Examine the samples given:

a. 20 g of He

b. 44.8 L of NH₃ at STP

c. 67.2 L of N₂ at STP

d. 1 mol of H₂SO₄

e. 180 g of water

Arrange the samples in increasing order of the number of molecules in each.

i) Calculation of number of molecules in each:

a. Given: Mass of He = 20g

Gram molecular mass of He = 4g

To calculate the number of molecules, first we apply the formula:

Number of gram molecules = 5

Now, number of molecules = 5 × 6.022 × 10²³

= 3.011 × 10²⁴

Thus, number of molecules of He is 3.011 × 10²⁴

b. Given: Volume of NH₃ at STP = 44.8L

Gram molecular mass of NH₃ = 17g

First we will calculate the number of moles so that we can find the number of molecules.

As we know that 1 mole of any gas occupies 22.4 litres of volume.

∴ 1 mole of NH₃ = 22.4 litre

22.4 × Number of moles = 44.8 litres

Number of moles = 2

Now, number of molecules = No. of moles × 6.022 × 10²³

= 2 × 6.022 × 10²³

= 1.204 × 10²⁴

Thus, number of molecules of NH₃ is 1.204 × 10²⁴

c. Given: Volume of N₂ at STP = 67.2L

Gram molecular mass of N₂ = 28g

First we will calculate the number of moles so that we can find the number of molecules.

As we know that 1 mole of any gas occupies 22.4 litres of volume.

∴ 1 mole of NH₃ = 22.4 litre

22.4 × Number of moles = 67.2 litres

Number of moles = 3

Now, number of molecules = No. of moles × 6.022 × 10²³

= 3 × 6.022 × 10²³

= 1.806 × 10²⁴

Thus, number of molecules of N₂ is 1.806 × 10²⁴

d. 1 mol of H₂SO₄

Given: Number of moles = 1mol

Number of molecules = No. of moles × 6.022 × 10²³

= 1 × 6.022 × 10²³

= 6.022 × 10²³

Thus, number of molecules of H₂SO₄ is 6.022 × 10²³

e. Given: Mass of water = 180g

Gram molecular mass of H₂O = 18g

To calculate the number of molecules, first we apply the formula:

Number of gram molecules = 10

Now, number of molecules = 10 × 6.022 × 10²³

= 6.022 × 10²⁴

Thus, number of molecules of H₂O is 6.022 × 10²⁴

The arrangement of the samples in increasing order of the number of molecules in each is:

44.8 L of NH₃ at STP < 67.2 L of N₂ at STP < 20 g of He < 1 mol of H₂SO₄ < 180 g of water