The molar enthalpy change for a reaction is calculated using Hess's Law and standard enthalpies of formation, followed by a normalization step if needed to express the change per mole of a specific substance.
Here's a breakdown of the process:
1. Understanding Hess's Law:
Hess's Law states that the enthalpy change for a reaction is independent of the pathway taken. This means that the overall enthalpy change is the sum of the enthalpy changes for individual steps in the reaction. A crucial application of this law allows us to calculate the enthalpy change of a reaction using standard enthalpies of formation.
2. Using Standard Enthalpies of Formation (ΔHfo):
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Definition: The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their standard states (usually 298 K and 1 atm). Standard enthalpies of formation are typically found in thermodynamic tables.
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Hess's Law Formula: The enthalpy change of a reaction (ΔHrxno) can be calculated as:
ΔHrxno = ΣnΔHfo(products) - ΣnΔHfo(reactants)
where:
- ΔHrxno is the standard enthalpy change of the reaction.
- ΔHfo(products) is the standard enthalpy of formation of each product.
- ΔHfo(reactants) is the standard enthalpy of formation of each reactant.
- n is the stoichiometric coefficient of each product and reactant in the balanced chemical equation.
3. Steps for Calculation:
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Write the balanced chemical equation for the reaction. This is critical because the stoichiometric coefficients are used in the calculation.
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Look up the standard enthalpies of formation (ΔHfo) for each reactant and product. These values are usually found in standard thermodynamic tables. The standard enthalpy of formation of an element in its standard state is zero.
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Apply Hess's Law formula. Multiply the ΔHfo of each product by its stoichiometric coefficient (n) and sum these values. Then, multiply the ΔHfo of each reactant by its stoichiometric coefficient and sum these values. Finally, subtract the sum of the reactant enthalpies from the sum of the product enthalpies.
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Calculate the overall enthalpy change (ΔHrxno). The result is the enthalpy change for the reaction as written, which corresponds to the molar quantities indicated by the balanced equation.
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Determine the molar enthalpy change for a specific substance. If the question asks for the molar enthalpy change per mole of a particular reactant or product, divide the calculated ΔHrxno by the stoichiometric coefficient of that substance in the balanced equation. This expresses the enthalpy change associated with one mole of that specific substance reacting or being produced.
Example:
Consider the reaction:
N2(g) + 3H2(g) → 2NH3(g)
Let's say you've calculated the ΔHrxno for this reaction to be -92.2 kJ. This means that when 1 mole of N2 reacts with 3 moles of H2 to produce 2 moles of NH3, 92.2 kJ of heat is released (exothermic reaction).
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To find the molar enthalpy change per mole of NH3 formed, divide the overall ΔHrxno by 2: -92.2 kJ / 2 mol NH3 = -46.1 kJ/mol NH3.
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To find the molar enthalpy change per mole of N2 reacted, divide the overall ΔHrxno by 1: -92.2 kJ / 1 mol N2 = -92.2 kJ/mol N2
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To find the molar enthalpy change per mole of H2 reacted, divide the overall ΔHrxno by 3: -92.2 kJ / 3 mol H2 = -30.73 kJ/mol H2.
Summary
The molar enthalpy change for a reaction is calculated using Hess's Law with standard enthalpies of formation, ensuring you account for stoichiometric coefficients. If you need the molar enthalpy change per mole of a specific substance, divide the overall enthalpy change by that substance's stoichiometric coefficient. This provides the heat absorbed or released when one mole of that particular substance reacts or is produced.
