A 19.2 -g quantity of dry ice (solid carbon dioxide) is...

A $19.2 -\mathrm{g}$ quantity of dry ice (solid carbon dioxide) is allowed to sublime (evaporate) in an apparatus like the one shown in Figure $6.5 .$ Calculate the expansion work done against a constant external pressure of $0.995 atm$ and at a constant temperature of $22^{\circ} \mathrm{C}$. Assume that the initial volume of dry ice is negligible and that $\mathrm{CO}_{2}$ behaves like an ideal gas.

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relation in thermodynamics that connects the pressure, volume, temperature, and number of moles of a gas. It is used to calculate the volume that a given amount of gas will occupy at a specified temperature and pressure, assuming the gas behaves ideally, which is a useful approximation under many conditions.

Expansion Work in Thermodynamics

Expansion work is the work done by a system when it expands against an external pressure. In thermodynamics, when a gas expands at constant external pressure, the work done is calculated by multiplying the pressure by the change in volume (w = -P?V). This concept is crucial for understanding energy changes during processes involving gas expansion or compression.

Mole Calculation from Mass

Converting a given mass of a substance into moles is an essential step in many thermodynamic calculations. It involves dividing the mass by the molar mass of the substance. This conversion allows for the use of the ideal gas law and other equations that require the number of moles rather than mass.

Phase Transition and Sublimation

A phase transition is the process where a substance changes from one state of matter to another. Sublimation is a specific type of phase transition where a substance transitions directly from the solid state to the gas state without passing through the liquid phase. In thermodynamic calculations involving sublimation, often the initial volume of the solid can be neglected compared to the gas phase volume.

Temperature Conversion in Thermodynamics

Temperature conversion, especially converting from degrees Celsius to Kelvin, is essential in thermodynamics since the Kelvin scale is the SI unit for temperature used in all gas law calculations. Ensuring that temperatures are in Kelvin guarantees consistency and accuracy when applying equations like the ideal gas law.

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