Explanation:
If you take the ideal gas law of PV = nRT and modify it to
P*molar mass = density*RT
(745/760)*M = 1.2*0.08206*293
Solve for M = molar mass.
Molar mass is the ratio of the mass of the and the moles of the substance. The molar mass of the gas at 20 degrees celsius is 29 g/mol.
The ideal gas equation is the relation of the pressure, temperature, volume, and moles of a compound. It can be used to know the molar mass of the substance.
The ideal gas equation is given as,
[tex]\rm PV = nRT[/tex]
Given,
Density (d) = 1.2 g/L
Pressure (P) = 0.980 atm
Tempertaure (T) = 293.15 K
Gas constant (R) = 0.08206
We know, that the volume is given as,
[tex]\rm V = \rm \dfrac{mass}{density} = \rm \dfrac{moles \times molar\; mass}{density}[/tex]
The molar mass of gas is calculated as:
[tex]\begin{aligned} \rm P \times (\dfrac{mole \times molar\; mass}{density} )&= \rm nRT\\\\\rm molar \; mass &= \rm \dfrac{dRT}{P}\\\\&= \dfrac{1.2 \times 0.08206\times 293.15}{0.980}\\\\&= 29.45\end{aligned}[/tex]
Therefore, 29 g/mol is the molar mass of the gas.
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