Phase Diagrams and Vapor Pressure Flashcards

Phase Diagram

• Phase Diagram: A graphical representation of the physical states of a substance under different conditions of temperature and pressure.
• Water Phase Diagram (Not to Scale):
  • Illustrates the conditions under which water exists as a solid (ice), liquid (water), or gas (water vapor).
  • Key points:
    • Triple Point (Ttp): The temperature and pressure at which solid, liquid, and gas phases coexist in equilibrium. For water, Ttp is approximately $0.001 \degree C$ and $P_{tp}$ is $0.006 atm$.
    • Critical Point: The temperature and pressure beyond which distinct liquid and gas phases do not exist; instead, a supercritical fluid forms. For water, the critical temperature ($T_{cr}$) is $374 \degree C$.
    • Normal Melting Point: The temperature at which solid transforms to liquid at 1 atm pressure.
    • Normal Boiling Point: The temperature at which liquid transforms to gas at 1 atm pressure (for water, $100 \degree C$).
• Phase Transition Lines:
  • Fusion Curve: Shows the equilibrium between solid and liquid phases.
    • Negative slope indicates that ice is less dense than water.
  • Vaporization Curve: Shows the equilibrium between liquid and gas phases.
  • Sublimation Curve: Shows the equilibrium between solid and gas phases.
• Properties Related to Phase Changes:
  • Melting/Freezing: Transition between solid and liquid phases.
  • Vaporization/Condensation: Transition between liquid and gas phases.
  • Sublimation/Deposition: Transition between solid and gas phases.
• Equilibrium:
  • At the triple point, solid (s), liquid (l), and gas (g) phases are in equilibrium.
  • The gas phase is less dense than solid/liquid phases when the fusion curve has a positive slope.

Vapor Pressure

• Dynamic Equilibrium:
  • Involves the rate of evaporation and the rate of condensation.
  • At equilibrium, these rates are equal.
• Vapor Pressure (P):
  • The pressure exerted by a vapor in equilibrium with its liquid (or solid) phase.
  • Represents a dynamic process where molecules are constantly evaporating and condensing.
• Intermolecular Forces (IMFs):
  • Must be overcome for a substance to transition into the gas phase.
  • Stronger IMFs result in a lower vapor pressure because molecules are less likely to enter the gas phase.
• Vacuum Pump:
  • Can be used to remove gas molecules, disrupting the equilibrium and promoting further evaporation of a liquid.
• Le Chatelier's Principle:
  • Removing gaseous molecules shifts the equilibrium toward the gas phase to re-establish equilibrium.

Barometer and Vapor Pressure Measurement

• Barometer:
  • Used to determine vapor pressure by measuring the height of a mercury (Hg) column.
  • The vapor pressure of a substance contributes to the overall pressure, affecting the height of the Hg column.
• Examples:
  • Water Vapor: At a certain temperature, the vapor pressure of water is 24 torr.
  • Ethanol Vapor: Ethanol ($C<em>2H</em>5OH$) has a vapor pressure of 65 torr.
  • Diethyl Ether Vapor: Diethyl ether ($(C<em>2H</em>5)_2O$) has a vapor pressure of 545 torr.
• Boiling Point (BP):
  • The temperature at which the vapor pressure of a liquid equals the surrounding atmospheric pressure.
  • Examples:
    • Diethyl Ether: BP = $34.6 \degree C$
    • Ethanol: BP = $78.37 \degree C$
    • Water: BP = $100 \degree C$

Vapor Pressure Comparison

• Experimental Setup:
  • Using a barometer-like setup with different liquids (A and B) to compare their vapor pressures.
  • The height of the Hg column is affected by the vapor pressure of the liquid.
• Equations:
  • $P<em>{atm} = h</em>2 + P_A$ (for liquid A)
  • $P<em>{atm} = h</em>3 + P_B$ (for liquid B)
  • $P<em>A = P</em>{atm} - h_2$
  • $P<em>B = P</em>{atm} - h_3$
• Conclusion:
  • If $h<em>2 < h</em>3$, then $P<em>A > P</em>B$, indicating that liquid A has a higher vapor pressure than liquid B.
  • A liquid with a higher vapor pressure has a lower boiling point.
• Explanation:
  • Liquids with fewer IMFs require less energy to overcome these forces and transition into the gas phase, resulting in higher vapor pressures and lower boiling points.

Vapor Pressure vs. Temperature Plots

• General Trend:
  • Vapor pressure increases with temperature for most liquids.
• Normal Boiling Point:
  • The temperature at which the vapor pressure equals 1 atm.
• Comparative Analysis:
  • Liquids with higher normal boiling points generally have stronger IMFs.
  • Liquids with lower normal boiling points have higher vapor pressures at a given temperature.
• Examples of Substances and Their Vapor Pressure Trends:
  • Diethyl Ether
  • Bromine
  • Ethanol
  • Water
  • n-Octane
  • Ethylene Glycol
  • Mercury

Clausius-Clapeyron Equation

• Equation:
  • Relates vapor pressure to temperature and enthalpy of vaporization.
  • $\ln\left(\frac{P<em>2}{P</em>1}\right) = \frac{\Delta H<em>{vap}}{R} \left(\frac{1}{T</em>1} - \frac{1}{T_2}\right)$
    • $P<em>1$ and $P</em>2$ are vapor pressures at temperatures $T<em>1$ and $T</em>2$, respectively.
    • $\Delta H_{vap}$ is the enthalpy of vaporization.
    • R is the ideal gas constant ($8.314 J/mol \cdot K$).
• Units:
  • $\Delta H_{vap}$ is typically given in KJ/mol (convert to J/mol for calculations).
  • Pressure can be in atm.
• Example Calculation:
  • Given: The vapor pressure of $H<em>2O$ is 1.0 atm at 373 K, and $\Delta H</em>{vap}$ is $40.7 KJ/mol$.
  • Estimate the vapor pressure at 363 K.
  • Calculation:
    • $\ln\left(\frac{1.0 atm}{P_2}\right) = \frac{40700 J/mol}{8.314 J/mol \cdot K} \left(\frac{1}{363 K} - \frac{1}{373 K}\right)$
    • $\ln\left(\frac{1.0 atm}{P_2}\right) \approx 0.3616$
    • $\frac{1.0 atm}{P_2} = e^{0.3616} \approx 1.436$
    • $P_2 \approx \frac{1.0 atm}{1.436} \approx 0.69659 atm \approx 0.70 atm$