Among the following, which surfactant will form micelles in aqueous solution at the lowest molar concentration at ambient conditions?
(a)`CH_(3)(CH_(2))_(15)N^(o+)(CH_(3))_(3)Br^(Θ)`
(b)`CH_(3)(CH_(2))_(11)OSO_(3)^(Θ)Na^(o+)`
(c)`CH_(3)(CH_(2))_(6)COO^(Θ)Na^(o+)`
(d)`CH_(3)(CH_(12))_(11)N^(o+)(CH_(3))_(3)Br^(Θ)`

Options

A. `CH_(3)(CH_(2))_(15)N^(o+)(CH_(3))_(3)Br^(Θ)`
B. `CH_(3)(CH_(2))_(11)OSO_(3)^(Θ)Na^(o+)`
C. `CH_(3)(CH_(2))_(6)COO^(Θ)Na^(o+)`
D. `CH_(3)(CH_(12))_(11)N^(o+)(CH_(3))_(3)Br^(Θ)`

Explanation

To determine which surfactant will form micelles in aqueous solution at the lowest molar concentration at ambient conditions, we need to analyze the given surfactants based on their molecular structure, particularly focusing on the number of carbon atoms in their hydrophobic tails. The more carbon atoms a surfactant has, the larger its surface area, which typically leads to a lower critical micelle concentration (CMC).

Let's analyze each option step by step:

### Step 1: Analyze the surfactants

1. **Surfactant (a)**: `CH₃(CH₂)₁₅N⁺(CH₃)₃Br⁻`
- Alkyl chain: 15 carbon atoms (from `CH₂` groups) + 3 from `N(CH₃)₃` = 18 carbon atoms total.

2. **Surfactant (b)**: `CH₃(CH₂)₁₁OSO₃⁻Na⁺`
- Alkyl chain: 11 carbon atoms (from `CH₂` groups) + 1 from `CH₃` = 12 carbon atoms total.

3. **Surfactant (c)**: `CH₃(CH₂)₆COO⁻Na⁺`
- Alkyl chain: 6 carbon atoms (from `CH₂` groups) + 1 from `CH₃` + 1 from `COO⁻` = 8 carbon atoms total.

4. **Surfactant (d)**: `CH₃(CH₂)₁₁N⁺(CH₃)₃Br⁻`
- Alkyl chain: 11 carbon atoms (from `CH₂` groups) + 3 from `N(CH₃)₃` = 14 carbon atoms total.

### Step 2: Compare the number of carbon atoms

- Surfactant (a): 18 carbon atoms
- Surfactant (b): 12 carbon atoms
- Surfactant (c): 8 carbon atoms
- Surfactant (d): 14 carbon atoms

### Step 3: Determine the surfactant with the highest number of carbon atoms

From the analysis, surfactant (a) has the highest number of carbon atoms (18). This suggests that it has the largest hydrophobic tail, which will lead to a lower CMC due to its larger surface area.

### Conclusion

Thus, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is **(a) `CH₃(CH₂)₁₅N⁺(CH₃)₃Br⁻`**.

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