Question

Calculate: 

(a) the mass of 1.0505 × 10²³ molecules of carbon dioxide (CO₂ ). 

(b) the number of molecules of 0.25 moles of NH₃ , 

(c) the formula unit mass of Na₂SO₃ . 

[Atomic mass: Na = 23 u, S = 32 u, O = 16 u, H = 1 u, NA = 6.022 × 10²³ mol ^–1 ]

Answer 1

(a) First we will convert 1.0505 × 10²³ molecules of carbon dioxide (CO₂ ) into number of moles: 

We know, 1 mole = 6.022 × 10²³ (Na = Avogadro’s number)

The number of moles = \(\frac{Given\,number\,of\,molecules}{Avogadro's\,number}\)

Number of moles = \(\frac{1.0505\times10^{23}}{6.022\times10^{23}}\)

Number of moles = 0.17 

Now, to calculate mass, apply the formula:

Number of moles(n) = \(\frac{Mass(m)}{Molar\,mass(M)}\)

We can write: 

Mass(m) = Number of moles (n) × Molar mass of CO₂ (M) 

Mass = 0.17 mol × 44g/mol 

Mass = 7.48g 

Thus, the mass of 1.0505 × 10 23 molecule of CO₂ is 7.48g.

(b) Given: Number of moles = 0.25 

We know, 1 mole = 6.022 × 10²³ (Na = Avogadro’s number)

The number of moles = \(\frac{Number\,of\,molecules}{Avogadro's\,number}\)

We can write: 

Number of molecules = Number of moles (n) × N_a 

Number of molecules = 0.25mol × 6.022 × 10²³ 

Number of molecules = 1.5 × 10²³ 

Thus, the number of molecules of 0.25 moles of NH₃ is 1.5 × 10²³ 

(c) Formula unit mass of Na₂SO₃ : 

2 × Atomic mass of Na + Atomic mass of sulphur + 3 × Atomic mass of O 

= 2 × 23 u + 32 u + 3 × 16 u 

= 126 u 

Thus, the formula unit mass of Na₂SO₃ is 126 u