A person has 15 g of dry ice and wants to completely fill a...

A person has 15 $\mathrm{g}$ of dry ice and wants to completely fill a bag that has a volume of 8 L with carbon dioxide gas. Is this enough dry ice to fill the bag with $\mathrm{CO}_{2}(g) ?$ Explain.

Key Concepts

Ideal Gas Law

The ideal gas law, represented by PV = nRT, relates the pressure (P), volume (V), number of moles (n), the gas constant (R), and temperature (T) for an ideal gas. It is fundamental for determining how much gas will occupy a specific volume at given conditions, which is essential when calculating whether a certain mass of a substance (like dry ice) will produce enough gas to fill a container.

Sublimation

Sublimation is the process by which a substance transitions directly from the solid phase to the gas phase without passing through an intermediate liquid phase. This is critical for dry ice (solid CO2), as understanding sublimation helps one determine how much gaseous carbon dioxide will be generated from a given mass of dry ice under appropriate conditions.

Molar Volume

Molar volume is the volume occupied by one mole of a gas at a specific temperature and pressure, commonly approximated as 22.4 liters per mole at standard temperature and pressure (STP). This concept is important for calculating how many moles (and thus what volume) of gas are produced from a given amount of dry ice once it undergoes sublimation.

Mass-to-Moles Conversion

Converting the mass of a substance to moles by using its molar mass is a fundamental step in applying the ideal gas law. For dry ice (CO2), knowing its molar mass allows one to determine the number of moles available for gas production, which is necessary to compute the volume the gas will occupy after sublimation.

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