At 0°C, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?
Density (d) of the substance at temperature (T) can be given by the expression,
`d = "Mp"/"RT"`
Now, density of oxide (d1) is given by,
`d_1 = (M_1p_1)/"RT"`
Where, M1 and p1 are the mass and pressure of the oxide respectively.
Density of dinitrogen gas (d2) is given by,
`d_2 = (M_2p_2)/"RT"`
Where, M2 and p2 are the mass and pressure of the oxide respectively.
According to the given question,
`d_1 = d_2`
`:. M_1p_1 = M_2p_2`
`p_1 = "2bar'`
`p_2 = "5 bar"`
Molecular mass of nitrogen, M2 = 28 g/mol
Now `M_1 = (M_2p_2)/p_1`
= 70 g/mol
Hence, the molecular mass of the oxide is 70 g/mol.
Using the expression, d =MP/RT , at the same temperature and for same density,
M1P1 = M2P2 (as R is constant)
(Gaseous oxide) (N2)
M1 x 2 = 28 x 5(Molecular mass of N2 = 28 u)
or M1 = 70u
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