Match the following processes with entropy change :
`{:("Reaction ", "Entropy change"),("(i) A liquid vapourises " ,"(a)" DeltaS=0),("(ii) Reaction is non-spontaneous at all temperatures and " DeltaH "is positive","(b)" DeltaS = "Positive"),("(iii) Adiabetic reversible expansion of an ideal gas","(c)" DeltaS= "negative"):}`

Answer

To solve the problem of matching the processes with their corresponding entropy changes, we will analyze each process step by step.

### Step 1: Analyze the first process - "A liquid vapourises"
- When a liquid vaporizes, it transitions from a more ordered state (liquid) to a less ordered state (gas). This increase in disorder or randomness corresponds to an increase in entropy.
- Therefore, the entropy change (ΔS) for this process is **positive**.

**Match:** (i) A liquid vapourises → (b) ΔS = Positive

### Step 2: Analyze the second process - "Reaction is non-spontaneous at all temperatures and ΔH is positive"
- A reaction that is non-spontaneous at all temperatures implies that the Gibbs free energy change (ΔG) is positive. According to the Gibbs free energy equation:
\[ ΔG = ΔH - TΔS \]
For ΔG to be positive while ΔH is also positive, ΔS must be negative. This is because a negative ΔS would make the term -TΔS positive, which could offset the positive ΔH, leading to a positive ΔG.
- Therefore, the entropy change (ΔS) for this process is **negative**.

**Match:** (ii) Reaction is non-spontaneous at all temperatures and ΔH is positive → (c) ΔS = Negative

### Step 3: Analyze the third process - "Adiabatic reversible expansion of an ideal gas"
- In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). For an ideal gas undergoing a reversible adiabatic expansion, the change in entropy (ΔS) is zero because the process is reversible and no heat is transferred.
- Therefore, the entropy change (ΔS) for this process is **zero**.

**Match:** (iii) Adiabatic reversible expansion of an ideal gas → (a) ΔS = 0

### Final Matches:
1. (i) A liquid vapourises → (b) ΔS = Positive
2. (ii) Reaction is non-spontaneous at all temperatures and ΔH is positive → (c) ΔS = Negative
3. (iii) Adiabatic reversible expansion of an ideal gas → (a) ΔS = 0

### Summary of Matches:
- (i) → (b)
- (ii) → (c)
- (iii) → (a)