A similar relative scale to the atomic mass scale could be developed
for gases using masses of equal volumes of gases as a base for
comparison. As gases exist as individual molecules, such a scale would
be termed the relative molecular mass scale.
As before, a parallel scale measuring mass in grams will link to moles of gases.
For example:1 mole of hydrogen gas contains 6.02 x 1023 H2 molecules
1 mole of carbon dioxide gas contains 6.02 x 1023 CO2 molecules.
We shall see shortly that the relative molecular mass and relative atomic mass scale can in fact be thought of as a single scale. We will also be able to include masses of ions on such a scale.
Example 1:
How many moles of carbon dioxide gas will you have if you are told that you have 18.06 x 1023 molecules of the gas in your breath?
Solution:
First we must remember that there are 6.02 x 1023 particles in 1 mole of any substance. So we can write this problem as a division:
We can also relate the number of moles of a substance
to the mass of the substance using the relationship between the mole of
a substance and the relative atomic (or molecular) mass.
Example 2:
How many moles of hydrogen gas will be produced from a
reaction that evolved 40 grams of the gas? (Molecular mass of hydrogen
gas, H2 = 2.0.)
Solution:
Example 3:
An oxygen cylinder contains 6.0 moles of gas. If one
mole of oxygen gas has a mass 32.0g, what will be the mass of the gas in
the cylinder?
Solution:
Mass of oxygen = 6.0 mol. x 32.0 g per mole
= 192.0 g
Defining and relating the terms
To formalise and extend our understanding of relative
atomic mass and the mole we can give a definition based on our modern
understanding of the atomic mass scale.
The relative atomic mass of an element is the ratio of the average mass of the atoms of the elements compared to the carbon−12 isotope that is allocated the mass of 12 units.
A mole of a substance is equivalent in mass to the relative atomic mass or relative molecular mass in grams.
The molarmass is the mass of one mole of a substance.
To consider the masses of atoms measured in grams, for example, would
be to deal inconveniently with extremely small numbers. Rather, the
mass of an atom is compared with that of an atom of carbon-12. The
relative atomic mass of carbon-12 is taken to be 12. Relative masses
have no units because they have cancelled in their calculation.
Some elements have isotopes. In calculating the relative atomic
mass of an element with isotopes, the relative mass and proportion of
each is taken into account. For example, naturally occurring chlorine
consists of atoms of relative isotopic masses 35 (75%) and 37 (25%). Its relative atomic mass is 35.5.
Ar = (75/100 x 35) + (25/100 x 37) = 35.5
The relative masses of atoms are measured using an instrument called a mass spectrometer,
invented by the English physicist Francis William Aston (1877-1945)
when he was working in Cambridge with J. J. Thomson. It was in his use
of this instrument that the existence of isotopes of elements was
discovered. Aston eventually discovered many of the naturally occurring
isotopes of non-radioactive elements. He was awarded the Nobel Prize for
Chemistry in 1922.
Briefly, the mass spectrometer works by bombarding gaseous atoms
with fast-moving electrons which knock out an electron from the atom.
The cations formed are brought down on to a detector in turn according
to their mass. The instrument provides a measure of the relative mass
(compared to 12C) and the relative number of each isotope.
The diagrams below represent the mass spectrum of naturally occurring chlorine.
The above right spectrum has been represented so that the most
abundant isotope has a relative abundance of 100%, with the other mass
peaks scaled in relation to this. The relative atomic mass of chlorine
is now calculated as shown below:
Mole: Mole is the measurement in chemistry. It is used to express the amount of a chemical substance.
One mole is defined as the amount of substance of a system which
contains as many entities like, atoms, molecules and ions as there are
atoms in 12 grams of carbon - 12".
Avogadro number: The number of the particles present in one mole of any substance is equal to 6.022x1023. This is called avogadro’s number or avogadro’s constant.
Number of particles in 1 mole: 1 mole of hydrogen atoms represents 6.022 × 1023 hydrogen atoms. 1 mole of hydrogen molecules represents 6.022 × 1023 hydrogen molecules. 1 mole of water molecules represents 6.022 × 1023 water molecules.
The Video Tutorial:
Atomic mass: The atomic mass of an element is the mass of one atom of that element in atomic mass units or (u).
Atomic mass unit (amu): 1/12th of the mass
of an atom of carbon-12 is called atomic mass unit. It is a unit of mass
used to express atomic masses and molecular masses.
Molar mass: The molar mass of an element is equal to
the numerical value of the atomic mass. However, in case of molar mass,
the units change from ‘u’ to ‘g’. The molar mass of an atom is also
known as gram atomic mass.
For example, the atomic mass of carbon =12 atomic mass units. So, the gram atomic mass of carbon = 12 grams.
Molecular mass of the molecule: The sum of the atomic masses of all the atoms in a molecule of a substance is called the molecular mass of the molecule.
Molecular mass - calculation: Generally we use relative
atomic masses of atoms for calculating the molecular mass of 1 mole of
any molecular or ionic substances.
Example: Molecular mass of H2SO4
Atomic mass of Hydrogen = 1 Atomic mass of sulphur = 32
Atomic mass of oxygen = 16
Molecular mass of H2SO4 = 2(Atomic mass of Hydrogen) + 1 (Atomic mass of sulphur) + 4 (Atomic mass of oxygen)
= 2×1 + 32 + 4× 16 = 98 u.
Calculation of molecular mass of hydrogen chloride:
Atomic mass of hydrogen + Atomic mass of chlorine = 1 + 35.5 = 36.5 u. Formula unit mass: The formula unit mass of a
substance is the sum of the atomic masses of all atoms in a formula
unit of a compound. The term ‘formula unit’ is used for those substances
which are made up of ions.
Formula unit mass of NaCl: 1 X Atomic mass of Na + 1 X Atomic mass of Cl
1x23 +1 x 35.5 = 58.5 atomic mass units.
Formula unit mass of ZnO:
= 1 X Atomic mass of Zn + 1 X Atomic mass O
= 1 X 65 + 1 X 16 = 81 u.
Avogadro's number, number of particles and moles - conversion formulae:
Number of moles (n) = Given number of particles (N) / Avogadro number (N0)
Example: Find the number of moles present in 24.088X1023 particles of carbon dioxide
1 mole of carbon dioxide contains 6.022x1023
Solution: The number of moles (n ) = Given number of particles (N) / Avogadro number (N0).
= 24.088X1023 / 6.022x1023
= 4 moles.
Number of atoms (n) = Given mass (m) / Molar mass (M) x Avogadro number (N0)
Example: Calculate the number of atoms in 48g of Mg
Solution: Number of atoms (n) = Given mass (m) / Molar mass (M) x Avogadro number (N0).
= 48/24 X 6.022x1023
= 12.04 X1023 atoms.
Number of molecules (n) = Given mass (m) / Molar mass (M) x Avogadro number (N0)
Example: Calculate the number of molecules in 3.6 g of water
Solution: The molecular weight of H2O = 18
18g of water - 6.022x1023 molecules
3.6g of water - 6.022x1023 X 3.6/18
= 1.206 X 1022 molecules.
Number of particles (n) = Number of moles of particles (n) x Avogadro number (N0)
Example: Calculate the number of atoms in 0.5 moles of carbon
Solution: Number of atoms = 0.5 X 6.022x1023
= 3.0115 atoms
Extra problems:
1) Calculate the number of moles in 12g of oxygen gas
Ans: 32g of oxygen gas = 1 mole
12g of oxygen gas = ?
= 12 X 1 / 32 = 0.375 mole.
2) Calculate the number of moles present in 14g of carbon monoxide .
Ans: 28g of CO = 1 mole
14g of CO = ?
= 14 X 1 / 28 = 1/2 = 0.5 mole.
3) Find the mass of 5 moles of aluminium atoms?
Ans: Atomic mass of aluminium atom = 27g 5 moles of aluminium atoms = 5 X 27g = 135 g.
4) Calculate the molar mass of sulphur.
Ans: Sulphur is a poly atomic molecule. It is made up of 8 sulphur atoms.
Atomic mass sulphur atom = 32 g.
Molar mass of sulphur = 8 X 32 = 256 g.
5) Calculate the mass of 0.2 mole of water molecules.
Ans: 1 mole of water molecules = 18g
0.2 mole of water molecules = ?
= 0.2 X 18 / 1 = 3.6 g.
6) Which has greater number of atoms, 100g of sodium or 100g of iron?
Atomic mass of Na = 23 u, Fe = 56 u.
Ans: 1 mole of substance contains the number of particles = Avagadro's constant.
1 mole of Na = 23g
23g of Na contains - 6.023 X 1023 atoms
100g of Na Contains - ?
= 100 X 6.023 X 1023/23
= 4.3 X 6.023 X 1023 atoms.
1 mole of Fe = 56g
56g of Fe contains - 6.023 X 1023 atoms
100g of Fe contains - ?
= 100 X 6.023 X 1023/ 56
= 1.78 X 6.023 X 1023 atoms
Therefore, 100g of Na has greater number of atoms than 100 g of Fe.
7) How many atoms of oxygen are present in 300 grams of CaCO3? Ans: Molecular mass of calcium carbonate = 40 + 12 + 3 X 16 = 40 + 12 + 48 = 100g 1 mole of Calcium carbonate contains – 3 mole of oxygen atoms. 100 g of calcium carbonate contains - 3 X 6.023 X 1023 atoms 300g of calcium carbonate contains - ? = 300 X 3 X 6.023 X 1023/100 = 54.207 X 1023 oxygen atoms.
8) The mass of one atom of an element 'A' is 2.65 X10-23 g. Calculate its atomic mass and name the element. Ans: The mass of one atom of an element A = 2.65 X10-23 g We know that 1 mole of an atom = 6.023 x 1023 atoms 1 mole of an atom = Its atomic weight Mass of one atom of an element = 2.65X10-23 g Mass of 6.023 x 1023 atoms of an element A = 2.65X10-23 X6.023 x 1023 = 15.69 g
The element is oxygen.
9) Calculate the number moles of magnesium in 0.478g of magnesium ?
Ans: Molecular weight of magnesium =24g
24g of magnesium = 1 mole
0.478g of magnesium = ?
= 0.478 X 1/24 = 0.019 mole.
10) In which of the following cases the number of hydrogen atoms is more ? Two moles of HCl or one mole of NH3.
Ans: Calculation of number of hydrogen atoms present in 2 moles of HCl 1 mole of HCl contains 6.023X1023 molecules of HCl 2 moles of HCl contains 2 X 6.023X1023 = 12.046X1023 molecules of HCl 1 molecule of HCl contains 1 hydrogen atom 12.046X1023 molecules of HCl contains12.046X1023 hydrogen atoms Calculation of number of hydrogen atoms present in 1 mole of NH3 1 mole NH3 Contains 6.023X1023 molecules of NH3 1 molecule of NH3 contains 3 atoms of hydrogen 6.023X1023 molecules of NH3 contains 3X 6.023X1023 atoms of hydrogen = 18.069 X1023 atoms of hydrogen Number of hydrogen atoms present in 2 moles of HCl = 12.046X1023 Number of hydrogen atoms present in 1 mole of NH3 = 18.069 X1023 Therefore, numbers of hydrogen atoms are more in 1 mole of NH3.
11) Find the number of oxygen atoms in 88g of CO2?
Ans: Molar mass of CO2 = 44 g/mol Number of moles of CO2 present in 88g of CO2 = 88g/44g mol-1 = 2 moles 1 mole of CO2 contains 2 moles of Oxygen atoms. 2 moles of CO2 contains 4 moles of Oxygen atoms 1 mole of oxygen contains 6.023 X 1023 atoms of oxygen 4 moles of oxygen contains = 4 X 6.023 X 1023 = 24.092 X 1023 = 2.4092 X 1024 atoms of oxygen
Therefore, 88g of CO2 Contains 2.4092 X 1024 atoms of oxygen.
12) Calculate the number of water molecules contained in a drop of water weighing 0.06g ?
Ans: 18g of water = 1 mole 0.06 g = ? = 0.06/18 = 3.33 X 10-3 mole of water 1 mole of water contains - 6.022X1023 molecules of water 3.33 X 10-3 mole of water contains -----? = 6.022X1023 X 3.33 X 10-3 = 2 X 1020 molecule of water ∴ 0.06g of water contains 2 X 1020 molecules of water.
13) Find the number of aluminium ions present in 0.051g of aluminium oxide(Al2O3).
(Atomic masses: Al= 27u;O= 16u)
Ans: Molecular weight of Al2O3 = 102 g 102 g of Al2O3 contains 6.022X1023 molecules 0.051g of Al2O3 contain X number of molecules X = 0.051 X 6.022X1023 /102 = 0.003 X 1020 X = 3 X 1020 1 molecule of Al2O3 contains – 2 Al+3ions 3 X 1020 molecules contains – 2 X 3 X 1020 = 6 X 1020 Al+3 ions ∴ 0.051 g of Al2O3 contains 6 X 1020 Al+3 ions.
