Study Notes on Heating Curves and Phase Diagrams

Learning Objectives

  • Describe heating and cooling curves, compute heat flows, and enthalpy changes.

  • Explain construction and use of phase diagrams.

  • Use phase diagrams to identify stable phases and describe phase transitions.

Heating Curve of Water

Segment 1: Adding Heat to Ice

  • Heating 1.00 mole of ice at -25.0 °C to 0.0 °C.

  • Heat Calculation: q=massimesCsimesΔTq = mass imes Cs imes \Delta T where:

    • mass = 18.0 g

    • Cs,ice=2.09 J/g⋅°CCs, ice = 2.09 \, J/g \cdot °C

Segment 2: Melting the Solid

  • Melting 1.00 mole of ice at 0.0 °C (T constant).

  • Heat Needed: q=nimesΔHfusq = n imes \Delta H_{fus} where:

    • n=1.00 molen = 1.00 \, mole

    • ΔHfus=6.02 kJ/mol\Delta H_{fus} = 6.02 \, kJ/mol

Segment 3: Heating the Liquid

  • Heating 1.00 mole of water from 0.0 °C to 100.0 °C.

  • Heat Calculation: q=massimesCsimesΔTq = mass imes Cs imes \Delta T where:

    • Cs,water=4.18 J/g⋅°CCs, water = 4.18 \, J/g \cdot °C

Segment 4: Vaporizing the Liquid

  • Boiling 1.00 mole of water at 100.0 °C (T constant).

  • Heat Needed: q=nimesΔHvapq = n imes \Delta H_{vap} where:

    • ΔHvap=40.7 kJ/mol\Delta H_{vap} = 40.7 \, kJ/mol

Segment 5: Heating the Vapour Phase

  • Heating 1.00 mole of steam from 100.0 °C to 125.0 °C.

  • Heat Calculation: q=massimesCsimesΔTq = mass imes Cs imes \Delta T where:

    • Cs,steam=2.01 J/g⋅°CCs, steam = 2.01 \, J/g \cdot °C

Worked Example

  • Calculate heat required to warm 10.0 g of ice at -10.0 °C to steam at 110.0 °C.

  • Total heat required: 30.5 kJ.

Phase Diagrams

  • Phase diagrams illustrate states and changes at various temperatures and pressures.

  • X-axis: Temperature; Y-axis: Pressure.

Regions

  • Each phase represented by a region reflecting stable states.

    • Low T, high P: Solid state.

    • High T, low P: Gas state.

    • Liquid state: Between gas and solid.

Lines

  • Fusion curve: transition between liquid and solid.

  • Vaporization curve: transition between gas and liquid.

  • Sublimation curve: transition between gas and solid.

Important Points

  • Triple Point: All three states at equilibrium.

  • Critical Point: Above this, substance acts as a supercritical fluid.

Extracting Information

  • Normal melting and boiling points found at 1 atm.

  • Vertical lines indicate relative density; horizontal lines indicate relative energy.

Special Case - Water

  • Ice floats because it is less dense than liquid water.