Introduction to Chemical Arithmetic

Atomic Number: It is the number of protons present in the nucleus of an atom. For example Carbon, an atom contains 6 protons. Therefore, the atomic number of carbon is 6. It is also the number of electron present in a neutral atom.

Atomic mass number: It is the sum of a number of protons and neutrons present in an atom of an element. For example Atomic mass number of Carbon = No. of protons + No. of neutrons = 6 + 6 = 12 The proton and neutron component of the nucleus are collectively known as nucleons i.e. the total number of nucleons is a mass number. The atomic number and atomic mass number of an atom can be denoted symbolically as

\(_A^XZ\)

where A Mass number ( neutrons + protons)

Z = Atomic number ( Number of protons or electrons)

X = symbol of element

For Example: \(_6^{12}C\)

Isotopes: Atoms of the same element having different mass number are called isotopes. It arises due to the difference in the number of protons.

Example: ¹₁H, ²₁H,³₁H (Isotopes of hydrogeN)

¹²₆C, ¹³₆C,¹⁴₆C ( Isotopes of carbon)

Isobars: Atoms of different elements having the different atomic number but the same atomic mass number are called isobars.

Example: ⁴⁰₁₈Ar, ⁴⁰₁₉K,⁴⁰₂₀Ca

Isotones: Atoms of different elements having the same number of neutrons are called isotones.

Example: ¹⁴₆C, ¹⁵₇N, ¹⁶₈O ( 8 neutrons each)

Atomic mass/ Atomic weight: Atomic mass of an element is defined as the number which shows how many times an atom of an element is heavier than one – twelfth of the mass of an atom of a C – 12 isotope. For example, The atomic mass of Magnesium is 24 amu means that one atom of Magnesium is 24 times heavier than one – twelfth of the mass of an atom of a C – 12 isotope.

Atomic mass = \( \frac {Mass \: of\: an\: atom\: of\: element}{ \frac{1}{12}\: th \: of \: mass\: of\: an\: atom\: of\: C-12\: isotope}\)

Atomic mass unit ( AMU): The mass of one-twelfth of the mass of an atom of a C – 12 isotopes is called one atomic mass unit ( 1 amu). The masses of all atoms and molecules are expressed with reference to the mass of 1 AMU.

Absolute mass of 1 amu

1 gram atomic mass of carbon = 12 gm of carbon

Mass of 6.023 x 10²³ atoms of carbon = 12 gm of carbon

Mass of 1 atom of carbon = \( \frac {12}{6.023 x 10^{23}}\) gm of carbon

\( \frac {1}{12}th\) of Mass of 1 atom of carbon = \( \frac {12}{6.023 x 10^{23}}\) gm of carbon = \( \frac {1}{12}\)\( \frac {12}{6.023 x 10^{23}}\) gm of carbon = 1.66 x 10^-24 gm of carbon

∴ 1 amu = 1.66 x 10^-24 gm

Average atomic mass

There are many cases where different atoms of the same element are naturally abundant and posses different mass number. Such atoms of the same element having different mass number are called isotopes. Such isotopes having different relative masses as well. In such case, the atomic mass of the element is the average relative masses of isotopes of the element.

Atomic mass = \( \frac {Mass \:of\: an\: atom\: of\: element\: }{ \frac{1}{12}th\: of \: mass\: of\: an\: atom\: of\: C-12\: isotope}\)

Atomic mass being an average mass, it is fractional in number. For example, 2 isotopes of chlorine having relative masses 35 and 37 are present in the chlorine in the ratio 3: 1 respectively. Therefore, average relative atomic mass of chlorine could be

\( \frac {35× 3 + 37 × 1}{3 + 1} \)

= 35.5

Hence, the fractional atomic mass of an element is due to the presence of different isotopes of elements in a natural mixture in different percentage or ratio.

Therefore, Average atomic mass =\( \frac {m_1 R_1 + m_2R_2}{R_1 + R_2} \) OR =\( \frac {m_1 R_1 + m_2R_2}{100\%} \)

Gram atomic mass ( Gram – atom): Atomic mass expressed in gram is known as gram atomic mass or simply gram atom or mole of an atom.

For example, 1 gm atom of Magnesium means 24 gm of Magnesium. It is also 1 mole of Magnesium.

1 gm atom of Carbon = 12gm of Carbon

1 gm atom of Sodium = 23 gm of Sodium

1 gm atom of Sulphur = 32gm of Sulphur

1gm atom of Oxygen = 16gm of Oxygen

No. of gram atom = \( \frac {Mass \:of\: an\: element\: in\: gram }{Atomic\: mass\: of\: an\: element }\)

Molecular mass: it is the mass of a molecule of a substance with respect to the one-twelfth of the mass of an atom of the C-12 isotope. A molecular mass is a relative term and it is unit less number. For example Molecular mass of sulphuric acid is 98 means that a molecule of sulphuric acid is 98 times heavier than one-twelfth of the mass of an atom of a C-12 isotope. A molecular mass can be calculated by the summation of atomic masses of all the atoms present in the given molecule.

For example: Molecular mass of C₆H₁₂O₆ = 12 x 6 + 12 x 1 + 16 x 6 = 180 amu.

Gram molecular mass ( Gram molecule): When the molecular mass is expressed in gram, then it is called 1 gram molecular mass or 1 gram mole.

No. of gram molecule = \( \frac {Mass\: in\: gram }{Molecular\:Mass}\)

Mole concept: It is found that a number of atoms present in 1gram atom of the element are equal to the number of molecules present in a 1gm mole of any substance. This number is experimentally determined and found to be equal to ( 6.023 x 10²³ ). This number is called Avogadro’s number or Avogadro’s constant.

Avogadro’s number = 6.023 x 10²³

The amount of substance containing Avogadro’s number of atoms or molecules is called mole or simply written as mol.

Thus, a mole can be defined as the amount of substance which contains the same number of elementary particles ( atoms / molecules/ ions) as the number of atoms present in 12 gm of C – 12 isotope. Simply, a mole is the collection of Avogadro’s number of particles i.e. number of atoms/ molecules/ions/electrons/protons/neutrons, etc.

Significance of mole

1. It gives a number of particles.

1 mole of the substance contains Avogadro's number of particles. 1 mole of H₂ molecule = 6.023 x 10²³ molecules of H₂

1 mole Hydrogen atom = 6.023 x 10²³ H atom

1 mole of ^Na+ ion = 6.023 x 10²³ ions of Na⁺

1 mole of electrons = 6.023 x 10²³ electrons

2. It gives the mass of substance in gram.

1 mole of atoms = 6.023 x 10²³ atoms = gram atomic mass of element

Eg: 1 mole of O atom = 6.023 x 10²³ atos of O = 16gm of oxygen

1 mole of Na = 6.023 x 10²³ atoms of Na = 23 grams of Na

1 mole of Sulphur atom = 6.023 x 10²³ atoms of S = 32 gm of S

1 mole of molecules = 6.023 x 10²³ molecules = gram molecular mass

Eg: 1 mole of O₂ = 6.023 x 10²³ atos of O = 32gm of oxygen

1 mole of CO₂ = 6.023 x 10²³ atoms of Na = 44 grams of CO₂

1 mole of CaCO₃ = 6.023 x 10²³ atoms of CaCO₃ = 100 gm of CaCO₃

3. It gives the volume of gaseous substances at NTP.

The volume occupied by 1 mole of any gaseous substance is known as gram molecular volume (GMV) which is equal to 22.4liter.