Determine the molar mass of a compound that has a density of 0.1633 g/L at STP.
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                     M.Mass  =  3.66 g/mol

Data Given:

                  M.Mass  =  M = ??

                  Density  =  d  =  0.1633 g/L

                  Temperature  =  T  =  273.15 K (Standard)

                  Pressure  =  P  =  1 atm (standard)

Solution:

              Let us suppose that the gas is an ideal gas. Therefore, we will apply Ideal Gas equation i.e.

                                             P V = n R T     (1)

Also, we know that;

                       Moles  =  n  =  mass / M.Mass

Or,                                   n  =  m / M

Substituting n in Eq. 1.

                                             P V = m/M R T   --- (2)

Rearranging Eq.2 i.e.

                                             P M = m/V R T   --- (3)

As,

                     Mass / Volume = m/V = Density = d

So, Eq. 3 can be written as,

                                             P M = d R T

Solving for M.Mass i.e.

                                             M = d R T / P

Putting values,

M  =  0.1633 g/L × 0.08205 L.atm.K⁻¹.mol⁻¹ × 273.15 K / 1 atm

M  =  3.66 g/mol

in the analysis of systems that involve fluid flow, we frequently encounter the combination of properties u and pv.