(a) When \(25.23 \mathrm{~g}\) of methanol, \(\mathrm{CH}_{3} \mathrm{OH}\), froze, \(4.01 \mathrm{~kJ}\) of heat was released. What is the enthalpy of fusion of methanol? (b) A sample of benzene was vaporized at \(25^{\circ} \mathrm{C}\). When \(37.5 \mathrm{~kJ}\) of heat was supplied, \(95 \mathrm{~g}\) of the liquid benzene vaporized. What is the enthalpy of vaporization of benzene at \(25^{\circ} \mathrm{C}\) ?

The enthalpy of fusion is a thermodynamic property describing the energy change when a substance transitions from a solid to a liquid phase. It's crucial in understanding phase transitions and is pivotal in fields such as meteorology and materials science.

When a solid melts, the substance requires an intake of energy to overcome intermolecular forces holding its rigid structure. This energy is the enthalpy of fusion. One interesting point is that, during this phase change, the temperature of the substance doesn't rise despite the heat addition; the energy is solely used to convert the solid into a liquid.

For example, when methanol freezes, energy is released since the transition goes from liquid to solid, and this process is the inverse of the melting process. By measuring this released energy, we can calculate the enthalpy of fusion, which is important for industrial applications such as designing cooling systems.

Similarly, the enthalpy of vaporization is the amount of energy required to transform a liquid into a gas. This conversion takes place during processes like boiling, where the liquid's molecules gain enough energy to escape into the gaseous state.

Think of boiling water: heat energy is absorbed by the water, not to increase its temperature past the boiling point, but to change its phase. The enthalpy of vaporization is notably higher than the enthalpy of fusion because the energy needed to separate molecules in a liquid to form a gas is much greater than that needed to merely loosen them from a solid to a liquid.

When benzene is vaporized, the substantial amount of energy required reflects its stronger intermolecular attractions compared to methanol, as shown by the computed enthalpy of vaporization. This knowledge is applied in various chemical processes, including distillation and other separation methods.

Thermochemistry is the branch of chemistry that deals with the heat involved in chemical reactions and physical transformations. It's essential in predicting reaction outcomes, such as whether a reaction will proceed spontaneously and how temperature changes affect reaction rates.

Undergoing all these systems is the Law of Conservation of Energy, which states that energy can neither be created nor destroyed, only transformed. Thermochemistry uses this principle to calculate the heat absorbed or released during physical or chemical changes using various equations, including the one for calculating the enthalpy changes in fusion and vaporization.

In thermochemistry, understanding the specific heat capacity, calorimetry, and Hess's law are fundamental. They allow scientists to gauge reaction energetics and design processes accordingly, ensuring safety and efficiency in thermal systems like engines and reactors.

Heat transfer is the movement of thermal energy from one thing to another due to the temperature difference. It's an underlying concept in thermochemistry and occurs in three main ways: conduction, convection, and radiation.

Conduction is the transfer of heat through direct contact, like when a pan heats up on the stove. Convection happens in fluids where the warmer part of the fluid rises, and cooler fluid moves down to take its place, creating a current. Radiation is the transfer of energy by electromagnetic waves, such as the heat felt from sunlight.

Understanding heat transfer helps explain how the energy needed for phase changes, including melting and vaporization, is conveyed. For instance, the heat needed for vaporizing benzene or melting methanol must be transferred effectively into the substance for the phase change to occur.