Answer:
115.25g/mol
Explanations:
According to the ideal gas equation:
[tex]PV=nRT[/tex]
where
• P is the ,pressure (,in atm)
,
• V is the ,volume ,in litres
,
• n is the ,number of moles
,
• R is the ,Gas constant
,
• T is the ,temperatur,e in kelvin
Recall that:
[tex]\begin{gathered} moles=\frac{mass}{molar\text{ mass}} \\ n=\frac{m}{M} \end{gathered}[/tex]
Substitute into the ideal equation to have:
[tex]\begin{gathered} PV=\frac{m}{M}\cdot RT \\ PM=\frac{m}{V}\cdot RT \\ Since\text{ }\rho=\frac{m}{V},hence; \\ PM=\rho RT \end{gathered}[/tex]
The expression for calculating the molar mass will be:
[tex]M=\frac{\rho RT}{P}[/tex]
Given the following parameters
[tex]\begin{gathered} density\text{ }\rho=3.55gL^{-1} \\ R=\frac{0.08205Latm}{molK} \\ T=110^0C+273=383K \\ P=736torr=0.968atm \end{gathered}[/tex]
Substitute the given parameters into the formula
[tex]\begin{gathered} M=\frac{3.55\times0.08205\times383}{0.968} \\ M=\frac{111.559}{0.968} \\ M=115.25gmol^{-1} \end{gathered}[/tex]
Hence the molar mass of the gas will be approximately 115.25g/mol
