Answer :

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 × 10^{23}

= 3.011 × 10^{24}

__Thus, number of molecules of He is__ __3.011 × 10 ^{24}__

b. Given: Volume of NH_{3} at STP = 44.8L

Gram molecular mass of NH_{3} = 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 NH_{3} = 22.4 litre

22.4 × Number of moles = 44.8 litres

Number of moles = 2

Now, number of molecules = No. of moles × 6.022 × 10^{23}

= 2 × 6.022 × 10^{23}

= 1.204 × 10^{24}

__Thus, number of molecules of NH _{3} is__

__1.204 × 10__

^{24}c. Given: Volume of N_{2} at STP = 67.2L

Gram molecular mass of N_{2} = 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 NH_{3} = 22.4 litre

22.4 × Number of moles = 67.2 litres

Number of moles = 3

Now, number of molecules = No. of moles × 6.022 × 10^{23}

= 3 × 6.022 × 10^{23}

= 1.806 × 10^{24}

__Thus, number of molecules of N _{2} is__

__1.806 × 10__

^{24}d. 1 mol of H_{2}SO_{4}

Given: Number of moles = 1mol

Number of molecules = No. of moles × 6.022 × 10^{23}

= 1 × 6.022 × 10^{23}

= 6.022 × 10^{23}

__Thus, number of molecules of H _{2}SO_{4} is__

__6.022 × 10__

^{23}e. Given: Mass of water = 180g

Gram molecular mass of H_{2}O = 18g

__To calculate the number of molecules, first we apply the formula:__

Number of gram molecules = 10

Now, number of molecules = 10 × 6.022 × 10^{23}

= 6.022 × 10^{24}

__Thus, number of molecules of H _{2}O is__

__6.022 × 10__

^{24}__T____he arrangement of the samples in increasing order of the number of molecules in each is:__

44.8 L of NH_{3} at STP < 67.2 L of N_{2} at STP < 20 g of He < 1 mol of H_{2}SO_{4} < 180 g of water

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