By calculating \(\Delta S_{\text {univ }}\) at each temperature, determine if the melting of 1 mole of \(\mathrm{NaCl}(s)\) is spontaneous at 500 \(^{\circ} \mathrm{C}\) and at \(700^{\circ} \mathrm{C}\). $$S_{\mathrm{NaCl}(s)}^{\circ}=72.11 \frac{\mathrm{J}}{\mathrm{mol} \cdot \mathrm{K}} \quad S_{\mathrm{NaCl}(l)}^{\circ}=95.06 \frac{\mathrm{J}}{\mathrm{mol} \cdot \mathrm{K}} \quad \Delta H_{\mathrm{fusion}}^{\circ}=27.95 \mathrm{kJ} / \mathrm{mol}$$ What assumptions are made about the thermodynamic information (entropy and enthalpy values) used to solve this problem?

When studying thermodynamics, we encounter the concept of 'entropy change', symbolized as ewline ewline ewline ewline ewline ewline ewline. Entropy, often referred to as ewline, is a measure of the randomness or disorder within a system. The entropy change of a system during a process is an important factor in determining the spontaneity of the process. A positive entropy change ewline ewline ewline ewline indicates that disorder has increased, which is often favorable in natural processes.ewline ewline ewline ewline ewline In the Melting of NaCl exercise, we observe that the entropy of the system increases when solid NaCl turns into liquid NaCl. After calculating ewline for both system and surroundings, we combine them to assess the total entropy change of the universe. If this value is positive, the melting is deemed spontaneous at that particular temperature.

The enthalpy of fusion, ewline ewline ewline ewline , is the energy required to change a substance from solid to liquid at its melting point. This thermodynamic quantity is significant in calculating entropy change of the surroundings. It represents the heat absorbed per mole when a solid melts, under constant pressure. In our NaCl example, the enthalpy of fusion is used to determine the entropy change of the surroundings, ewline , by the formula: ewline ewline ewline ewline. Understanding the enthalpy of fusion is critical in predicting whether a phase change will be spontaneous under given conditions.

Gibbs free energy, symbolized by ewline ewline ewline ewline, is a pivotal concept in chemical thermodynamics that combines entropy and enthalpy to predict the spontaneity of a process. The Gibbs free energy equation, ewline, where ewline is enthalpy change and ewline is absolute temperature, allows us to determine whether a process will occur spontaneously. A negative ewline ewline ewline ewline value signifies a spontaneous process at constant temperature and pressure. Although the melting of NaCl problem doesn't directly calculate Gibbs free energy, understanding this concept enriches our grasp on the principles that govern chemical reactions and phase changes.

Chemical thermodynamics delves into the energy changes that accompany chemical reactions and phase transitions. It is the backbone of understanding how different variables such as temperature, pressure, and volume affect a system's spontaneity.ewline ewline ewline ewline ewline The principles of chemical thermodynamics are employed to deduce whether the melting of NaCl is spontaneous. This entails the use of entropy, enthalpy, and Gibbs free energy concepts. Students often assume that temperature is the only driving force for spontaneity, but chemical thermodynamics teaches us that entropy change also plays an essential role. By grasping the interplay between these thermodynamic quantities, students can better appreciate the conditions under which chemical reactions and phase changes occur.