calculate mass of oxygen

Question

A cylinder has a volume of 0,075 m³ and is filled with oxygen at a pressure of 380 kPa at a temperature of 50 °C. Later it is found that the pressure has dropped to 280 kPa and the temperature has decreased to 25 °C, due to a leakage. Calculate The mass of oxygen originally in the cylinder if the gas constant is 265 J/kgK. Calculate The mass of oxygen that leaked if the volume of the cylinder remains constant

Answer 1

Volume of the tank,V = 0.075 mm³

Initial pressure,P₁=380 kPa =380000 Pa

Initial temperature,T₁ =50°C =323 K

Gas constant,R =  265 J/kgK.

Calculate the  mass by using the ideal gas equation.

P₁V₁ =m₁RT₁

(380000)(0.075)= m₁(265)(323)

m₁ =0.333 kg

Therefore, the original mass of oxygen is 0.333 kg

Answer 2

After that the oxygen was leaked:

Final pressure,P₂ =280 kPa =280000 Pa

Final temperature,T₂ =25°C =298 K

Calculate the leaked mass by using the ideal gas equation.

P₂V₂ =m₂ RT₂

(280000)(0.075)=m₂ (265)(298)

m₂ =0.266 kg

Calculate leaked mass of the oxygen.

mleak = m1-m2 =0.333-0.266 =0.0267 kg

Therefore, the leaked mass of the oxygen is 0.0267 kg