The standard enthalpy change for the reaciton of SO3(g) with H2O(l) to yield H2SO4(aq) is ΔH° = -227.8 kJ. Use the information in Problem 9.104 to calculate ΔH°f for H2SO4(aq) in kJ/mol. [For H2O(l), ΔH°f = -285.88 kJ/mol.]

Verified step by step guidance

1. Identify the given reaction: \( \text{SO}_3(g) + \text{H}_2\text{O}(l) \rightarrow \text{H}_2\text{SO}_4(aq) \).
2. Recognize that the standard enthalpy change for the reaction, \( \Delta H^\circ \), is given as -227.8 kJ.
3. Recall that the standard enthalpy of formation, \( \Delta H^\circ_f \), for a compound is the enthalpy change when one mole of the compound is formed from its elements in their standard states.
4. Use the formula for the enthalpy change of a reaction: \( \Delta H^\circ = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants}) \).
5. Substitute the known values into the equation: \( -227.8 = \Delta H^\circ_f(\text{H}_2\text{SO}_4(aq)) - [\Delta H^\circ_f(\text{SO}_3(g)) + (-285.88)] \), and solve for \( \Delta H^\circ_f(\text{H}_2\text{SO}_4(aq)) \).

Key Concepts

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is a measure of the heat absorbed or released during a chemical reaction at constant pressure. A negative ΔH indicates that the reaction is exothermic, meaning it releases heat. Understanding ΔH is crucial for calculating the standard enthalpy of formation (ΔH°f) of compounds, as it reflects the energy changes associated with forming products from reactants.

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. It is a key value used in thermodynamic calculations to determine the energy changes in reactions. Knowing the ΔH°f values of reactants and products allows for the calculation of the overall enthalpy change for a reaction.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps, regardless of the pathway taken. This principle allows for the calculation of ΔH°f for compounds by using known ΔH values from related reactions. It is particularly useful when direct measurement of ΔH°f is not possible, enabling the use of other thermodynamic data to find the desired value.