Question

Which has more atoms,50g of Na or 50g of Ca?

Answer 1

23 g of Na contains 6.022 × 10^23 atoms
50 g of Na will contain = 6.022 × 50/23 × 10^23
= 1.3 × 10^24

40 g of Ca contains 6.022 × 10^23 atoms
50 g of Ca will contain = 50/40 × 6.022 × 10^23
= 7.5 × 10^23

∴ 50g of Na has more atoms.

Answer 2

Given: Mass of Na(m₁) = 50 g  Molecular mass of Na(M₁) = 23g

           Mass of Ca(m₂) = 50g   Molecular mass of Ca(M₂) = 40g

To Find: Number of atoms of Na and Ca (N₁ and N₂)

Solution:

Formula Used:-

• number of moles-n = given no. of atoms(N)/Avogadro number(N°)

•    Also n = given mass(m)/ molecular mass(M)

• Hence m/M = N/N°      Avagadro number = 2.303 × 10²³ atoms

Applying the Formula:

N₁ = m₁/M₁ × N°

N₁ = 50/23 × 6.023 × 10²³

N₁= 2.173 × 6.023 × 10²³

N₁ = 13.1 × 10²³ atoms of Na

Similarly,

N₂ = m₂/M₂ × N°

N₂ = 50/40 × 6.023 × 10²³

    = 1.25 × 6.023 × 10²³

    = 7.53 × 10²³ atoms of Ca

Hence N₁ - atoms of 50g of Na > N₂ - atoms of 50g of Ca

Moreover, this can also be interpreted by an alternative method:

m₁ = m₂ (Given)

M₁ < M₂

N° is the same in both cases.

∴ it depends only on molecular masses and according to the formula

N is inversely proportional to molecular mass.

∴if M is high N is less

Hence if M₁ < M₂

          then N₁ > N₂