Question

How many molecules of ${\text{H}}_2$ gas are present in a container of dimensions 2 m $\times$ 2 m $\times$ 3 m at STP?

• A. $32.22\times {10}^{25}$
• B. $32.22\times {10}^{23}$
• C. $32.22\times {10}^{22}$
• D. $32.22\times {10}^{27}$

Answer 1

The correct option is A

$32.22\times {10}^{25}$

Measurement of container = $2m\times 2m\times 3m$

Volume of hydrogen gas at STP (Volume of the container) = $12m^3$
Volume of hydrogen gas at STP = 12,000 L $[\because 1m^3=1000L]$

Molar volume at STP (litres) = 22.4 L
In case of gases at STP,
Number of moles = $\frac{\text{Volume at STP (litres)}}{\text{Molar volume at STP (litres)}}$ .... (i)

Inserting the values of the volume of hydrogen at STP and molar volume at STP (litres) in equation (i) we have:

Number of moles = $\frac{12000}{22.4}$
= $5.35\times {10}^2$

Also, number of moles = $\frac{\text{Number of molecules}}{\text{Avogadro number}}$ .... (ii)

Number of molecules = Number of moles x Avogadro number ....(iii)

Inserting the value of number of moles and avogadro number in equation (iii) we have:

Number of molecules = $5.35\times {10}^2\times 6.022\times {10}^{23}$
Number of molecules = $32.22\times {10}^{25}$