Thermal Properties of Matter

Question

A welder using a tank of volume 0.075m ^ 3 fills it with oxygen (molar mass 32g / mol ) at a gauge pressure of 3.00 x 10 ^ 5 Pa and temperature of 37.0°C. The tank has a small leak, and in time some of the oxygen leaks out. On a day when the temperature is 22.0°C, the gauge pressure of the oxygen in the tank is 1.8 x 10 ^ 5 Pa. Find (a) the initial mass of oxygen and (b) the mass of oxygen that has leaked out.

Answer 1

The original moles of oxygen can be obtained from the ideal gas law n = PV/RT with P = 4.013x10⁵ (P_guage + P_atm = P_abs) T = 310 K and R = 8.314 m³ •Pa/mole•K

m = (32 g/mole)n

The final moles of gas are obtained by the same equation, but with P = 2.813x10⁵, T = 295 K

The amount of O₂ leaked is the difference between the two masses.

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