Write balanced equations that describe the formation of the following compounds from elements in their standard states, and then look up the standard enthalpy of formation for each substance in Appendix C: (a) \(\mathrm{H}_{2} \mathrm{O}_{2}(g),(\mathbf{b}) \mathrm{CaCO}_{3}(s)\) (c) \(\mathrm{POCl}_{3}(l),(\mathbf{d}) \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) .\)

Each compound should be formed from its constituent elements, which exist in their standard states. Write down the balanced chemical equation for each reaction. (a) For H2O2(g): \( \frac{1}{2} \) O2(g) + H2(g) \( \rightarrow \) H2O2(g) (b) For CaCO3(s): Ca(s) + C(graphite) + \( \frac{3}{2} \) O2(g) \( \rightarrow \) CaCO3(s) (c) For POCl3(l): \( \frac{1}{2} \) P4(s) + \( \frac{3}{2} \) O2(g) + \( \frac{3}{2} \) Cl2(g) \( \rightarrow \) POCl3(l) (d) For C2H5OH(l): 2 C(graphite) + \( \frac{3}{2} \) H2(g) + \( \frac{1}{2} \) O2(g) \( \rightarrow \) C2H5OH(l)

Using Appendix C, find the standard enthalpy of formation, \( \Delta H_{f}^{\circ} \), for each substance: (a) For H2O2(g): \( \Delta H_{f}^{\circ} \) = -136.0 kJ/mol (b) For CaCO3(s): \( \Delta H_{f}^{\circ} \) = -1206.9 kJ/mol (c) For POCl3(l): \( \Delta H_{f}^{\circ} \) = -945.9 kJ/mol (d) For C2H5OH(l): \( \Delta H_{f}^{\circ} \) = -277.7 kJ/mol

After completing the steps above, we can conclude that the balanced equations for the formation of the given compounds from elements in their standard states, along with their standard enthalpies of formation, are: (a) \( \frac{1}{2} \) O2(g) + H2(g) \( \rightarrow \) H2O2(g) \( \Delta H_{f}^{\circ} \) = -136.0 kJ/mol (b) Ca(s) + C(graphite) + \( \frac{3}{2} \) O2(g) \( \rightarrow \) CaCO3(s) \( \Delta H_{f}^{\circ} \) = -1206.9 kJ/mol (c) \( \frac{1}{2} \) P4(s) + \( \frac{3}{2} \) O2(g) + \( \frac{3}{2} \) Cl2(g) \( \rightarrow \) POCl3(l) \( \Delta H_{f}^{\circ} \) = -945.9 kJ/mol (d) 2 C(graphite) + \( \frac{3}{2} \) H2(g) + \( \frac{1}{2} \) O2(g) \( \rightarrow \) C2H5OH(l) \( \Delta H_{f}^{\circ} \) = -277.7 kJ/mol