Solved Problems

Atoms and Molecules (Science)

SOLVED PROBLEMS

I. Calculation of molar mass

Calculate the gram molar mass of the Â­following.

1) H2O        2) CO2        3) Ca3 (PO4)2

Solution:

1) H2O

Atomic masses of H = 1, O = 16

Gram molar mass of H2O

= (1 × 2) + (16 × 1)

= 2 + 16

Gram molar mass of H2O = 18 g

2) CO2

Atomic masses of C = 12, O = 16

Gram molar mass of CO2

= (12 × 1) + (16 × 2)

= 12 + 32

Gram molar mass of CO2 = 44 g 3)

3) Ca3 (PO4)2

Atomic masses of Ca = 40, P = 30, O = 16.

Gram molar mass of Ca3 (PO4)2

= (40 × 3) + [30 + (16 × 4)] × 2

= 120 + (94 × 2)

= 120 + 188

Gram molar mass of Ca3(PO4)2 = 308 g

II. Calculation based on number of moles from mass and volume

1) Calculate the number of moles in 46 g of sodium?

= 46 / 23

2 moles of sodium

2) 5.6 litre of oxygen at S.T.P

3) Calculate the number of moles of a sample that contains 12.046 × 1023 atoms of iron ?

III. Calculation of mass from mole

Calculate the mass of the following

1) 0.3 mole of aluminium (Atomic mass of Al = 27)

Mass = No. of moles × atomic mass

So, mass of Al = 0.3 × 27

= 8.1 g

2) 2.24 litre of SO2 gas at S.T.P

Molecular mass of SO2 = 32 + (16 × 2)

= 32 + 32 = 64

Mass = No. of moles × molecular mass

Mass = 0.1 × 64

Mass of SO2 = 6.4 g

3) 1.51 × 1023 molecules of water

Molecular mass of H2O = 18

0.25 = mass / 18

Mass = 0.25 × 18

Mass = 4.5 g

4) 5 × 1023 molecules of glucose ?

Molecular mass of glucose = 180

= (180 × 5 × 1023) / 6.023 × 1023

= 149.43 g

IV. Calculation based on number of atoms/ molecules.

1) Calculate the number of molecules in 11.2 litre of CO2 at S.T.P

= 11.2 / 22.4

= 0.5 mole

Number of molecules of CO2 = number of moles of CO2 Ã— Avogadro’s number

= 0.5 × 6.023 × 1023

= 3.011 × 1023 molecules of CO2

2) Calculate the number of atoms present in 1 gram of gold (Atomic mass of Au = 198)

Number of atoms of Au = 3.042 × 1021 g

3) Calculate the number of molecules in 54 gm of H2O?

Number of molecules of water = 6.023 × 1023 Ã— 54 / 18

= 18.069 × 1023 molecules

4) Calculate the number of atoms of oxygen and carbon in 5 moles of CO2.

1 mole of CO2 contains 2 moles of oxygen

5 moles of CO2 contain 10 moles of oxygen

Number of atoms of oxygen = Number of moles of oxygen × Avogadro’s number

= 10 × 6.023 × 1023

= 6.023 × 1024 atoms of Oxygen

1 mole of CO2 contains 1 mole of carbon

5 moles of CO2 contains 5 moles of carbon

No. of atoms of carbon = No.of moles of carbon × Avogadro’s number

= 5 × 6.023 × 1023

= 3.011 × 1024 atoms of Carbon

V. Calculation based on molar volume

Calculate the volume occupied by:

1) 2.5 mole of CO2 at S.T.P

2) 3.011 × 1023 of ammonia gas molecules

= 2 moles

Volume occupied by NH3

= number of moles × molar volume

= 2 × 22.4

= 44.8 litres at S.T.P

3) 14 g nitrogen gas

Number of moles = 14 / 28

= 0.5 mole

Volume occupied by N2 at S.T.P

no. of moles × molar volume

0.5 × 22.4

11.2 litres.

VI. Calculation based on % composition

Calculate % of S in H2SO4

Molar mass of H2SO4

= (1 × 2) + (32 × 1) + (16 × 4)

= 2 + 32 + 64

= 98 g