6.3 Hess's Law

HESS'S LAW (6.3)

A) Enthalpy (H)

• Definition: Enthalpy is a state function which means it is a property that depends solely on the initial and final states of a system, irrespective of the path taken.

Key Equation:

• Change in enthalpy, represented as $\Delta H$, is defined as the heat absorbed or released during a reaction.
  • Example: $\Delta H = 68 \text{ kJ}$ (indicating heat is absorbed, denoted as +).
  • Example Reaction:
  • $\text{N}<em>2 + 2\text{O}</em>2 \rightarrow 2\text{NO}_2$
  • Alternative Reaction: $\text{N}<em>2 + \text{O}</em>2 \rightarrow 2\text{NO}$
  • Another Reaction: $2\text{NO} + \text{O}<em>2 \rightarrow 2\text{NO}</em>2$

Path Function vs State Function:

• State Function:

  • Depends only on the start and end points.
  • Example: Elevation.

• Path Function:

  • Depends on the process or the way the system transitions from one state to another.
  • Example: Distance traveled in a specific path.

B) Characteristics of Enthalpy Changes

1. It is acceptable to reverse a reaction and change the sign of $\Delta H$ accordingly.
   • Example: If $\text{H}<em>2(g) + \text{O}</em>2(g) \rightarrow \text{H}_2\text{O}(l)$ has $\Delta H = -286 \text{ kJ}$, then its reverse reaction has $\Delta H = +286 \text{ kJ}$.
2. Magnitude of $\Delta H$: The magnitude of the change in enthalpy is proportional to the quantities of the reactants and products involved in a reaction.
   • Example: For the reaction $\text{H}<em>2(g) + \text{O}</em>2(g) \rightarrow \text{H}<em>2\text{O}(l)$, the enthalpy change is $\Delta H = -286 \text{ kJ}$ per mole of $\text{O}</em>2$ consumed.

C) Sample Problem #1: Calculation of Entropy Change for Carbon Forms

• Problem: Calculate $\Delta H$ for the conversion of graphite to diamond: $\text{C(graphite)} \rightarrow \text{C(diamond)}$

Given Information:

1. Reaction: $\text{C(graphite)} + \text{O}<em>2 \rightarrow \text{CO}</em>2$

   • Enthalpy Change: $\Delta H = -394 \text{ kJ}$

2. Reaction: $\text{C(diamond)} + \text{O}<em>2 \rightarrow \text{CO}</em>2$

   • Enthalpy Change: $\Delta H = -396 \text{ kJ}$

Steps to Calculate:

1. Flip the equation for diamond to align with the desired reaction.
   • This means taking the equation for diamond and changing the sign in front of its enthalpy:
     $\Delta H = +396 \text{ kJ}$
2. Combine equations:
   • \text{C(graphite)} + \frac{9}{10} \text{O}_2
     ightarrow ext{C(diamond)} will have its enthalpy added to that for graphite.

Final Calculation:

• $\Delta H = -394 \text{ kJ} + 396 \text{ kJ} = +2 \text{ kJ}$

C) Sample Problem #2: Calculation of Enthalpy for Boranes Formation

• Problem: Calculate $\Delta H$ for the formation of $\text{B}<em>2\text{H}</em>6(g)$ from elemental boron and hydrogen: $2\text{B}(s) + 3\text{H}<em>2(g) \rightarrow \text{B}</em>2\text{H}_6(g)$

Given Information:

1. Reaction: $2\text{B}(s) + \frac{3}{2} \text{O}<em>2(g) \rightarrow \text{B}</em>2\text{O}_3(s)$

   • Enthalpy Change: $\Delta H = -1273 \text{ kJ}$

2. Reaction: $\text{B}<em>2\text{H}</em>6(g) + 3 \text{O}<em>2(g) \rightarrow \text{B}</em>2\text{O}<em>3(s) + 3\text{H}</em>2\text{O}(g)$

   • Enthalpy Change: $\Delta H = -2035 \text{ kJ}$

3. Reaction: $\text{H}<em>2(g) + \text{O}</em>2(g) \rightarrow \text{H}_2\text{O}(l)$

   • Enthalpy Change: $\Delta H = -286 \text{ kJ}$

4. Reaction for water formation, decomposing water into gas:

   • $\text{H}<em>2\text{O}(l) \rightarrow \text{H}</em>2\text{O}(g)$

Final Calculation Steps:

1. Total heat for the reactions needed, adjustments for stoichiometry:

   • Multiply the needed reactions for proper substance formation and apply the corresponding enthalpy changes.
   • Upon calculation through rearranging, arrive at total enthalpy for full reaction.

2. Example Calculation (illustrative):

   • $\Delta H = 3(-286 \text{ kJ}) - 1273 \text{ kJ} + - (-2035 \text{ kJ}) + \text{others}$

3. Compute the specific enthalpy changes involved, ensuring to adhere to signs and states of matter in calculations.

   • Empirical values require all terms to be collected accordingly, for example:

• Final Result including calculations = $\text{Final } \Delta H = !Final Value!$