Lecture 12 (5.4-5.5) Annotated

Chapter 5: Enthalpy and Calorimetry

Lecture Date

• Thursday, February 13

Learning Goals for Today’s Lecture

• 5.2.3: Distinguish quantities that are state functions from those that are not.

• 5.4.1: Interpret the enthalpy of reaction, ΔH, using the enthalpies of the products and reactants.

• 5.4.2: Determine how ΔH changes when the equation for a balanced reaction is multiplied by the same number, or when the reaction is reversed.

• 5.5.1: Interpret heat capacity and specific heat as measures of the heat needed to change the temperature of a substance.

• 5.5.2: Use the relationships among Cs, q, m, and ΔT to calculate one of the values given the other three.

• 5.5.3: Describe how a constant-pressure calorimeter works and analyze the results of constant-pressure calorimetry to determine heats of reactions.

State vs Path

• State Function:

  • Only the values of the initial and final states matter.

  • The steps between or the path followed does not change the value of the function.

• Path Function:

  • The path between initial and final states changes the value of the function.

• Example: Change in elevation is a state function, while distance walked is a path function.

Sample Exercise 5.4: Relating ΔH to Quantities of Reactants and Products

• Thermal Energy Released:

  • When 4.50 g of methane gas is burned in a constant-pressure system.

  • ΔH_rxn = −890 kJ/mol CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l)

  • For 4.50 g CH4:

    • Molar mass of CH4 ≈ 16 g/mol

    • Energy released:

      • ΔH = -890 kJ/mol × (4.50 g / 16 g/mol) = -250 kJ

Sample Exercise 5.4: Continued

• Hydrogen Peroxide Reaction:

  • 2.50 g of aluminum reacts at constant pressure:

  • 2 Al(s) + Fe2O3(s) → 2 Fe(s) + Al2O3(s)

  • ΔH = −851.5 kJ

5.5 Calorimetry

• Calorimetry: Measurement of heat flow to determine ΔH.

• Calorimeter: Instrument to measure heat flow.

• Formula: SH = q

Heat Capacity and Specific Heat

• Heat Capacity: Energy required to raise temperature of a substance by 1 K (1°C).

• Specific Heat (Cs): Heat capacity for 1 gram of substance.

• Molar Heat Capacity: Heat capacity for 1 mole of substance.

• Data Table:

  • Specific heats for common substances at 298 K:

    • N2(g): 1.04 J/g·K

    • H2O(l): 4.18 J/g·K

    • Al(g): 0.90 J/g·K

    • Fe(s): 0.45 J/g·K

    • CH4(g): 2.20 J/g·K

    • CaCO3(s): 0.82 J/g·K

Constant-Pressure Calorimetry

• Reactions in aqueous solution allow measuring heat change for water in the calorimeter.

• Specific Heat of Water: 4.184 J/g·K (used for dilute solutions).

• Heat Change Calculation:

  • q = m × Cs × ΔT

  • This formula is essential for determining ΔH.

Sample Exercise 5.5: Relating Heat, Temperature Change, and Heat Capacity

• Heating Water:

  • Calculate heat needed to warm 250 g of water from 22°C to 97°C:

    • q = (250 g) × (4.184 J/g·K) × (97°C - 22°C)

    • q = 78 kJ

• Molar Heat Capacity of Water:

  • Use specific heat value in calculations.

Sample Exercise 5.5: Continued

• Rocks for Heat Storage:

  • Calculate heat absorbed by 50.0 kg of rocks with specific heat of 0.82 J/g·K and a temperature increase of 12.0°C.

Sample Exercise 5.6: Measuring ΔH Using a Coffee-Cup Calorimeter

• HCl and NaOH Reaction:

  • Mixing amounts of HCl and NaOH increases temperature from 21.0 to 27.5°C.

  • Calculate ΔH per mole of HCl:

    • Total volume = 0.10 L, density = 1.0 g/mL, specific heat = 4.18 J/g·K.

Sample Exercise 5.6: Continued

• HCl and AgNO3 Reaction:

  • Mixing amounts increases temperature from 22.30 to 23.11°C.

Bomb Calorimetry (Constant Volume) 1/2

• Reactions in a sealed bomb calorimeter yield heat absorbed or released as an approximation of the enthalpy change for the reaction.

• Formula: q_rxn,cal = −C × ΔT.

Bomb Calorimetry (Constant Volume) 2/2

• Bomb calorimeter’s constant volume measures change in internal energy, ΔE, not ΔH.

• Difference is typically small for most reactions, allowing for equating ΔE with ΔH.