Question

Estimate the following: a) The volume occupied by 18 kg of ethylene at 55°C and 35 bar. b) The mass of ethylene contained in a 0.25-m3 cylinder at 50°C and 115 bar.

Answer 1

Explanation:

(a)   The given data is as follows.

             T = $55^{o}C$ = (55 + 273) K

                = 328 K

             P = 35 bar = 3500 kPa

Let us assume that moles of ethylene present are 1 kmol and according to the ideal gas equation, PV = nRT.

Or,            V = $\frac{nRT}{P}$

                    = $\frac{1 \times 8.314 \times 328}{3500 kPa}$

                   = 0.779 $m^{3}$

Hence, the volume occupied by 18 kg of ethylene at $55^{o}C$ and 35 bar is 0.779 $m^{3}$.

(b)   The given data is as follows.

              V = 0.25 $m^{3}$

               T = $50^{o}C$ = (50 + 273) K

                  = 323 K

                P = 115 bar = 11500 kPa

Using ideal gas equation first, we will calculate its moles as follows.

            n = $\frac{PV}{RT}$

               = $\frac{11500 \times 0.25}{8.314 \times 323 K}$

               = 1.07 mol

Since,  moles = $\frac{mass}{\text{molar mass}}$

Hence, mass of ethylene will be calculated as follows.

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

             1.07 mol = $\frac{mass}{28 g/mol}$

                   mass = 29.96 g

Therefore, mass of given ethylene is 29.96 g.