Question

A tank with volume of 2.4 cu ft is filled with Methane to a pressure of 1500 psia at 104 degrees F. Determine the molecular weight and specific gravity of the gas and the pound mols, pounds, and density of gas in the tank.

Answer 1

Explanation:

It is known that equation for ideal gas is as follows.

               PV = nRT

The given data is as follows.

     Pressure, P = 1500 psia,     Temperature, T = $104^{o}F$ = 104 + 460 = 564 R

     Volume, V = 2.4 cubic ft,      R = 10.73 $psia ft^{3}/lb mol R$

Also, we know that number of moles is equal to mass divided by molar mass of the gas.

                n = $\frac{mass}{\text{molar mass}}$

            m = $n \times W$

                = $0.594 \times 16.04$

                = 9.54 lb

Hence, molecular weight of the gas is 9.54 lb.

• We will calculate the density as follows.

                d = $\frac{PM}{RT}$

                    = $\frac{1500 \times 16.04}{10.73 \times 564}$

                    = 3.975 $lb/ft^{3}$

• Now, calculate the specific gravity of the gas as follows.

  Specific gravity relative to air = $\frac{\text{density of methane}}{\text{density of air}}$

                         = $\frac{3.975 lb/ft^{3}}{0.0765 lb/ft^{3}}$

                         = 51.96