Question

Two vessels of the same size are at the same temperature. One of them holds 1 kg of N2 gas. (i) Which of the vessels contains more molecules? (ii) Which of the vessels is under greater pressure and why? (iii) In which vessel is the average molecular speed greater? How many times is it greater?

Answer 1

(i) Hydrogen vessel

(ii) Hydrogen vessel

(iii) The average molecular speed in Hydrogen vessel is 3.74 times greater than nitrogen vessel.  

 

Explanation:

=> (i) The vessel hydrogen gas contains more molecules.

As 2 g of hydrogen contains N molecule,

1000 g  (1 kg) of hydrogen contains:

= N * 1000 / 2

= 500 N molecules

In the case of N₂, 28 g of nitrogen contains N molecules.

Therefore, 1 kg of nitrogen contains

N/28 * 1000

≈ 36 N

(ii) Hydrogen vessel is under greater pressure because,

P = 1 M / 3 V C², P ∝ C²

Since M and V are the same in both the cases, $C_{H2} > C_{N2}$.

Thus, the pressure exerted by hydrogen is more than that of nitrogen.

(iii) The average molecular speed in vessels:

$C_{H2} / C_{N2}$ = √ρ$_{N2}$ / ρ$_{H2}$

= √14 / 1

≈ 3.74

C$_{H2}$ = 3.74 C$_{N2}$

Thus, The average molecular speed in Hydrogen vessel is 3.74 times greater than nitrogen vessel.  

 

Learn more:

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