1) In terms of intermolecular forces of attraction, explain why the \( H_{v} \) value is so mucn nigner than the \( H_{f} \) value for any given substance.

The \( H_{v} \) value, or enthalpy of vaporization, is significantly higher than the \( H_{f} \) value, which is the enthalpy of fusion, primarily due to the strength of the intermolecular forces involved. When a substance transitions from liquid to gas (vaporization), it must overcome the attractive forces holding the molecules together in the liquid state, which often include hydrogen bonds, dipole-dipole interactions, or van der Waals forces. This requires more energy, resulting in a higher \( H_{v} \) value. In contrast, the transition from solid to liquid (melting or fusion) involves breaking only some of the intermolecular forces, leading to a lower energy requirement and thus a lower \( H_{f} \) value. This is why vaporization generally demands more energy—you're unlocking a state of liberty for the molecules that they don't possess in the more constrained liquid or solid states!