A package having a void volume of 1500 cm^3 is to be flushed with nitrogen to displace oxygen p

step 1 Good day. In this question, we will be solving for the gauge pressure in kilo -pascal of the gas

A package having a void volume of 1500 cm^3 is to be...

A package having a void volume of $1500 \mathrm{~cm}^3$ is to be flushed with nitrogen to displace oxygen prior to sealing. The process used involved drawing a vacuum of $700 \mathrm{~mm} \mathrm{Hg}$ on the package, breaking the vacuum with nitrogen gas, and drawing another $700 \mathrm{~mm} \mathrm{Hg}$ vacuum before sealing. The solids in the package prevents total collapse of the package as the vacuum is drawn, therefore the volume of gases in the package may be assumed to remain constant during the process. If the temperature is maintained constant at $25^{\circ} \mathrm{C}$ during the process, calculate the number of gmoles of oxygen left in the package at the completion of the process. Atmospheric pressure is $760 \mathrm{~mm} \mathrm{Hg}$.

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Key Concepts

Partial Pressure

Partial pressure is the pressure that a single gas in a mixture would exert if it alone occupied the entire volume. It is directly proportional to the mole fraction of the gas in the mixture. In the context of flushing an oxygen?containing package with nitrogen, the remaining oxygen’s partial pressure is a key factor in determining how many moles of oxygen remain.

Successive Dilution (Sequential Replacement)

Successive dilution via repeated evacuation and replacement is a process where a gas mixture is progressively diluted by repeatedly removing a portion of the existing mixture and replacing it with another gas. Each evacuation step removes a fixed fraction of the gases present. When combined with a nitrogen flush, this process gradually reduces the quantity of oxygen, and the cumulative effect can be calculated using ratios of the pressures before and after each step.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relationship in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas. In problems like this, it is used to determine the number of moles of gas originally present or which remain after changes in pressure while the volume and temperature are constant.

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