Let us try to explore how do we do that.For example one mole of sodium means we have 23 gram of sodium metal and 6.022×1023 number of sodium atoms. Similarly one mole of hydrogen reveals that one gram of hydrogen contains 6.022×1023 atoms of hydrogen.However one mole of both these elements means Avogadro's number of atoms but on the other hand there would be a lot of difference so far as their masses are concerned.
In order to dive deep into this concept of moles first we have to get acquainted with masses of these atoms.All atoms of elements have two kinds of masses :
1) Absolute mass
2) Relative mass
Let us take the example of carbon atom whose atomic number is six and mass number is 12.In this example the actual mass of single carbon atom is 1.99×10-23 g. Where as its relative mass is 12 u.Now we know this without doubt that through some sophisticated & technical methods like spectroscopy and complex calculations we have figured out negligible masses of these tiny atoms but questions arises which method is used to calculate the relative masses of these atoms.
As these atoms are terribly small and in the beginning of 20th century due to the lack of sophisticated technology chemists of that time devised a scale in which they took 12 gram of carbon element and divided this amount with Avogadro's number 6.022×1023 .In this way they got the weight of one carbon atom which comes out to be 1.99×10-23 g.Then the later value was divided with number 12 to get new number 1.66×10-24 g.
This value was used as a unit to frame a scale which is known as amu scale. On this scale this value1.66×10-24 g. has been assigned one unit. Later on this unit was brought into practice by the chemists in order to compare the atomic masses of all other atoms.For example on amu scale one atom of sodium weighs 23 u which simply means one atom of sodium is 23 times heavier than one amu. Similarly the relative atomic mass of Aluminum atom is 27 u, which means one atom of this element is 27 times heavier than one amu on the atomic mass unit scale.
Let us try to define few terms related to mole concept then we will discuss the numerical aspect of Mole concept:
ATOMIC MASS
WHAT IS ONE AMU ?
One amu or simply u is the mass equal to one-twelfth of the mass of an atom of carbon-12 isotope.Atomic
mass of an element indicates the number of times one atom of that
element is heavier than one amu.E.g. atomic mass of sodium is 23 amu
which means one atom of sodium element is 23 times heavier than one amu.
TYPES OF ATOMIC MASSES
Atomic masses are of two types:
1. Actual Atomic mass.
2. Relative Atomic mass .
WHAT IS ACTUAL MASS ?
The mass of one atom of an element or one molecule of an element or a compound is known as actual mass or absolute mass.
E.g. Actual mass of one carbon atom is :- 1.99×10-23 g.
ACTUAL MASS OF 1 AMU
Actual mass of one amu that is mass of 1/12th the mass of an atom of carbon-12 isotope.It can be calculated as follow:
1.99×10-23 g/12 = 1.66×10-24 g.
RELATIVE ATOMIC MASS
RELATIVE MOLECULAR MASS
It is the average relatives mass of one molecule of a substance as compared to one amu or 1/12th the mass of one atom of carbon-12.
E.g., Molecular mass of methane, (CH4)
= (12.011 u) + 4 (1.008 u) = 16.043 u.
Similarly, molecular mass of water (H2O):
=2 atomic mass of hydrogen + 1 atomic mass of oxygen
= 2 (1.008 u) + (16.00 u) = 18.02 u.
Molecular mass of glucose (C6H12O6):
= 6(12.011 u) + 12(1.008 u) + 6(16.00 u)
= (72.066 u) + (12.096 u) + (96.00 u)
= 180.162 u
GRAM ATOMIC MASS
The relative atomic mass of an element expressed in grams is called gram atomic mass. It is also called gram atom.
E.g. relative atomic mass of
Oxygen is 16 amu And its gram atomic mass is 16 gram. Similarly
Nitrogen = 14 g
Sodium = 23 g
GRAM MOLECULAR MASS
The molecular mass of a substance expressed in grams is called gram molecular mass. It is also known as gram molecule.
E.g. Water(H2O ) = 18 g
Methane(CH4) = 16 g
Glucose(C6H12O6) = 180 g
Sulphuric acid(H2SO4) = 98 g
FORMULA MASS
Some
substances such as sodium chloride do not contain discrete molecules as
their constituent units. In such compounds, positive (sodium) and
negative (chloride) entities are arranged in a three-dimensional
structure. The formula such as NaCl is used to calculate the formula
mass instead of molecular mass .Because in the solid-state sodium
chloride does not exist as a single entity.
Thus, formula mass of sodium chloride :
= atomic mass of sodium + atomic mass of chlorine
= 23.0 u + 35.5 u = 58.5 u.
GRAM FORMULA MASS
The formula mass of an ionic compound expressed in grams is known as gram formula mass.
E.g. NaCl = 58.5 g
Na2CO3 = 106 g
The formula mass of an ionic compound expressed in grams is known as gram formula mass.
E.g. NaCl = 58.5 g
Na2CO3 = 106 g
MOLE
It is defined as amount of the substance containing Avogadro’s number of particles .(electrons, atoms, molecules etc).
MOLAR MASS
The mass of one mole of any substance is called its molar mass. It is equal to gram atomic mass or gram molecular mass .
E.g. Sodium = 23 g and
Water(H2O ) = 18 g
AVOGADRO’S NUMBER
The number of particles present in one mole of any substance is called Avogadro’s number or Avogadro’s constant. It is equal to 6.022×1023.
MOLAR VOLUME
The volume occupied by one mole of any gas at STP is known as molar volume. It is equal to 22.4L.The mass of this volume of gas is equal to its molecular mass.
For example one mole of carbon dioxide gas will occupy 22.4 liter of volume at STP and mass of this volume of gas will be 44 gram
Numerically in order to find out the number of moles we use following three formulae which are quiet interesting when we play with them to solve numerical problem related to mole concept:
I) CALCULATION OF NUMBER OF MOLES FROM MASS OF SUBSTANCE
a) From the atomic mass of an element:
b) From the molecular mass of a compound:
II) FROM THE NUMBER OF PARTICLES OF A SUBSTANCE
III FROM THE VOLUME OF GAS
Loschmidt number :-number of molecules present in one centimeter cube of a gas at STP is known as Loschmidt number
NUMERICALS ON MOLES
1) Calculation of actual mass
- actual mass of 1 amu. (1.66 × 10-24 g )
- Calculate actual mass of an atom of Ag. (1.79 × 10-22 g )
- one molecule of oxygen. (5.31 × 10-23 g )
- one molecule of water . (2.99 × 10-23 g )
- and one molecule of carbon dioxide. (7.31 × 10-23 g )
- Calculate actual mass of an atom of C-12. (1.99 × 10-23 g )
2) Calculation of moles from mass:
- 5 g of C .(0.42 mol)
- 15 g of Al.(0.56 mol)
- 0.9 g of Fe. (0.0161)
3) Calculation of moles from number:
How many moles are there in :
- 1.02× 1023
molecules of CO2 (0.166 mol)
- 12.044 × 1023 C atoms (2 mol )
- 6.022 × 1023 molecules of H2SO4 .(1 mol)
- 1.5× 1023 atoms of sodium .(0.25 mol)
- 1.673 × 1021 molecules of water.(0.00272 mol)
4) Calculation
from volume of gas at STP :
Calculate number of moles in:
1) 70,000 L of ammonia at STP. (3125 mol )
2) 11200 L of hydrogen gass at STP . (500 mol )
3) 11.2 L of sulphur dioxide gas at STP. (0.5 mol )
4) 5.6 L of carbon dioxide gas at STP . (0.25 mol )
5) From moles to mass and number
1)Cal mass and number of atoms in 54 moles of He. (216 gram & 3.252 × 1025 )
2) number of molecules in one drop of water having mass 0.05 g.(1.67 × 1021 )
3)calculate mass of 4.5 moles of C-12. (54 gram)
6) Calculation of moles using ideal gas equation
IDEAL GAS EQUATION
PV = nRT
Here P = pressure in atm
V = volume in centimeter cube or Liter
n = number of moles
R = gas constant
T = temperature in K
NUMERICAL
1) Using Ideal gas equation calculate the number of molecules of ammonia in 350 cm3 volume at 273 K and 2 atmospheric pressure.
Value of R = 0.0821 L atm K-1mol-1
Value of R = 82.1 cm3 atm K-1mol-1
Ans :- 1.88× 1022 molecules
2) Using Ideal gas equation calculate the moles of oxygen in 35 cm3 volume at 6 degree Celsius temperature and 1.5 atmospheric pressure.
Value of R = 0.0821 L atm K-1mol-1
Value of R = 82.1 cm3 atm K-1mol-1
Ans :- 2.29 × 10-3 mol
3) Using Ideal gas equation calculate the number of moles of a gas having volume 42 cm3 volume at 27 degree Celsius temperature and 1140 mm of Hg pressure.
Value of R = 0.0821 L atm K-1mol-1
Value of R = 82.1 cm3 atm K-1mol-1
Ans :- 2.56 × 10-3 mol
4) Calculate volume, radius and diameter of one molecule of water .Density of water is 1 g/cm3 .
Sol :- 1) Find the volume of one molecule of water :-
Volume occupied by one mol of water that is 18 gram of water is :
d = m/v
v = m/d
v = 18g/1 g/cm3
v = 18 cm3
Hence Volume occupied by one molecule of water
= 18 cm3/6.022 × 1023
= 2.99 × 10-23cm3
2) Find the radius of one molecules of water :-
Water molecule has spherical shape hence volume of a sphere is given by:
= 4/3×Ï€r3
Hence 2.99 × 10-23cm3 = 4/3×Ï€r3
r3 = 3 × 7 × 2.99 × 10-23cm3/4 × 22
r3 = 7.133 × 1024cm3
r = ( 7.133 × 1024cm3)1/3
r =1.925 × 10-8 cm
3) Find the diameter of one molecule of water :-
Diameter = 2 × r
= 2 × 1.925 × 10-8 cm
= 3.85 × 10-8 cm
TABLE OF ELEMENTS WITH ATOMIC MASSES
| AT.NO | SYMBOL | ELEMENT | AT. MASS |
| 1 | H | Hydrogen | 1.008 |
| 2 | He | Helium | 4.0026 |
| 3 | Li | Lithium | 6.94 |
| 4 | Be | Beryllium | 9.0122 |
| 5 | B | Boron | 10.81 |
| 6 | C | Carbon | 12.011 |
| 7 | N | Nitrogen | 14.007 |
| 8 | O | Oxygen | 15.999 |
| 9 | F | Fluorine | 18.998 |
| 10 | Ne | Neon | 20.18 |
| 11 | Na | Sodium | 22.99 |
| 12 | Mg | Magnesium | 24.305 |
| 13 | Al | Aluminium | 26.982 |
| 14 | Si | Silicon | 28.085 |
| 15 | P | Phosphorus | 30.974 |
| 16 | S | Sulfur | 32.06 |
| 17 | Cl | Chlorine | 35.45 |
| 18 | Ar | Argon | 39.948 |
| 19 | K | Potassium | 39.098 |
| 20 | Ca | Calcium | 40.078 |
| 21 | Sc | Scandium | 44.956 |
| 22 | Ti | Titanium | 47.867 |
| 23 | V | Vanadium | 50.942 |
| 24 | Cr | Chromium | 51.996 |
| 25 | Mn | Manganese | 54.938 |
| 26 | Fe | Iron | 55.845 |
| 27 | Co | Cobalt | 58.933 |
| 28 | Ni | Nickel | 58.693 |
| 29 | Cu | Copper | 63.546 |
| 30 | Zn | Zinc | 65.38 |
1 Comments
Thank you..very well explained by you.
ReplyDelete