Chemistry

Chemistry

Problem

One mole of H2_2O(s) at −20 ∘ ⁣C-20\,^{\circ}\!\text{C} is subjected to a series of steps in an insulated system: 1. The ice is warmed to 0 ∘ ⁣C0\,^{\circ}\!\text{C}. 2. The ice melts completely at 0 ∘ ⁣C0\,^{\circ}\!\text{C}. 3. The resulting liquid is heated to 100 ∘ ⁣C100\,^{\circ}\!\text{C}. 4. The liquid vaporizes completely at 100 ∘ ⁣C100\,^{\circ}\!\text{C}. 5. The water vapor is electrolyzed at 25 ∘ ⁣C25\,^{\circ}\!\text{C} to form H2_2(g) and O2_2(g). Relevant data: • cice=2.09 J g−1 ∘ ⁣C−1c_{\text{ice}} = 2.09\,\text{J\,g}^{-1}\,^{\circ}\!\text{C}^{-1} • cliq=4.18 J g−1 ∘ ⁣C−1c_{\text{liq}} = 4.18\,\text{J\,g}^{-1}\,^{\circ}\!\text{C}^{-1} • csteam=2.01 J g−1 ∘ ⁣C−1c_{\text{steam}} = 2.01\,\text{J\,g}^{-1}\,^{\circ}\!\text{C}^{-1} (use only if needed) • ΔHfus(H2O)=6.01 kJ mol−1\Delta H_{\text{fus}}(\text{H}_2\text{O}) = 6.01\,\text{kJ\,mol}^{-1} • ΔHvap(H2O)=40.7 kJ mol−1\Delta H_{\text{vap}}(\text{H}_2\text{O}) = 40.7\,\text{kJ\,mol}^{-1} • ΔHrxn\Delta H_{\text{rxn}} for H2O(l)→H2(g)+12 O2(g)\text{H}_2\text{O}(l) \rightarrow \text{H}_2(g)+\tfrac12\,\text{O}_2(g) at 25 ∘ ⁣C25\,^{\circ}\!\text{C} is +286 kJ mol−1+286\,\text{kJ\,mol}^{-1} (a) Calculate the total energy, in kilojoules, required to complete steps 1–4 (the purely physical changes). Show each contribution separately before giving the sum. (b) Determine the ratio of the energy required for the chemical decomposition in step 5 to the total energy calculated for the physical changes in part (a). (c) Interpret the numerical ratio from part (b) in terms of the relative strengths of chemical bonds versus intermolecular forces in water. (d) If the available energy supply were limited to 300 kJ300\,\text{kJ}, identify which steps in the sequence could be completed and which could not. Justify your answer quantitatively.

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