A You want to determine the value for the enthalpy of formation of CaSO4(s), but the reaction ca

A You want to determine the value for the enthalpy of...

A You want to determine the value for the enthalpy of formation of $\mathrm{CaSO}_{4}(\mathrm{s}),$ but the reaction cannot be done directly. $$ \mathrm{Ca}(\mathrm{s})+\mathrm{S}(\mathrm{s})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CaSO}_{4}(\mathrm{s}) $$ You know, however, that (a) both calcium and sulfur react with oxygen to produce oxides in reactions that can be studied calorimetrically, and (b) the basic oxide CaO reacts with the acidic oxide $\mathrm{SO}_{3}(\mathrm{g})$ to produce $\mathrm{CaSO}_{4}(\mathrm{s})$ with $\Delta_{r} H^{\circ}=$ $-402.7 \mathrm{kJ} .$ Outline a method for determining $\Delta_{f} H^{\circ}$ for $\mathrm{CaSO}_{4}(s),$ and identify the information that must be collected by experiment. Using information in Appendix $L_{y}$ confirm that $\Delta_{f} H^{\circ}$ for $\mathrm{CaSO}_{4}(\mathrm{s})=-1433.5 \mathrm{kJ} / \mathrm{mol}.$

A You want to determine the value for the enthalpy of formation of $\mathrm{CaSO}_{4}(\mathrm{s}),$ but the reaction cannot be done directly.
$$
\mathrm{Ca}(\mathrm{s})+\mathrm{S}(\mathrm{s})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CaSO}_{4}(\mathrm{s})
$$
You know, however, that (a) both calcium and sulfur react with oxygen to produce oxides in reactions that can be studied calorimetrically, and
(b) the basic oxide CaO reacts with the acidic oxide $\mathrm{SO}_{3}(\mathrm{g})$ to produce $\mathrm{CaSO}_{4}(\mathrm{s})$ with $\Delta_{r} H^{\circ}=$
$-402.7 \mathrm{kJ} .$ Outline a method for determining $\Delta_{f} H^{\circ}$ for $\mathrm{CaSO}_{4}(s),$ and identify the information that must be collected by experiment. Using information in Appendix $L_{y}$ confirm that $\Delta_{f} H^{\circ}$ for $\mathrm{CaSO}_{4}(\mathrm{s})=-1433.5 \mathrm{kJ} / \mathrm{mol}.$

Key Concepts

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same regardless of the number of steps or the pathway taken, provided the initial and final conditions are identical. This principle allows us to determine the enthalpy change for reactions that are difficult or impossible to measure directly by combining other reactions with known enthalpy changes.

Standard Enthalpy of Formation

The standard enthalpy of formation is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. It is a fundamental concept used to quantify the energy involved in forming compounds and is essential for evaluating reaction energetics using Hess's Law.

Calorimetry

Calorimetry is the experimental method used to measure the heat exchanged in chemical reactions. In the context of determining reaction enthalpies indirectly, calorimetry can provide accurate measurements of the heat released or absorbed during related reactions, such as the formation of oxides from elements, which are then used to calculate the enthalpy change of the target reaction.

Indirect Determination of Reaction Enthalpies

Indirect determination involves using a series of related reactions with known enthalpy changes to construct an energy cycle or Hess's Law pathway, from which the enthalpy change of the target reaction can be deduced. This method requires careful experimental measurement of accessible reactions and the proper combination of their enthalpy changes to cancel out intermediates, ultimately yielding the desired enthalpy of formation for compounds that cannot be formed by a direct reaction.