# Relative Atomic Mass and Molecular Mass

There are many cases where different atoms of the same element possess different relative masses. Such atoms of the same element which have different relative masses are called isotopes. In such cases atomic mass of the element is average of relative masses of different isotopes of the element. For example, chlorine contains two types of atoms having relative masses 35 u and 37 u. The relative abundance of these isotopes in nature is in the ratio 3 : 1. Thus, atomic mass of chlorine is the average of these different relative masses as described below:

Atomic mass of chlorine = (35 X 3 + 37 X 1) / 4    = 35.5 u.

Thus, the atomic mass of an element may be defined as the average relative mass of an atom of the element a compared with the mass of an atom of carbon (C-12) taken as 12 u.

SOLVED EXAMPLES

Example 10.1  Nitrogen occurs in nature in the form of two isotopes with atomic masses 14 and 15 respectively. 1f average atomic mass of nitrogen is 14.0067, what is the% abundance of the two isotopes?

Solution. Let% abundance of N-14 isotope = x

Then % abundance of N-15 isotope = (100 –x)

The average atomic mass = X x 14 +(100-x)15 / 100

Now , 14x + (100-x) 15 / 100 = 14.0067

– x = 1400.67 – 1500 = – 99.33 or x = 99.33

Thus ,  % abundance of N-14 isotope = 99.33%

%abundance of N-15 isotope = 0.67%.

Example 10.2. Use the data given in the table to calculate the molar mass of carbon:

Isotope                        Relative Abundance                           At. mass

12c                              98.892                                                   12

13c                              1.108                                                   13.00335

14c                              2 x 10-10                                              14.00317

Solution.

Molar mass of carbon

= Σ isotopic mass x Relative abundance / Σ Relative abundance

= 0.98892 X (12 U) + 0.01108 X (13.0033 u) + 2 x10– 12 x (14.00317 u)

= 12.011 u.

GRAM ATOMIC MASS (GAM)

It may be defined as that much quantity of the element whose mass in gram is numerically equal to its atomic mass. Gram atomic mass is also called one gram-atom of the

element. For example, atomic mass of magnesium (Mg) is 24 u,. therefore,

1 gram-atom of Mg = gram atomic mass of Mg        =24g

2 gram-atom of Mg = 2 x gram atomic mass of Mg         = (2 X 24) g = 48 g.

From the above discussion, we can get the relationship between mass of the element and its gram-atoms as:

Number of gram atom = Mass in gram / Gram atomic mass = W (g) / GAM

MOLECULAR MASS

Like atoms, the molecules are also very small in size and hence, their actual masses cannot be detennined by direct weighing. Therefore, masses of molecules are also determined relative to the mass of carbon atom (C-12) taken as 12 u. These relative masses of molecules are called molecular masses.

Molecular mass of a substance (element or compound) may be defined as the average relative mass of a molecule of the substance as compared with mass of an atom of carbon (C-12) taken as 12 u. Molecular mass of a substance tells us the number of times a molecule of the substance is heavier than 1/12th of mass of a carbon (C-12) atom. For example, molecular mass of water (H2O) is 18 u. It means that a molecule of water is 18 times heavier than 1/12th of mass of a carbon atom (C-12).

Molecular mass of a substance can be obtained by adding the atomic masses of all the. atoms present in a molecule of the substance. For example,

Molecular masses of  NH3= atomic mass of N + 3 (atomic mass of H)

= 14 + 3 X 1 = 17 U.

GRAM MOLECULAR MASS (GMM)

It may be defined as that much quantity of the substance (element or compound) whose mass in gram is numerically equal to its molecular mass. Gram molecular mass is also called one gram-molecule of the substance. For example, molecular mass of ammonia is 17 u; therefore,

1 gram-molecule of  NH3    = gram molecular mass of NH3

= 17 g

2 gram-molecule of NH3= 2 x gram molecular mass of NH3

= (2x 17) g = 34 g.

From the above discussion it follows that

Number of gram-molecule = Mass in gram / Gram atomic mass  = W(g) / GMM

SOLVED EXAMPLES

Example 10.3. (a) Calculate the mass of 2.5 gram-atom of calcium. Atomic mass of calcium is 40 u.

(b) Calculate the mass of 1.5 gram-molecule of water (H20).

Solution. (a) 1 gram-atom of calcium

= gram atomic mass of calcium = 40 g

2.5 gram-atom of calcium

= 40 X 2.5 = 100 g.

(b) Molecular mass of water (H20)

= 1 x 2 + 16 = 18 U

1 gram-molecule of ~0

= gram molecular mass of H20 = 18 g.

1.5 gram-molecule of H20

= 18 x 1.5 = 27 g.

Example 10.4  Calculate the number of gram-atom and gram molecule in 25.4 mg of iodine (12). Atomic mass of!= 127 u.

Solution. Gram-atom = mass (g) / GAM = 25.4 x 10-3 g / 127 g

= 2 x 10-4 g-atom

Gram – molecule = mass (g) / GAM = 25.4 x 10-3 g / 127 g  /254 g

= 1 x 10-4 g-molecule.

Example 10.5 Calculate the molar mass of glucose ( C6H120 6) and the number of atoms of each kind in it.

Solution. Molecular mass of glucose (C6H120t»

= 6 x (12.011 u) + 12 x (1.008 u)

+ 6 x (l6.00 u)

= 72.066 u + 12.096 u + 96.00 u

= 180.162 u

Calculation of number of atoms of each kind

1 mole of glucose (C6H1Pt»

= 6 moles of carbon + 12 moles of hydrogen

+ 6 moles of oxygen

Hence, Atoms of carbon = 6 x 6.02 x 1023

= 36.12 x 1023

Atoms of hydrogen = 12 x 6.02 x 1023

= 72.24 x 1023

Atoms of oxygen = 6 x 6.02 x1023

= 36.12 x 1023