A tank having a volume of 0.10m' is filled with oxygen at a pressure of 4.0 x 10'Pa and temperature of 47C. Later it is found that, because of a leak, the pressure has dropped to 3.0 x 10'Pa and the temperature has decreased to 27C. Find. (a) the initial mass of oxygen and (b) the mass that has leaked out.

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22-11-2021
Physics

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A tank having a volume of 0.10m' is filled with oxygen at a pressure of 4.0 x 10'Pa and temperature of 47C. Later it is found that, because of a leak, the pressure has dropped to 3.0 x 10'Pa and the temperature has decreased to 27C. Find. (a) the initial mass of oxygen and (b) the mass that has leaked out.

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Eduard22sly Eduard22sly · Answer 1 · 2021-11-25T12:55:37+01:00

A. The initial mass of oxygen in the tank is 480.96 g

B. The mass of oxygen that leaked out is 384.96 g

A. Determination of the initial mass of oxygen in the tank.

We'll begin by calculating the initial number of mole of oxygen in the tank

Volume (V) = 0.1 m³

Pressure (P) = 4×10⁵ Pa

Temperature (T) = 47 °C = 47 + 273 = 320 K

Gas constant (R) = 8.314 Pa.m³/Kmol

number of mole (n) = ?

PV = nRT

0.1 × 4×10⁵ = n × 8.314 × 320

40000 = n × 2660.48

Divide both side by 2660.48

n = 40000 / 2660.48

n = 15.03 moles

Finally, we shall determine the initial mass of oxygen.

mole = 15.03 moles

molar mass of oxygen gas = 32 g/mol

mass of oxygen gas = ?

Mass = mole × molar mass

Mass of oxygen gas = 15.03 × 32

Mass of oxygen gas = 480.96 g

Therefore, the initial mass of oxygen in the tank is 480.96 g

B. Determination of the mass of oxygen that leaked out of the tank.

We'll begin by calculating the number of mole of oxygen that leaked out of the tank

Volume (V) = 0.1 m³

Pressure (P) = 3×10⁵ Pa

Temperature (T) = 27 °C = 27 + 273 = 300 K

Gas constant (R) = 8.314 Pa.m³/Kmol

number of mole (n) = ?

PV = nRT

0.1 × 3×10⁵ = n × 8.314 × 300

30000 = n × 2494.2

Divide both side by 2494.2

n = 30000 / 2660.48

n = 12.03 moles

Finally, we shall determine the mass of oxygen that leaked out of tank.

mole = 12.03 moles

molar mass of oxygen gas = 32 g/mol

mass of oxygen gas = ?

Mass = mole × molar mass

Mass of oxygen gas = 12.03 × 32

Mass of oxygen gas = 384.96 g

Therefore, the mass of oxygen that leaked out of tank is 384.96 g

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