Match the following
`{:("(i) Entropy of vapourisation ","(a) decreases"),("(ii) K for spontaneous process positive","(b) is always "),("iii Crystalline solid state ","(c) lowest entropy "),("(iv)" DeltaU " in adiabatic expansion of ideal gas ","(d)" (DeltaH_("vap"))/(T_(b))):}`

Answer

To solve the matching question, we need to analyze each statement and match it with the correct option. Let's break it down step by step.

### Step 1: Analyze Each Statement

1. **Entropy of vaporization**: This refers to the change in entropy when a substance transitions from a liquid to a vapor. Generally, the entropy of vaporization is associated with the heat absorbed during the phase change and is typically expressed as ΔH_vap/T_b, where ΔH_vap is the enthalpy of vaporization and T_b is the boiling temperature.

2. **K for spontaneous process positive**: The equilibrium constant (K) for a spontaneous process is always greater than 1, which indicates that the reaction favors the formation of products.

3. **Crystalline solid state**: Crystalline solids have a well-ordered structure, which typically corresponds to lower entropy compared to liquids and gases, as the molecules are more constrained in their positions.

4. **ΔU in adiabatic expansion of ideal gas**: In an adiabatic process, there is no heat exchange with the surroundings, and the internal energy change (ΔU) is equal to the work done on or by the system.

### Step 2: Match Each Statement with Its Correct Option

- **(i) Entropy of vaporization**: This corresponds to **(d) ΔH_vap/T_b**. The entropy of vaporization is calculated using this formula.

- **(ii) K for spontaneous process positive**: This corresponds to **(b) is always**. The equilibrium constant for a spontaneous process is always positive.

- **(iii) Crystalline solid state**: This corresponds to **(c) lowest entropy**. Crystalline solids have the lowest entropy due to their ordered structure.

- **(iv) ΔU in adiabatic expansion of ideal gas**: This corresponds to **(a) decreases**. In an adiabatic expansion, the internal energy decreases as the gas does work on the surroundings.

### Final Matching

1. (i) Entropy of vaporization - (d) ΔH_vap/T_b
2. (ii) K for spontaneous process positive - (b) is always
3. (iii) Crystalline solid state - (c) lowest entropy
4. (iv) ΔU in adiabatic expansion of ideal gas - (a) decreases

### Summary of Answers

- (i) - (d)
- (ii) - (b)
- (iii) - (c)
- (iv) - (a)

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