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Ideal Gas Equation

Equal masses ...

Question

Equal masses of $N_{2}$ and $O_{2}$ gases are filled in vessel A and B. The volume of vessel B is double of A. The ratio of pressure in vessel A and B will be

A

16:7

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B

16:14

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C

32:7

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D

32:28

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Solution

The correct option is A 16:7
The mathematical form of the Ideal Gas Law is:
PV = nRT and n = m/MW
Where:P - pressure
V - volume
n - number of moles
T - temperature
m - mass
MW - Molecular Weight
R - ideal gas constant
So we can write,
$\frac{P_{a}}{P_{b}}$ = $\frac{M_{b} \times V_{b}}{M_{a} \times V_{a}}$
here, $V_{b} = 2 V_{a}$ and $M_{a}$ = atomic wt of $O_{2}$ = 8 and $M_{b}$ = atomic wt of $N_{2}$ = 7
Putting these values we get,
$P_{a} / P_{b}$ = 16/7

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