An oxygen cylinder of volume 30 Hire has an initial gauge pressure of 15 atmosphere and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atmosphere and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder. (R = 8.31 J mol-1 K-1, molecular mass of O2 = 32 u.)

Asked by Sagar 15/12/2021 Last Modified 14/04/2024

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An oxygen cylinder of volume 30 Hire has an initial gauge pressure of 15 atmosphere and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atmosphere and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder. (R = 8.31 J mol-1 K-1, molecular mass of O2 = 32 u.)

Asked by Sagar 15/12/2021 Last Modified 14/04/2024

1 Answer

Learn Unit 9-Kinetic Theory of Gases

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Answer

Nazia Khanum · Accepted Answer

As a seasoned tutor registered on UrbanPro, I can assure you that UrbanPro is one of the best platforms for finding online coaching tuition. Now, let's delve into the problem at hand.
To estimate the mass of oxygen taken out of the cylinder, we can utilize the ideal gas law equation:
PV=nRTPV=nRT
Where:

PP is the pressure,
VV is the volume,
nn is the number of moles of gas,
RR is the ideal gas constant, and
TT is the temperature in Kelvin.

We are given the initial conditions and the conditions after some oxygen is withdrawn. Let's denote the initial state with subscript ii and the final state with subscript ff.
For the initial state:

Pi=15Pi=15 atm
Ti=27+273=300Ti=27+273=300 K (converting Celsius to Kelvin)

For the final state:

Pf=11Pf=11 atm
Tf=17+273=290Tf=17+273=290 K

We also know the volume VV is constant, so it cancels out in the calculation. Thus, the ideal gas equation simplifies to:
PiTi=PfTfTiPi=TfPf
Let's use this equation to find the number of moles of oxygen initially and finally.
For the initial state: 15&thinsp;atm300&thinsp;K=ni&times;R32&thinsp;g/mol300K15atm=32g/molni&times;R
For the final state: 11&thinsp;atm290&thinsp;K=nf&times;R32&thinsp;g/mol290K11atm=32g/molnf&times;R
Solving these equations will give us the number of moles of oxygen initially (nini) and finally (nfnf). The mass of oxygen taken out of the cylinder can then be calculated by finding the difference between the initial and final number of moles and multiplying it by the molecular mass of oxygen (32&thinsp;g/mol32g/mol).
Let's proceed with the calculations.

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