Number of Mole and Mass of a Substance

Molar Mass

  1. The mass of one mole of atoms is its relative atomic mass in grams, and is called a molar mass.
  2. A Molar mass is the mass of a substance containing the Avogadro Constant of particles.
Element
Relative atomic mass
Mass of 1 mol of particle
Molar Mass
Hydrogen
1
1 g
1 g mol-1
Carbon
12
12 g
12 g mol-1
Oxygen
16
16 g
16 g mol-1
Copper
64
27 g
27 g mol-1
Iron
56
56 g
56 g mol-1

Example

  1. The relative atomic mass of copper is 64, therefore the mass of 1 mole copper is 64g
  2. The RAM of sodium is 23, therefore the mass of 2 mole sodium is 46g
  3. The RAM of nitrogen is 14, therefore the mass of 2.5 mole l nitrogen is 35g
  4. The RAM of calcium is 20, therefore the mass of 0.3 mole calcium is 6g

Conclusion

Note:

The relationship between the mass of a substance and the number of mole of the particles in the substance can be summarised by using the following equation:
n= m Molar Mass
If you are given the mass of substance and asked to find the number of mole of the substance (or vice versa), the problem can be solved by using this equation.

Example:
Find the number of mol of atoms in 4.6g sodium [Relative atomic mass: Na=23]

Answer:
Number of mole, [n = frac{{4.6}}{{23}} = 0.2mol]

Example
How many moles of each substance are there in 191 g NaOH [Relative atomic mass: Na=23, O=16, H=1]

Answer:
Relative Formula Mass of NaOH = 23 + 16 + 1 = 40
Number of mole of 191g NaOH,
[n = frac{{191}}{{40}} = 4.775mol]

Question
What is the mass of 7.12 mol NaI. [Relative atomic gas: Iodine = 131; Sodium = 23]

Answer:
The relative formula mass of NaI = 23 + 131 = 154.

The mass of 7.12 mol NaI

= Number of mole x Relative Foemula Mass of NaI
= 7.12 x 154
= 1096.48g

Mass of Substance and Number of Particles

  1. Sometime, you may be given the mass of a substance, and asked to find the number of particles (or vice versa). 
  2. To solve the problem, we must find the number of mole of the substance then only we can find the number of particles (or mass of the substance).
Example:

How many molecules are there in 16 g of oxygen (O2)? [ Ar: O =.16, Avogadro Number = 6 x 1023]

Answer:
The relative molecular mass of  O2 = 2(16) = 32
Number of mole of oxygen molecules = Mass of oxygen Molar mass of oxygen = 16 g 32 g mol -1 =0.5 mol
Question:
Find the number of atoms in 34g of ammonia gas (NH3). [Relative atomic mass: Nitrogen: 14; Hydrogen: 1]

Answer:
Relative molecular mass of NH3
= 14 + 3(1)
= 17

Number of mole of ammonia = 34 17 =2 mole


Number of  NH3 molecules = 2 x 6.02 x 1023 = 1.204 x 1024


Each NH3 molecule contain 4 atoms (1 nitrogen atom and 3 hydrogen atoms).


Therefore, number of atoms
= 4 x 1.204 x 1024
= 4.816 x 1024

Question 2
Find the mass of methane (CH4) that contain  1.806 x 1023 of methane molecules. [Relative atomic mass: Carbon: 12; Hydrogen: 1]

Answer:
The relative molecular mass of CH4
= 12 + 4(1)
= 16

Number of mole of C H 4 = 1.806× 10 23 6.02× 10 23 =0.3 mole
Mass of CH4
 = Number of mole x molar mass 
= 0.3 x 16 = 4.8g