Answer:
The molar mass of the gas is 6758 g/mol.
Given:
Density of gas, ρ = 94 mg/cc = 0.094 g/cc
Temperature, T = 15°C = 15+273 = 288 K
Pressure, P = 250 mm of Hg = 250/760 atm = 0.3289 atm
Find:
Molar mass of gas.
Solution:
According to Ideal gas equation, we have
PV = nRT ------------------- (i)
where P = Pressure of gas
V = Volume of gas
n =Number of moles of gas
R = Universal gas constant = 0.0821 L atm K⁻¹mol⁻¹ = 82.1 cc atmK⁻¹mol⁻¹
T = Temperature of gas
Now, Number of moles of the gas = m/M
where m = mass in gram
M = Molar mass of the gas
Putting the value of n in equation (i), we get
[tex]PV = \frac{m}{M} RT[/tex]
[tex]PM=\frac{m}{V} RT[/tex]
But m/V = Density of gas, ρ
[tex]PM = \rho RT[/tex]
[tex]M = \frac{\rho RT}{P}[/tex]
Putting values in the above formula, we get
[tex]M = \frac{(0.094)(82.1)(288)}{0.3289}[/tex]
[tex]M = 6758 g/mol[/tex]
Hence, the molar mass of the gas is 6758 g/mol.
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