Set up a Hess's law cycle, and use the following information to calculate ΔH°f for aqueous nitiric acid, HNO3(aq). You will need to use fractional coefficients for some equations. 3 NO2(g) + H2O(l) → 2 HNO3(aq) + NO(g) ΔH° = -137.3 kJ 2 NO(g) + O2(g) → 2 NO2(g) ΔH° = -116.2 kJ 4 NH3(g) + 5 O2(g) → 4 NO (g) + 6 H2O(l) ΔH° = -1165.2 kJ NH3(g) ΔH°f = -46.1 kJ/mol H2O(l) ΔH°f = -285.8 kJ/mol

Verified step by step guidance

1. Identify the target reaction for which you need to find the standard enthalpy of formation (ΔH°f) of HNO3(aq). This is the formation of HNO3(aq) from its elements in their standard states: 1/2 N2(g) + 1/2 O2(g) + 1/2 H2(g) → HNO3(aq).
2. Write the given reactions and their enthalpy changes: (1) 3 NO2(g) + H2O(l) → 2 HNO3(aq) + NO(g) ΔH° = -137.3 kJ, (2) 2 NO(g) + O2(g) → 2 NO2(g) ΔH° = -116.2 kJ, (3) 4 NH3(g) + 5 O2(g) → 4 NO(g) + 6 H2O(l) ΔH° = -1165.2 kJ.
3. Use the enthalpy of formation values for NH3(g) and H2O(l) to express their formation reactions: NH3(g) → 1/2 N2(g) + 3/2 H2(g) ΔH°f = 46.1 kJ/mol, H2O(l) → H2(g) + 1/2 O2(g) ΔH°f = 285.8 kJ/mol.
4. Reverse and adjust the given reactions as needed to form a Hess's law cycle that starts from the elements in their standard states and ends with the formation of HNO3(aq). This may involve reversing reactions and changing their ΔH° signs.
5. Add the adjusted reactions together, ensuring that all intermediate species cancel out, leaving only the formation of HNO3(aq) from its elements. Sum the enthalpy changes to find ΔH°f for HNO3(aq).

Key Concepts

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the number of steps taken to complete the reaction. This principle allows us to calculate the enthalpy change of a reaction by summing the enthalpy changes of individual steps, making it particularly useful for reactions that cannot be measured directly.

Standard Enthalpy of Formation (ΔH°f)

The standard enthalpy of formation (ΔH°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. This value is crucial for calculating the enthalpy changes in reactions, as it provides a reference point for the stability of compounds and their formation from elemental forms.

Fractional Coefficients in Reactions

Using fractional coefficients in chemical equations allows for the accurate representation of stoichiometry when balancing reactions, especially in Hess's Law calculations. This approach is necessary when the stoichiometric ratios do not yield whole numbers, ensuring that the enthalpy changes can be correctly scaled to match the desired reaction.