Give the definition of the standard enthalpy of formation for a substance. Write separate reactions for the formation of \(\mathrm{NaCl}\) , \(\mathrm{H}_{2} \mathrm{O}, \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) and \(\mathrm{PbSO}_{4}\) that have \(\Delta H^{\circ}\) values equal to $\Delta H_{\mathrm{f}}^{\circ}$ for each compound.

The standard enthalpy of formation (\( \Delta H_{\mathrm{f}}^{\circ} \)) is defined as the change in enthalpy when one mole of a substance in its standard state is formed from its constituent elements in their standard states at a fixed temperature, usually 298.15 K.

Now, we will write the formation reactions for NaCl, H2O, C6H12O6, and PbSO4. It is essential to make sure that you have precisely one mole of the product in each formation reaction, and the reactants are in their standard states. 1. Formation of NaCl: In the standard state, sodium is a solid, and chlorine is a gas. Therefore, the formation reaction for NaCl would be: \[ \mathrm{Na} (s) + \frac{1}{2} \mathrm{Cl}_{2} (g) \rightarrow \mathrm{NaCl} (s) \] 2. Formation of H2O: In the standard state, hydrogen and oxygen are both gases. The formation reaction for H2O, considering it as a liquid, is: \[ \mathrm{H}_{2} (g) + \frac{1}{2} \mathrm{O}_{2} (g) \rightarrow \mathrm{H}_{2} \mathrm{O} (l) \] 3. Formation of C6H12O6 (glucose): In the standard state, carbon is a solid (graphite), hydrogen is a gas, and oxygen is a gas. The formation reaction for glucose, considering it as a solid, is: \[ 6 \mathrm{C} (graphite) + 6 \mathrm{H}_{2} (g) + 3 \mathrm{O}_{2} (g) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} (s) \] 4. Formation of PbSO4: In the standard state, lead is a solid, sulfur is a solid, and oxygen is a gas. The formation reaction for PbSO4, considering it as a solid, is: \[ \mathrm{Pb} (s) + \mathrm{S} (s) + 2 \mathrm{O}_{2} (g) \rightarrow \mathrm{PbSO}_{4} (s) \] These reactions represent the formation of one mole of the compound in its standard state from its constituent elements in their standard states. The associated enthalpy changes, \(\Delta H^{\circ}\), for each of these reactions are equal to the standard enthalpy of formation, \(\Delta H_{\mathrm{f}}^{\circ} \), for the respective substances.