A research team is studying solid–liquid–gas equilibria of carbon dioxide near its…
CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures
Problem
A research team is studying solid–liquid–gas equilibria of carbon dioxide near its triple point. A sealed, rigid 250.0 mL vessel initially contains exactly 11.0 g of CO₂ at 56 atm and 216.6 K (just above the triple-point temperature). As the vessel is slowly warmed to 298 K, the CO₂ first becomes entirely liquid and then eventually exists entirely as a gas.
Molar mass of CO₂ = 44.01 g mol⁻¹.
(a) Calculate the initial molar volume of CO₂ in the vessel at 216.6 K and 56 atm, assuming the contents are an equilibrium mixture of solid and gas with negligible volume contribution from the solid. (Hint: Use the vessel volume.)
(b) The density of liquid CO₂ at 298 K and its vapor pressure (64 atm) is 0.619 g cm⁻³. Calculate the molar volume of liquid CO₂ under these conditions.
(c) When all of the CO₂ in the vessel reaches the gaseous state at 298 K and 64 atm, calculate its molar volume assuming ideal-gas behavior.
(d) Using your answers from parts (a)–(c), construct a qualitative argument that accounts for the observed sequence of phase changes (solid + gas → liquid → gas) as the temperature increases while the vessel volume remains fixed. Your argument should reference relative molar volumes and the effect of temperature on kinetic energy.
(e) Propose one modification to the experimental setup that would allow the researchers to observe solid and gas in equilibrium at 298 K. Justify how your modification affects molar volume relationships to enable the coexistence of those two phases.