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Energetics / Thermochemistry - Hess’s Law

Grade 12IBChemistry

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Hess's Law states that the total enthalpy change (ΔH)(\Delta H) for a chemical reaction is independent of the route by which the chemical change occurs, provided the initial and final conditions are the same. This is an application of the Law of Conservation of Energy.

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Enthalpy is a state function, meaning its value depends only on the state of the substance (temperature, pressure, phase) and not on the path taken to reach that state.

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The Standard Enthalpy of Formation (ΔHf⊖)(\Delta H_f^\ominus) is the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions (298 K298\text{ K} and 100 kPa100\text{ kPa}). By definition, ΔHf⊖\Delta H_f^\ominus of any element in its standard state is 0 kJ mol−10\text{ kJ mol}^{-1}.

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The Standard Enthalpy of Combustion (ΔHc⊖)(\Delta H_c^\ominus) is the enthalpy change when one mole of a substance is completely burned in excess oxygen under standard conditions.

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Enthalpy cycles (Hess cycles) can be constructed to calculate unknown enthalpy changes. If the cycle uses formation data, arrows point from the elements to the reactants/products. If using combustion data, arrows point from the reactants/products to the combustion products (e.g., CO2CO_2 and H2OH_2O).

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Mathematical manipulation: If a reaction is reversed, the sign of ΔH\Delta H is flipped. If the coefficients of a reaction are multiplied by a factor nn, ΔH\Delta H is also multiplied by nn.

📐Formulae

ΔHreaction⊖=∑ΔHf⊖(products)−∑ΔHf⊖(reactants)\Delta H_{reaction}^\ominus = \sum \Delta H_f^\ominus (\text{products}) - \sum \Delta H_f^\ominus (\text{reactants})

ΔHreaction⊖=∑ΔHc⊖(reactants)−∑ΔHc⊖(products)\Delta H_{reaction}^\ominus = \sum \Delta H_c^\ominus (\text{reactants}) - \sum \Delta H_c^\ominus (\text{products})

ΔHroute1=ΔHroute2\Delta H_{route 1} = \Delta H_{route 2}

💡Examples

Problem 1:

Calculate the standard enthalpy change for the reaction: C2H4(g)+H2(g)→C2H6(g)C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g). Given the following standard enthalpies of combustion (ΔHc⊖)(\Delta H_c^\ominus): C2H4(g)=−1411 kJ mol−1C_2H_4(g) = -1411\text{ kJ mol}^{-1}, H2(g)=−286 kJ mol−1H_2(g) = -286\text{ kJ mol}^{-1}, and C2H6(g)=−1560 kJ mol−1C_2H_6(g) = -1560\text{ kJ mol}^{-1}.

Solution:

ΔHrxn⊖=∑ΔHc⊖(reactants)−∑ΔHc⊖(products)\Delta H_{rxn}^\ominus = \sum \Delta H_c^\ominus (\text{reactants}) - \sum \Delta H_c^\ominus (\text{products}) ΔHrxn⊖=[(−1411)+(−286)]−[−1560]\Delta H_{rxn}^\ominus = [(-1411) + (-286)] - [-1560] ΔHrxn⊖=−1697+1560=−137 kJ mol−1\Delta H_{rxn}^\ominus = -1697 + 1560 = -137\text{ kJ mol}^{-1}

Explanation:

Since combustion data is provided, the Hess cycle involves burning both reactants and products to the same combustion products (CO2CO_2 and H2OH_2O). According to Hess's Law, the enthalpy change of the reaction is the sum of the combustion of reactants minus the sum of the combustion of products.

Problem 2:

Given the following thermochemical equations:

  1. N2(g)+O2(g)→2NO(g)ΔH1=+180.5 kJN_2(g) + O_2(g) \rightarrow 2NO(g) \quad \Delta H_1 = +180.5\text{ kJ}
  2. 2NO2(g)→2NO(g)+O2(g)ΔH2=+114.4 kJ2NO_2(g) \rightarrow 2NO(g) + O_2(g) \quad \Delta H_2 = +114.4\text{ kJ} Calculate ΔH\Delta H for the reaction: N2(g)+2O2(g)→2NO2(g)N_2(g) + 2O_2(g) \rightarrow 2NO_2(g).

Solution:

Step 1: Keep equation (1) as it is: N2(g)+O2(g)→2NO(g)ΔH=+180.5 kJN_2(g) + O_2(g) \rightarrow 2NO(g) \quad \Delta H = +180.5\text{ kJ}. Step 2: Reverse equation (2): 2NO(g)+O2(g)→2NO2(g)ΔH=−114.4 kJ2NO(g) + O_2(g) \rightarrow 2NO_2(g) \quad \Delta H = -114.4\text{ kJ}. Step 3: Add the equations: N2(g)+2O2(g)→2NO2(g)N_2(g) + 2O_2(g) \rightarrow 2NO_2(g). ΔHtotal=ΔH1+(−ΔH2)=180.5 kJ+(−114.4 kJ)=+66.1 kJ\Delta H_{total} = \Delta H_1 + (-\Delta H_2) = 180.5\text{ kJ} + (-114.4\text{ kJ}) = +66.1\text{ kJ}

Explanation:

To find the target equation, we manipulate the given equations. Reversing equation (2) allows 2NO(g)2NO(g) to cancel out when the reactions are summed, resulting in the desired synthesis of NO2NO_2 from its elements. The enthalpy values are summed accordingly.

Hess’s Law - Revision Notes & Key Formulas | IB Grade 12 Chemistry