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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 :

The estimated volume occupied by 18 kg of ethylene at 55℃ and 35 bar is approximately 476.6 liters. The mass of ethylene contained in a [tex]0.25m^3[/tex] cylinder at 50℃ and 115 bar is approximately 3.03 kg.

To estimate the volume occupied by 18 kg of ethylene at 55℃ and 35 bar, we can use the ideal gas law expressed as PV = nRT. First, we need to calculate the number of moles (n) using the molar mass of ethylene ([tex]C_2H_4[/tex]) which is approximately 28 g/mol. Therefore, n = 18000 g / 28 g/mol = 642.86 moles. The gas constant (R) is 0.08314 L*bar/mol*K. Converting the temperature to Kelvin, T = 55 + 273 = 328 K. Now, we can solve for V:

V = (nRT) / P = (642.86 mol * 0.08314 L*bar/mol*K * 328 K) / 35 bar = 476.6 L

To determine the mass of ethylene in a 0.25-[tex]m^3[/tex] cylinder at 50℃ and 115 bar, we apply the ideal gas law again. We first convert the volume to liters (V = 0.25 [tex]m^3[/tex] * 1000 L/[tex]m^3[/tex] = 250 L), and temperature to Kelvin (T = 50 + 273 = 323 K). The pressure is already in bar. Now, we calculate the number of moles, solving for n:

n = PV / RT = (115 bar * 250 L) / (0.08314 L*bar/mol*K * 323 K) = 108.14 moles

The mass of ethylene is then m = n * molar mass = 108.14 moles * 28 g/mol = 3027.92 g or approximately 3.03 kg of ethylene.

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