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Spontaneity in chemical processes tells us whether a process will occur on its own without any external input. To determine spontaneity, we use Gibbs free energy ( \( \Delta G \)). The formula is:

• \( \Delta G = \Delta H - T\Delta S \)
• \( \Delta H \) represents the change in enthalpy, or heat change during the process.
• \( \Delta S \) is the change in entropy, which measures the disorder of the system.
• \( T \) is the temperature in Kelvin.

When \( \Delta G \) is negative, the process is spontaneous, meaning it can happen on its own. If positive, it needs external energy input, and if zero, the system is at equilibrium.

In our exercise, to check if ammonia (\( \text{NH}_{3}(s)\)) melts spontaneously at 200 K, we calculated \( \Delta G \) using the given \( \Delta H \) and \( \Delta S \). Our result was \( -0.13 \text{ kJ/mol} \), indicating that the melting is spontaneous under these conditions.

The melting point is the temperature at which a solid turns into a liquid. At this point, the solid's Gibbs free energy change (\( \Delta G \)) is zero. This equilibrium condition means there's no net energy input needed for the phase change.

To find this point, we start with the equation:

• \( \Delta G = \Delta H - T\Delta S = 0 \)

Rearranging gives:

• \( T = \frac{\Delta H}{\Delta S} \)

Using the values provided for ammonia: \( \Delta H = 5.65 \text{ kJ/mol} \) and \( \Delta S = 28.9 \times 10^{-3} \text{ kJ/K mol} \), we calculate the approximate melting point. By plugging into the formula, we find the melting point to be about 195.5 K.

Understanding enthalpy and entropy is vital in predicting chemical behavior. Enthalpy ( \( \Delta H \)) is about the heat absorbed or released in a reaction. It gives insight into the energy changes involving bonds breaking or forming. When substances change phases, \( \Delta H \) often helps determine whether heat is needed or provided.

Entropy ( \( \Delta S \)) measures a system's disorder. A high \( \Delta S \) indicates a tendency towards increased disorder or randomness. The melting of a solid generally leads to a higher entropy since the molecules in a liquid have more freedom to move.

Together, these concepts combined with temperature in the Gibbs free energy equation help us predict the spontaneity of a process. In the case of ammonia, looking at both \( \Delta H \) and \( \Delta S \) in the context of the right temperature was essential to understanding when and why its melting process is spontaneous.