Answer :
Certainly! Let's discuss and present the detailed step-by-step solution to fill in the missing information based on the given table of substances. This table lists the heats of fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]) and vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]) for several substances.
### Table of Substances with [tex]\(\Delta H_{\text{fus}}\)[/tex] and [tex]\(\Delta H_{\text{vap}}\)[/tex]
| Substance | [tex]\(\Delta H_{\text{fus}} (kJ/mol)\)[/tex] | [tex]\(\Delta H_{\text{vap}} (kJ/mol)\)[/tex] |
|-----------|-----------------------------------|----------------------------------|
| [tex]\(H_2O\)[/tex] | 6.01 | 40.7 |
| [tex]\(CO_2\)[/tex] | 7.94 | 25.2 |
| [tex]\(O_2\)[/tex] | 0.443 | 6.81 |
| [tex]\(N_2\)[/tex] | 0.719 | 5.58 |
| Fe | 14.9 | 354 |
| Al | 10.7 | 255 |
| Cu | 13.0 | 304 |
| NaCl | 30.2 | 171 |
| CH4 | 0.936 | 8.53 |
#### Explanation of the Table
1. Substance [tex]\(H_2O\)[/tex] (Water):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 6.01 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 40.7 kJ/mol
2. Substance [tex]\(CO_2\)[/tex] (Carbon Dioxide):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 7.94 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 25.2 kJ/mol
3. Substance [tex]\(O_2\)[/tex] (Oxygen):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 0.443 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 6.81 kJ/mol
4. Substance [tex]\(N_2\)[/tex] (Nitrogen):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 0.719 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 5.58 kJ/mol
5. Substance Fe (Iron):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 14.9 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 354 kJ/mol
6. Substance Al (Aluminum):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 10.7 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 255 kJ/mol
7. Substance Cu (Copper):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 13.0 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 304 kJ/mol
8. Substance NaCl (Sodium Chloride):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 30.2 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 171 kJ/mol
9. Substance CH4 (Methane):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 0.936 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 8.53 kJ/mol
These values illustrate the energy required to change substances from solid to liquid (fusion) and from liquid to gas (vaporization). This information is essential for understanding the phase changes and thermal properties of these substances.
### Table of Substances with [tex]\(\Delta H_{\text{fus}}\)[/tex] and [tex]\(\Delta H_{\text{vap}}\)[/tex]
| Substance | [tex]\(\Delta H_{\text{fus}} (kJ/mol)\)[/tex] | [tex]\(\Delta H_{\text{vap}} (kJ/mol)\)[/tex] |
|-----------|-----------------------------------|----------------------------------|
| [tex]\(H_2O\)[/tex] | 6.01 | 40.7 |
| [tex]\(CO_2\)[/tex] | 7.94 | 25.2 |
| [tex]\(O_2\)[/tex] | 0.443 | 6.81 |
| [tex]\(N_2\)[/tex] | 0.719 | 5.58 |
| Fe | 14.9 | 354 |
| Al | 10.7 | 255 |
| Cu | 13.0 | 304 |
| NaCl | 30.2 | 171 |
| CH4 | 0.936 | 8.53 |
#### Explanation of the Table
1. Substance [tex]\(H_2O\)[/tex] (Water):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 6.01 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 40.7 kJ/mol
2. Substance [tex]\(CO_2\)[/tex] (Carbon Dioxide):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 7.94 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 25.2 kJ/mol
3. Substance [tex]\(O_2\)[/tex] (Oxygen):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 0.443 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 6.81 kJ/mol
4. Substance [tex]\(N_2\)[/tex] (Nitrogen):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 0.719 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 5.58 kJ/mol
5. Substance Fe (Iron):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 14.9 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 354 kJ/mol
6. Substance Al (Aluminum):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 10.7 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 255 kJ/mol
7. Substance Cu (Copper):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 13.0 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 304 kJ/mol
8. Substance NaCl (Sodium Chloride):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 30.2 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 171 kJ/mol
9. Substance CH4 (Methane):
- Heat of Fusion ([tex]\(\Delta H_{\text{fus}}\)[/tex]): 0.936 kJ/mol
- Heat of Vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]): 8.53 kJ/mol
These values illustrate the energy required to change substances from solid to liquid (fusion) and from liquid to gas (vaporization). This information is essential for understanding the phase changes and thermal properties of these substances.
