Enthalpy and the First Law

Introduction to Thermodynamics

• Focus on enthalpy and the first law of thermodynamics in this session.

• Note on notation: ( Δ E ) and ( Δ U ) may be used interchangeably depending on the edition of the textbook.

First Law of Thermodynamics

• Key Equation: ( Δ U = Q + W )

  • Where ( W = -P Δ V )

  • Substitute for work: ( Δ U = Q - P Δ V )

Constant Volume Conditions

• Under constant volume:

  • ( Δ V = 0 )

  • No work done: ( Δ U = Q )

Constant Pressure Conditions

• Under constant pressure:

  • Work done: ( W = P Δ V )

  • Rearranging leads to: ( Q = Δ U + P Δ V )

  • Define enthalpy: ( Δ H = Δ U + P Δ V )

• Definition of Enthalpy:

  • Enthalpy as a state function: ( H = U + PV )

• Interpretation of enthalpy:

  • Enthalpy is heat at constant pressure conditions.

  • Many reactions in aqueous solutions occur at constant pressure.

Change in Enthalpy (( Δ H ))

• Defined as: ( Δ H = H_final - H_initial )

• For a chemical reaction:

  • ( Δ H = H_{products} - H_{reactants} )

• Exothermic Process:

  • Losing heat leads to negative ( \Delta H ). ( (H_{products} < H_{reactants}) )

• Endothermic Process:

  • Gaining heat leads to positive ( \Delta H ). ( (H_{products} > H_{reactants}) )

Thermochemical Equations

• Convention:

  • Write ( \Delta H ) as if reading from left to right.

• Example of Exothermic Reaction: Combustion of hydrogen.

• Example of Endothermic Reaction: Decomposition of mercury oxide.

Using Enthalpy in Reactions

• Relationship between enthalpy and energy in reactions.

• Most changes in internal energy (( \Delta U )) are in terms of enthalpy or heat, rather than work.

• Activation Energy: Energy required to initiate reactions.

Calculating Enthalpy Changes

• For a physical process like melting ice:

  • Heat of fusion: ( \Delta H = 6.01 \text{ kJ/mol} ).

  • Double for two moles: ( 12.02 \text{ kJ} ).

• For freezing: ( \Delta H = -6.01 \text{ kJ/mol} ).

Summary of Thermochemical Rules

• Coefficients correspond to moles in reactions.

• If the reaction is reversed, ( \Delta H ) changes sign.

• If an equation is multiplied/divided, adjust ( \Delta H ) accordingly.

• Always specify states of matter for reactions since enthalpy depends on state.

Importance of States of Matter in Reactions

• Gases are primarily considered for ( \Delta N ) in calculations.

• Only changes in moles of gases do work.

Practical Example: Vaporization of Water

• Calculate ( \Delta U ) for vaporization at 100°C:

  • ( \Delta H_{vaporization} = +40.66 \text{ kJ/mol} )

• Use proper equations to solve for internal energy changes.

Other Considerations in Reactions

• Look for balancing in combustion reactions and check for energy required to initiate reactions.

• Work is often a small fraction of total energy changes in combustion.

Conclusion

• Understand relationships between internal energy, enthalpy, and work in reactions.

• Prepare for lab applications of these concepts and subsequent topics like calorimetry and Hess's law in future classes.