Thermodynamics: Internal Energy and Heat

• Thermodynamics studies the interconversion of heat and other forms of energy.
• The first law of thermodynamics is based on the law of conservation of energy.
• Energy can be converted, but not created or destroyed.
• The change in internal energy (∆U) equals the net heat transferred (Q) plus the net work done (W): ∆U = W + Q.

Internal Energy and Heat

• Positive heat (Q) adds energy to the system.
• Positive work (W) adds energy to the system.
• Internal energy can be increased by heating a system or doing work on it.
• The change in internal energy (∆U) depends on the sum of heat and work (Q + W).
• Altering the path from initial to final state impacts Q and W values, while ∆U remains consistent.

Work

• Work (W) is defined as force (F) multiplied by distance (d): W = F * d.
• Work can manifest as mechanical, electrical, or surface work.
• Mechanical work includes the compression and expansion of a gas, defined as W = -P(∆V).
• ∆V is the change in volume (Vf – Vi), and P is the external atmospheric pressure.

Example Calculation of Work

• Gas expands from 2.0L to 6.0L at constant temperature:
• Against a vacuum, no work is done because external pressure is zero.
• Against 1.2 atm, W = - 4.8 atm*L, which converts to -4.9 x 10^2 J.
• Gas expansion indicates work done by the system, hence the negative sign.

Heat (Q)

• Heat is a component of internal energy.
• Example: 4184 J is required to raise 100g of water from 20°C to 30°C.
• Heat can be gained directly, by doing work, or a combination of both.

Enthalpy and Hess's Law

• Enthalpy and Hess's Law build upon the first law of thermodynamics.
• Enthalpy allows calculation of enthalpy changes in reactions using Hess's Law.

What is Enthalpy (H)?

• It's a thermodynamic property: H = U + PV.
• H (Enthalpy) has energy units like joule, calorie, or BTU.
• Change in enthalpy (∆H) is calculated, as total enthalpy cannot be measured.
• Change is measured under constant pressure conditions

Enthalpy of Reaction (∆Hrxn)

• For reaction: reactants -> products.
• ∆Hrxn = H(Products) – H(Reactants).
• ∆H can be positive (endothermic, heat absorbed) or negative (exothermic, heat released).

Hess's Law

• Enthalpy change in a chemical reaction is independent of the pathway.
• If reactants A convert to products B, ∆H remains the same.

Example Problem: Finding Enthalpy Change

• CS2(l) + 3 O2(g) → CO2(g) + 2 SO2(g).
• Given:
  • C(s) + O2(g) → CO2(g); ΔHf = -393.5 kJ/mol
  • S(s) + O2(g) → SO2(g); ΔHf = -296.8 kJ/mol
  • C(s) + 2 S(s) → CS2(l); ΔHf = 87.9 kJ/mol
• Strategy:
  • Use reactions with one mole reactant/product.
  • Adjust reactions to match target equation.
  • Reverse reactions as needed, changing the sign of ΔHf.
  • Add reactions and their ΔHf values.
• Solution: ΔHf = -1075 kJ/mol.

Summaries and Colligative Properties

• Colligative properties depend on the number of solute particles.
• Colligative properties include freezing point depression and boiling point elevation.

Boiling Point Elevation (∆Tb)

• ∆Tb = Kbm; Kb = 0.514 K/mol*Kg.
• T_b(solution) =T_b(solvent) + ∆Tb.

Freezing Point Depression (∆Tf)

• Vapor pressure of solution is lower than solvent causing solution freezes at a lower temp.
• ∆Tf = Kfm, where Kf = 1.86 °C*Kg/mol.
• Van't Hoff factor is incorporated for electrolyte solutions.