An experiment requires a gas mixture containing 20 % CO2, 0.5 % O2, and 79.5 % N2 at 1 atm and

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An experiment requires a gas mixture containing 20 % CO2,...

An experiment requires a gas mixture containing $20 \% \mathrm{CO}_2, 0.5 \% \mathrm{O}_2$, and $79.5 \% \mathrm{~N}_2$ at $1 \mathrm{~atm}$ and $20^{\circ} \mathrm{C}$. This gas mixture is purchased premixed and comes in a $10 \mathrm{~L}$ tank at a pressure of 130 atm gauge. The gas will be used to displace air from packages using a packaging machine that operates by drawing a vacuum completely inside a chamber where the packages are placed, displacing the vacuum with the gas mixture, and sealing the packages. The chamber can hold four packages at a time, and the total void volume chamber with the packages in place is 2500 $\mathrm{cm}^3$. How many packages can be treated in this manner before the pressure in the gas tank drops to $1 \mathrm{~atm}$ gauge.

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) provides a relationship between the pressure, volume, temperature, and number of moles of a gas. It is essential for determining how much gas is contained in a pressurized tank and for calculating the change in volume or pressure when the gas is used to displace air or perform other work.

Pressure Conversion (Gauge vs Absolute Pressure)

Understanding the difference between gauge pressure and absolute pressure is crucial. Gauge pressure is measured relative to ambient atmospheric pressure, whereas absolute pressure includes atmospheric pressure. This conversion is necessary when applying the Ideal Gas Law or other formulas that assume absolute pressures.

Compressed Gas Storage

Compressed gas storage deals with containing a gas in a pressurized vessel, where high pressure enables a large number of moles of gas to be stored in a relatively small volume. This concept is important for calculating the usable amount of gas and understanding how pressure decreases as gas is dispensed.

Volume and Pressure Relationships

The interdependency of gas volume and pressure, often described by Boyle’s Law when temperature remains constant, is key to understanding how gas will expand or contract when moving between different containers or operating under different pressures. This relationship helps in determining how many cycles or packages can be processed from a given amount of stored gas.

Vacuum Displacement in Packaging

Vacuum displacement involves removing air from a sealed chamber by first creating a vacuum and then introducing a specific gas mixture. It is important to understand how much gas is required to replace the void volume and how this relates to the initial pressurized gas supply, ensuring efficient operation in packaging processes.

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