CHM110: Phases and Phase Changes

Introduction to Phase Diagrams

• Overview of phase diagrams and their significance in understanding material states.

• Distinction made between water and other solutions regarding phase diagrams. Each solution has a unique phase diagram.

Basic Components of Phase Diagrams

• Phases of Matter: The diagrams illustrate the interactions among the three primary phases of a substance: solid, liquid, and gas.

• Phase Equilibria: The lines on a phase diagram, known as phase equilibria, represent conditions where two phases can coexist.

  • Example: A solid and gas can exist simultaneously along a line in the phase diagram.

Phase Transitions

• Sublimation: The transition from solid to gas without passing through the liquid phase.

• Deposition: The transition from gas directly to solid.

• Vaporization: The transition from liquid to gas.

• Condensation: The transition from gas back to liquid.

• Critical Point: A specific condition where above a certain temperature and pressure, the substance exists as a supercritical fluid, exhibiting properties distinct from gases and liquids.

  • The unique characteristics of supercritical fluids include:

  • Diffusion-like behavior.

  • Ability to dissolve nonpolar compounds.

Specifics of Water's Phase Diagram

• Freezing Point: At 0 degrees Celsius and 760 mmHg (1 atm), water transitions to ice.

  • At this point, ice does not immediately begin melting, and liquid water does not begin to freeze until temperature changes occur.

• Normal Boiling Point: The boiling point at standard atmospheric pressure where liquid and gaseous water exist simultaneously.

  • Important note: Both liquid water (at boiling point) cannot condense and gaseous water cannot revert to liquid at this specific pressure.

• Triple Point: Points at which solid, liquid, and gas phases coexist. Essential for understanding phase stability in thermodynamics.

• Measurement Units: Mention that water's boiling and freezing points are indicated in mmHg instead of atm in this context.

  • Clarification: 1 mmHg = 1 Tor, hence the appearance of values may differ from standard atmospheric measurements.

Clausius-Clapeyron Equation

• Used for calculating vapor pressure at different temperatures.

• This equation has the model: $\ln\left(\frac{P<em>2}{P</em>1}\right) = -\frac{\Delta H<em>{vap}}{R} \left(\frac{1}{T</em>2} - \frac{1}{T_1}\right)$

  • Where:

  • $P_1$ = Initial pressure

  • $P_2$ = Final pressure

  • $\Delta H_{vap}$ = Enthalpy of vaporization

  • R = Ideal gas constant (8.314 J/(mol·K))

  • $T_1$ = Initial temperature

  • $T_2$ = Final temperature

Practical Example: Boiling Point of Water at Different Pressures

• Scenario: Determining boiling point of water at 2 atm.

• Given data:

  • The enthalpy of vaporization ($\Delta H_{vap}$) of water = 40,770 J/mol.

  • Water's boiling point at 1 atm = 100 degrees Celsius (373 Kelvin).

• Calculation Steps:

  1. Input values into the Clausius-Clapeyron equation and solve for $T_2$:

  • Set up:
    $\ln\left(\frac{2 atm}{1 atm}\right) = -\frac{40,770}{8.314} \left(\frac{1}{T_2} - \frac{1}{373 K}\right)$

  1. Solve the equation step by step, computing the natural log and rearranging to isolate $T_2$.

  2. Achieve result:

  • Final boiling point of water at 2 atm = 354.35 K (units must be indicated).

Significant Figures and Rounding in Calculations

• Emphasis on maintaining significant figures for accuracy in calculations.

  • Instruction: Keep all decimal places provided by the calculator. The choice of significant figures can significantly affect outcomes.

• R value to be used in calculations should be the full figure of $R = 8.314 J/(mol·K)$ without any abbreviation.