Question

3. Under STP if you collect 3 litre of \( O _{2}, 5 \) litre of \( Cl _{2} \) and 6 litre of \( H _{2} \), i. Which has the highest number of molecules? ii. Which has the lowest number of molecules?

Answer 1

We know that, the volume occupied by one mole of gas at STP = 22.4 L and we also know that - one mole of molecule contain 6.023 x 10²³ number of molecules

therefore,

Number of moles O₂ = \(\frac{volume\,of\,O_2\,(L)}{22.4L/mol}\) 

= \(\frac{3}{22.4}\)

= 0.134 mol

So, number of O₂ molecule in 0.134 mol

= 0.134 x 6.023 x 10²³

= 8.07 x 10²²molecules of O₂

Number of mole of Cl₂ =  \(\frac{volume\,of\,Cl_2\,(L)}{22.4L/mol}\) 

= \(\frac{5}{22.4}\) mol

= 0.223 mol

So, Number of Cl₂ molecules in 0.223 mol = 0.223 x 6.023 x 10²³

= 1.343 x 10²³ molecules of Cl₂

Similarly,

Number of moles of H₂ =  \(\frac{volume\,of\,H_2\,(L)}{22.4(L/mol)}\) 

= \(\frac{6}{22.4\,L/mol}\) 

= 0.268 mol

So, Number of H₂ molecule in 0.268 mole of H₂ = 0.268 x 6.023 x 10²³

 = 1.614 x 10²³molecules of H₂

Hence, 6 Litre of H₂ gas has highest number of H₂ molecules and 3 Litre of O₂ gas has lowest Number of O₂ molecules.

(i) 6 litre of H₂ has highest number of molecules of H₂

(ii) 3 litre of O₂ has lowest number of molecules of O₂