special name of SI unit | Symbol for SI unit |
| Area | A | m2 | ||
| Density | p | Kg.m-3 | ||
| Force | F | Kg.m.s-2 | Newton | N |
| Pressure | P | Nm-2 = kg m-1s-2 | Pascal | Pa |
| Energy | E | Nm = kg m2s-2 | Joule | J |
| Viscosity | ɳ | Nm-2s = kg.m-1.s-1 | Poiseuille | P |
| Surface tension | γ | Nm-1 = kg.s-2 | ||
| Electrical potential | V | Kg.m2.s-3.A-1 | Volt | V |
| Electrical resistance | R | Kg.m2.s-3.A-2 | Ohm | Ω |
| Electric charge | I | A.s | Coulomb | C |
| Frequency ( cycles per second) | Ʋ | s-1 | hertz | Hz |
| power | Js-1 = kg.m2.s-2 | watt | W |
Mass and Weight
Mass of a substance is the amount of matter present in it while weight is the force exerted by gravity on an object. The mass of a substance is constant whereas its weight may vary from one place to another due to change in gravity. One should be careful in using these terms.
The mass of a substance can be determined very accurately in the laboratory by using an analytical balance.
The SI unit of mass is kilogram. However, its fraction gram (1 kg = 1000 g), is used in laboratories due to the smaller amounts of chemicals used in chemical reactions.
Maintaining the National Standards of Measurement
The system of units including unit definitions keeps on changing with time. Whenever the accuracy of measurement of a particular unit was enhanced substantially by adopting new principles, member nations of metre treaty (signed in 1875), agreed to change the formal definition of that unit. Each modern industrialized country including India has a National Metrology Institute (NMI) which maintains standards of measurements. This responsibility has been given to the National Physical Laboratory (NPL). New Delhi. This laboratory establishes experiments to realize the base units and derived units of measurement and maintains National Standards of Measurement. These standards are periodically inter-compared with standards maintained at other National Metrology Institutes in the world as well as those established at the International Bureau of Standards in Paris.
Volume has the units of (length)3. So in SI system, volume has units of m³. But again, in chemistry laboratories smaller volume is often denoted in cm3 or dm3 units.
A common unit, litre (L) which is not an SI unit, is used for measurement of volume of liquids.
1 L= 1000 mL, 1000 cm³ = 1 dm³
10 cm=1dm. 1cm3 = 1ml
In the laboratory, volume of liquids or solutions can be measured by graduated cylinder, burette, pipette etc. A volumetric flask is used to prepare a known volume of a solution.
Density
Density of a substance is its amount of mass per unit volume. So SI units of density can be obtained as follows:
SI unit of density = SI unit of mass/ SI unit of volume = Kg/m3 or kg m-3
This unit is quite large and a chemist often expresses density in g cm-3, where mass is expressed in gram and volume is expressed in cm³.
Temperature
There are three common scales to measure
temperature -°C (degree celsius), °F (degree fahrenheit) and K (kelvin). Here, K is the SI unit. The thermometers based on these scales are shown in Fig. 5.8. Generally, the thermometers with celsius scale are calibrated from 0° to 100° where these two temperatures are the freezing point and the boiling point of water respectively. The fahrenheit scale is represented between 32° to 212°.
The temperatures on two scales are related to each other by the following relationship:
°F = (°C) +32
The kelvin scale is related to celsius scale as follows:
K = °C+273.15
In Celsius scale temperature below 0°C that is negative values are possible. In Kelvin scale no negative values for temperature.
A number of units which are decimal fractions or multiples derived SI units have special names. Some of these are given ins following table :
Table -Decimal Fractions and Multiples of SI Units having Special Names
| Physical quantity | Name of unit | Symbol for unit | Definition of unit |
| Length | Angstrom | A | 10-10m |
| Length | micron | µ | 10-6m = µm |
| Force | dyne | dyn | 10-5N |
| Pressure | bar | bar | 105Nm-2 |
| Energy | erg | erg | 10-7J |
| Volume | litre | L | 10-2.m3 =1 dm3 |
Certain units not part of the SI are approved for a limited time during the changeover to SI units. Some of these are:
Angstrom. 1 Å=0.1 nm=10-10 m.
Standard atmosphere. 1 atm=101.325 N m-2 = =1’013× 104 N m-2.
bar. 1 bar=105 N m-2.
Table -Conversion of CGS Units to SI Units.
| Quantity | Unit | Equivalent |
| Length | Å | 10-10 m=10-1 nm=103 pm |
| Volume | litre | 10-3m3 = 1dm3 |
| force | dyne | 10-5N |
| energy | erg | 10-7J |
| cal | 4.184J | |
| ev/mole | 1.6021 x 10-19J | |
| ev/mole | 98.484kJ | |
| pressure | atmosphere | 101.325kN. m-2 |
| mmhg( or Torr) | 133.32 N. m-2 | |
| Bar(106dynes/cm2 | 105 N. m-2 | |
| viscosity | poise | 10-1kg.m-1s-1 |
Many times in chemistry we observe the difference between theoretical value and experimental value.
Chemistry deals with study of atoms and molecules which have extremely low masses and are present in large numbers. It is highly difficult to write or count them.
This problem is solved by using scientific notation for such numbers. In this method any number can be represented in the form of N 10n. Where ‘n’ is exponent. It can have any number having positive or negative value. N is a number between 1.000.. to 9.999… . That is only one number left to decimal point.
Example:
459.567 can be written as 4.59567 102. Observe here the decimal is moved left by two places so the exponent is ‘2’.
0.000548 can be written as 5.48 10-4. Observe here the decimal is moved right by four places so the exponent is ‘-4’.
With this method multiplication, division, addition and subtraction can be done as we do in normal mathematics, the only difference is N must contain only one number left to decimal. Every number must be organized like that before doing calculations.
Example 1: (69.45 103) multiplied by (432.5 102).
First write them like this.
(6.945 104 ) (4.325 104) = (6.945 4.325) (104+4) = 30.037125 108. = 30.037 108.
Example 2: (2.7 x 10-3) divided by (5.5 x 104).
It is equal to (2.7 5.5)(10-3)(10-4) = 14.85 x 10-7 = 1.485 x 10-6.
Addition and subtraction.
For these calculations the numbers have to be rearranged so that their exponentials are same.
Example:
(6.65 x 104) + (0.895 x 103) is equal to (0.665 x 105) + (0.00895 x 105). Exponent is made same.
= (0.665 + 0.00895) x 105 = 0.67395 x 105 =6.74 x 104.
Example:
(2.5 x 10-2) – (4.8 x 10-3) is equal to (2.5 x 10-2) – (0.48 x 10-2). Exponent is made same.
= (2.5 – 0.48) x 10-2 = 2.02 x 10-2.
Significant numbers:
Every experimental measurement will have some amount of uncertainty associated with it. It is because of many reasons like the skill of the person doing the experiment, quality of the instrument used, atmospheric conditions under which experiment is performed etc.
We need the results to be precise and accurate. These two terms have different meaning.
When two or more persons do the same experiment there will some difference between the values. The closeness of the various measurements for the same is referred as precision.
Accuracy is the agreement of a particular value to the true value of the result.
That means the individual observed values are neither precise nor accurate.
Precision = individual value – arithmetic mean value.
Accuracy = mean value – true value.
There is uncertainty both in experimental or calculated values. That is why the concept of significant numbers is introduced. For example we say the volume is 11.2ml. Here ‘11’ is certain and ‘2’ is uncertain.
Significant figures are the meaningful digits in a measured or calculated quantity. It includes all those digits that are known with certainty plus one more which is uncertain or estimated.
Greater the number of significant figures in a measurement, smaller the uncertainty.
There are certain rules to for determining significant numbers.
1. All non zero digits are significant. Example in 147 cm there are three significant numbers.
2. Zero is not considered as significant if the number starts with zero. For example 0.06 has only one significant number, 0.00567 has 3significant numbers.
3. If there is zero between non zero numbers it is considered as significant number. For example in 4.008 there are 4 significant numbers.
4. If zero is at the end or at right to a number it is significant number. Example ‘0.600’ has three significant numbers.
5. exact numbers have infinite significant figures. Example 2 = 2.0 = 2.00000……
Calculations involving signifigures.
Example. In addition.
2.512(four significant numbers)
+ 2.2 (two significant numbers)
+9.942 (four significant numbers)
= 9.942.
It is rounded as 9.9.
Similar calculation for subtraction also.
Example. Multiplication.
15.724 x 0.41 = 6.44684. It is rounded as 6.4.
15.724 0.41 = 38.35121951219512. It is rounded as 38.35.