Hess's Law of Constant Heat Summation — Revision Notes

⚡ 30-Second Revision

Hess's Law: — $\Delta H_{overall} = \sum \Delta H_{steps}$
Enthalpy (H): — A state function; path independent.
Manipulation Rules:

- Reverse reaction: Reverse sign of $\Delta H$. - Multiply reaction by 'n': Multiply $\Delta H$ by 'n'. - Add reactions: Add $\Delta H$ values.

Applications: — Calculate $\Delta H_f^\circ$, $\Delta H_c^\circ$, or any reaction $\Delta H$ indirectly.
Key Formula (from $\Delta H_f^\circ$): — $\Delta H_{reaction}^\circ = \sum n \Delta H_f^\circ (products) - \sum m \Delta H_f^\circ (reactants)$

2-Minute Revision

Hess's Law of Constant Heat Summation is a fundamental principle in thermochemistry, stating that the total enthalpy change ($\Delta H$) for a chemical reaction is independent of the pathway taken, depending only on the initial reactants and final products.

This is because enthalpy is a state function. To apply Hess's Law, you manipulate given thermochemical equations to match a target reaction. If you reverse an equation, you must reverse the sign of its $\Delta H$.

If you multiply an equation by a coefficient, you must multiply its $\Delta H$ by the same coefficient. Finally, you algebraically sum the manipulated equations and their corresponding $\Delta H$ values.

This method is invaluable for calculating enthalpy changes for reactions that are difficult or impossible to measure directly, such as standard enthalpies of formation or combustion. Always ensure intermediate species cancel out and pay close attention to stoichiometry and signs.

5-Minute Revision

Hess's Law is a powerful tool in thermochemistry, rooted in the fact that enthalpy is a state function, meaning its change depends solely on the initial and final states, not the path. The law states that if a reaction can be written as a sum of several steps, the overall enthalpy change is the sum of the enthalpy changes for those steps. This allows us to calculate $\Delta H$ for complex or unmeasurable reactions.

Steps for Application:

1
Identify the Target Reaction: — Clearly write down the reaction for which $\Delta H$ is required.
2
Examine Given Reactions: — List all provided thermochemical equations with their $\Delta H$ values.
3
Manipulate Given Reactions: — For each given reaction, adjust it to match the target reaction's components:

* If a reactant/product is on the wrong side, reverse the equation and change the sign of its $\Delta H$. * If the stoichiometric coefficient of a substance doesn't match, multiply the entire equation and its $\Delta H$ by the required factor.

1
Sum and Cancel: — Add all manipulated equations. Ensure that any intermediate species (present in both reactants and products of the summed equations) cancel out, leaving only the target reaction. Sum the corresponding manipulated $\Delta H$ values.

Example: Calculate $\Delta H$ for $C(s) + 2H_2(g) \to CH_4(g)$ given: (1) $C(s) + O_2(g) \to CO_2(g)$, $\Delta H_1 = -393.5 \text{ kJ}$ (2) $H_2(g) + \frac{1}{2}O_2(g) \to H_2O(l)$, $\Delta H_2 = -285.8 \text{ kJ}$ (3) $CH_4(g) + 2O_2(g) \to CO_2(g) + 2H_2O(l)$, $\Delta H_3 = -890.3 \text{ kJ}$

Keep (1) as is: $C(s) + O_2(g) \to CO_2(g)$, $\Delta H_1 = -393.5 \text{ kJ}$
Multiply (2) by 2: $2H_2(g) + O_2(g) \to 2H_2O(l)$, $\Delta H_2' = 2 \times (-285.8) = -571.6 \text{ kJ}$
Reverse (3): $CO_2(g) + 2H_2O(l) \to CH_4(g) + 2O_2(g)$, $\Delta H_3' = +890.3 \text{ kJ}$

Add: $C(s) + O_2(g) + 2H_2(g) + O_2(g) + CO_2(g) + 2H_2O(l) \to CO_2(g) + 2H_2O(l) + CH_4(g) + 2O_2(g)$ Cancel: $C(s) + 2H_2(g) \to CH_4(g)$ Sum $\Delta H$: $-393.5 + (-571.6) + 890.3 = -74.8 \text{ kJ}$.

Remember to be precise with signs and stoichiometry, as these are common sources of error.

Prelims Revision Notes

Hess's Law of Constant Heat Summation is a critical concept for NEET, allowing calculation of reaction enthalpies indirectly. The core principle is that **enthalpy ($\Delta H$) is a state function, meaning its change depends only on the initial and final states, not the path. This implies path independence** for $\Delta H$.

Key Rules for Manipulating Thermochemical Equations:

1
Reversing a Reaction: — If $A \to B$ has $\Delta H = X$, then $B \to A$ has $\Delta H = -X$. Always change the sign of $\Delta H$ when reversing an equation.
2
Multiplying/Dividing a Reaction: — If $A \to B$ has $\Delta H = X$, then $nA \to nB$ has $\Delta H = nX$. Multiply or divide $\Delta H$ by the same factor as the equation.
3
Adding Reactions: — If multiple reactions sum up to a target reaction, their $\Delta H$ values are algebraically summed to get the $\Delta H$ for the target reaction.

Common Applications:

Calculating **standard enthalpy of formation ($\Delta H_f^\circ$)** for compounds that cannot be formed directly from elements.
Calculating **standard enthalpy of combustion ($\Delta H_c^\circ$)** or any other reaction enthalpy.

Formula for $\Delta H_{reaction}^\circ$ from $\Delta H_f^\circ$:

$$\Delta H_{reaction}^\circ = \sum n \Delta H_f^\circ (products) - \sum m \Delta H_f^\circ (reactants)$$

where $n$ and $m$ are stoichiometric coefficients. Remember that $\Delta H_f^\circ$ for elements in their standard states (e.g., $O_2(g)$, $C(s, graphite)$, $H_2(g)$) is zero.

Common Pitfalls:

Forgetting to change the sign of $\Delta H$ when reversing an equation.
Failing to multiply $\Delta H$ by the correct stoichiometric factor.
Arithmetic errors during summation.
Not cancelling intermediate species correctly.
Confusing Hess's Law (thermodynamics) with reaction rates (kinetics).

Practice systematically: identify target, manipulate given equations one by one to match target components, sum, and verify cancellations.

Vyyuha Quick Recall

Heats Every Step Summed: Hess's Excellent State Summary. (Hess's Law, Enthalpy, State function, Summation)