Which of the following standard enthalpy of formation values is not zero at \(25^{\circ} \mathrm{C} ? \mathrm{Na}(s), \mathrm{Ne}(g)\) \(\mathrm{CH}_{4}(g), \mathrm{S}_{8}(s), \mathrm{Hg}(l), \mathrm{H}(g)\)

When studying chemical reactions, understanding the enthalpy of formation is crucial. The enthalpy of formation, or \standard enthalpy of formation\, is a measure of the energy change when one mole of a substance is formed from its elements in their most stable form under standard conditions, typically at a pressure of 1 bar and a temperature of 298.15 K (\(25^{\rc}C\)). For example, when methane (\(CH_4\) is formed from carbon and hydrogen, energy will be absorbed or released, and this change is quantified as the enthalpy of formation.

In the context of homework exercises, it can be tricky to determine whether a substance has a non-zero enthalpy of formation. Compounds, unlike elements, always have a non-zero enthalpy of formation since they do not exist naturally as singular atoms and must be formed through chemical reactions. A useful tip for solving these kinds of problems is to remember that pure elements in their standard state, such as solid sodium (\(Na(s)\) or gaseous neon (\(Ne(g)\) have an enthalpy of formation of zero, because there is no formation involved—they are already in their stable form.

Chemical thermodynamics deals with the energy changes associated with chemical reactions and the properties of substances. It helps us understand processes such as why certain reactions occur spontaneously while others require additional energy. The first law of thermodynamics states that energy cannot be created or destroyed, only transformed. This principle applies to enthalpy of formation. The energy required to break bonds in the reactants must come from somewhere, such as the energy released when new bonds form in the products.

Moreover, the third law of thermodynamics can help explain why the standard enthalpy of formation for elements in their standard state is zero: the entropy of a perfectly crystalline substance at absolute zero temperature is itself zero. This serves as a reference point in determining the absolute entropies of substances, which in turn contribute to calculating the enthalpy of formation for compounds.

Elements have a standard state, the form in which they are most stable under standard conditions. For instance, oxygen is most stable as \(O_2(g)\) and hydrogen as \(H_2(g)\), both of which are diatomic gases at room temperature and atmospheric pressure. It is important to remember that the standard enthalpy of formation values for these elements in their standard states are defined to be zero. This is because they are already in their most stable form and thus, conceptually, no formation from simpler elements is required.

However, for a substance like atomic hydrogen (\(H(g)\) is not in its standard state and has an associated positive or negative enthalpy value reflecting its formation from diatomic hydrogen gas. Similarly, liquids like mercury (\(Hg(l)\) or solids like sulfur (\(S_{8}(s)\) would have zero enthalpy of formation in their standard states. This concept helps students understand the differences between elemental and molecular substances and their corresponding energy changes during formation.