Thermochemistry Equations & Formulas - Lecture Review & Practice Problems

Thermochemistry Overview

  • Focus on thermochemistry and important equations relevant to the subject.

Internal Energy

  • Internal Energy Change Equation:

    [ \Delta E = Q + W ]

    • Q: Heat energy entering (+) or leaving (-) the system.

    • W: Work done on (+) or by (-) the system.

Example of Q

  • System at 100°C and surroundings at 50°C:

    • Heat flows from the system to surroundings.

    • Therefore, Q is negative for the system (exothermic) and positive for surroundings (endothermic).

    • Measurement Units:

      • 1 kJ = 1,000 J

      • 1 Cal = 4.184 J

      • 1 kcal = 1,000 Cal

Work (W)

  • Equation for Work:

    [ W = P \Delta V ]

  • Positive W occurs when work is done on the system and negative W when done by the system.

  • Expansion or Compression:

    • Expansion: Gas does work, leads to negative W.

    • Compression: Force applied to gas, leads to positive W.

Example Calculation

  • 300 J of heat absorbed (Q = +300), gas expands from 2 L to 3 L with P = 5 atm:

    [ \Delta V = 3 \text{L} - 2 \text{L} = 1 \text{L} ]

    • Convert pressure-volume work into Joules:

      [ W = P \Delta V = 5 \text{atm} \times 1 \text{L} = 5 \text{atm} \cdot \text{L} = 5 \times 101.3 \text{J} = 506.5 \text{J} ]

      • Thus, W = -506.5 J (work done by gas).

  • Calculate change in internal energy:

    [ \Delta E = Q + W = 300 - 506.5 = -206.5 \text{J} ]

    • Energy lost = -206.5 J.

Calculating Heat (Q)

  • Heat equation:

    [ Q = mC \Delta T ]

    • m: Mass (g), C: Specific heat capacity (J/g°C), ΔT: Change in temperature (°C).

  • Example: Heating 50 g of water from 25°C to 75°C:

    [ \Delta T = 75 - 25 = 50 \text{°C} ]

    • Calculate energy:

      [ Q = 50 \text{g} \times 4.184 \text{J/g°C} \times 50 °C = 10,460 ext{J} ]

Phase Changes

  • Heat absorbed or released during phase changes:

    [ Q = m \Delta H ] (where ΔH refers to heat of fusion/vaporization).

  • Example: Melting 54 g of ice at 0°C:

    • Molar mass of water = 18 g/mol, heat of fusion for water = 6 kJ/mol.

    • Convert grams into moles and then calculate kJ:

      [ \text{Moles of ice} = \frac{54\text{g}}{18\text{g/mol}} = 3 \text{mol} ]

      [ Q = 3 \text{mol} \times 6 \text{kJ/mol} = 18 \text{kJ} ]

Thermochemical Equations

  • Example: Combustion of propane:

    • Balanced reaction releases 12,200 kJ of heat.

    • Exothermic if heat is a product.

  • Question: How many kJ released by 64 g of O2?

    • Molar mass O2 = 32 g/mol.

    • Use mole ratio to find kJ per moles:

      • 12,200 kJ for every 5 moles of O2.

    • Calculate:

      [ ext{Moles of O2} = \frac{64}{32} = 2 \text{mol} ]

      [ \text{Heat} = \frac{2 \times 12,200}{5} = 4,880 \text{kJ} ]

Hess's Law

  • Used to find enthalpy from enthalpies of other reactions:

    • Sum of products – sum of reactants.

  • Example Reaction: 2 A + 2 B → D + E

    • Two additional reactions provided to find required reaction enthalpy.

  • Steps:

    • Adjust coefficients as needed and reverse reactions ensuring enthalpy sign changes accordingly.

    • Gather information, add, and simplify to find enthalpy of desired reaction.

Conclusion

  • Key equations and principles of thermochemistry important for mastering concepts in energy exchanges, work, and phase changes.