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in States of Matter - Gas and Liquid by (48.1k points)

Pressure of 1 g of an ideal gas A at 27°C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature, the pressure becomes 3 bar. Find a relationship between their molecular masses.’

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Given that:

Mass of gas A, WA = 1 g
Mass of gas B, WB = 2 g
Pressure exerted by the gas A = 2 bar
Total pressure due to both the gases = 3 bar
As temperature and volume remain constant.
Now if MA and MB are molar masses of the gases A and B respectively, therefore
PAV = WART/MA
or, 2 × V = 1 × RT/MA ….. (i)
Also,
Ptotal V = (WA / MA + WB / MB)RT
3 × V = (1/ (MA + WB/MB)RT …….. (ii)
Dividing equation (ii) by (i), we get

Thus, a relationship between the molecular masses of A and B is given by 4MA = MB.

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