Which statements in each of the following paris would you except to have the higher standard molar entropy?
(I) `C_(2)H_(2)(g)` or `C_(2)H_(6)`(g), (II) `CO_(2) (g)` or CO(g), (III) `I_(2)`(s) or `I_(2)` (g)
The correct choice is:

Options

A. `C_(2)H_(2)(g), CO_(2)(g), I_(2)(g)`
B. `C_(2)H_(6)(g), CO(g), I_(2)(g)`
C. `C_(2)H_(2)(g), CO_(2)(g), I_(2)(g)`
D. `C_(2)H_(6)(g),CO_(2)(g), I_(2)(g)`

Explanation

To determine which substance in each pair has the higher standard molar entropy, we need to consider the factors that influence entropy. Entropy is a measure of the disorder or randomness of a system. The key points to consider are:

1. **Phase of Matter**: Gases generally have higher entropy than liquids, and liquids have higher entropy than solids due to the greater freedom of movement of gas molecules compared to those in a solid or liquid state.

2. **Molecular Complexity**: Larger molecules or those with more atoms typically have higher entropy because they can have more ways to arrange themselves and more vibrational modes.

Now, let's analyze each pair step by step:

### Step 1: Compare `C2H2(g)` and `C2H6(g)`
- **C2H2 (Acetylene)** is a smaller molecule with fewer atoms compared to **C2H6 (Ethane)**.
- Ethane (C2H6) has more atoms and thus more ways to distribute energy and more molecular motion.
- **Conclusion**: `C2H6(g)` has a higher standard molar entropy than `C2H2(g)`.

### Step 2: Compare `CO2(g)` and `CO(g)`
- **CO2 (Carbon Dioxide)** is a linear molecule with two oxygen atoms, while **CO (Carbon Monoxide)** is a diatomic molecule.
- CO2 has more atoms and thus more degrees of freedom for molecular motion compared to CO.
- **Conclusion**: `CO2(g)` has a higher standard molar entropy than `CO(g)`.

### Step 3: Compare `I2(s)` and `I2(g)`
- **I2 (Iodine)** in solid form has its molecules closely packed and limited movement, while **I2 in gaseous form** has much more freedom of movement and higher randomness.
- **Conclusion**: `I2(g)` has a higher standard molar entropy than `I2(s)`.

### Final Answer
The correct choices for higher standard molar entropy in each pair are:
1. `C2H6(g)` (higher than `C2H2(g)`)
2. `CO2(g)` (higher than `CO(g)`)
3. `I2(g)` (higher than `I2(s)`)

Thus, the correct answer is:
- **C2H6(g), CO2(g), I2(g)**

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