Read the passage given below and answer the following questions:
Nucleophilic substitution reaction of haloalkane can be conducted according to both `S_(N)^(1)` and `S_(N)^(2)` mechanisms. However, which mechanism it is based on is related to such factors as the structure of haloalkane, and properties of leaving group, nucleophilic reagent and solvent.
Influences of halogen : No matter which mechanism the nucleophilic substitution reaction is based on, the leaving group always leave the central carbon atom with electron pair. This is just the opposite of the situation that nucleophilic reagent attacks the central carbon atom with electron pair. Therefore, the weaker the alkalinity of leaving group is , the more stable the anion formed is and it will be more easier for the leaving group to leave the central carbon atom, that is to say, the reactant is more easier to be substituted. The alkalinity order of halogen ion is `I^(-) lt Br^(-) lt Cl^(-) lt F^(-)` and the order of their leaving tendency should be `I^(-) gt Br^(-) gt Cl^(-) gt F^(-)` . Therefore, in four halides with the same alkyl and different halogens, the order of substitution reaction rate is `RI gt RBr gt RCl gt RF` . In addition, if the leaving group is very easy to leave, many carbocation intermediates are generated in the reaction and the reaction is based on `S_(N)^(1)` mechanism. If the leaving group is not easy to leave, the reaction is based on `S_(N)^(2)` mechanism.
Influences of solvent polarity: In `S_(N)^(1)` reaction, the polarity of the system increases from the reactant to the transition state, because polar solvent has a greater stabilizing effect on the transition state than the reactant, thereby reduce activation energy and accelerate the reaction. In `S_(N)^(2)` reaction, the polarity of the system generally does not change from the reactant to the transition state and only charge dispersion occurs. At this time, polar solvent has a great stabilizing effect on Nu than the transition state, thereby increasing activation energy and slow down the reaction rate. For example, the decomposition rate `(S_(N)^(1))` of tertiary chlorobutane in `25^(@)C` water (dielectric constant 79) is 300000 times faster than in ethanol (dielectric constant 24). The reaction rate `(S_(N)^(2))` of 2-bromopropane and NaOH in ethanol containing 40% water is twice slower than in absolute ethanol. In a word, the level of solvent polarity has influence on both `S_(N)^(1)` and `S_(N)^(2)` reactions, but with different results. Generally speaking, weak polar solvent is favorable for `S_(N)^(2)` reaction, while strong polar solvent is favorable for `S_N^(1)` reaction, because only under the action of polar solvent can halogenated hydrocarbon dissociate into carbocation and halogen ion and solvents with a strong polarity is favorable for solvation of carbocation, increasing its stability. Generally speaking, the substitution reaction of tertiary haloalkane is based on `S_(N)^(1)` mechanism in solvents with a strong polarity (for example, ethanol containing water).
(Ding, Y. (2013). A Brief Discussion on Nucleophilic Substitution Reaction on Saturated Carbon Atom. In Applied Mechanics and Materials (Vol. 312, pp. 433-437). Trans Tech Publications Ltd.)
`S_(N)^(1)` mechanism is favoured in which of the following solvents:

Options

A. benzene
B. carbon tetrachloride
C. acetic acid
D. carbon disulphide

Answer

To determine which solvent favors the `S_N^1` mechanism for nucleophilic substitution reactions, we need to analyze the properties of the solvents provided in the question. The `S_N^1` mechanism is favored in polar solvents because they stabilize the carbocation intermediate formed during the reaction.

### Step-by-Step Solution:

1. **Understanding the `S_N^1` Mechanism**:
- The `S_N^1` mechanism involves the formation of a carbocation intermediate after the leaving group departs. This step is crucial because the stability of the carbocation is influenced by the polarity of the solvent.

2. **Identifying the Solvents**:
- We need to evaluate the solvents provided in the question:
- **Benzene (C₆H₆)**: Non-polar solvent with no significant dipole moment.
- **Carbon Tetrachloride (CCl₄)**: Also a non-polar solvent with a zero dipole moment.
- **Acetic Acid (CH₃COOH)**: A polar solvent that can stabilize ions and carbocations due to its ability to donate protons and form hydrogen bonds.
- **Carbon Disulfide (CS₂)**: Non-polar solvent similar to benzene and carbon tetrachloride.

3. **Evaluating Solvent Polarity**:
- The `S_N^1` mechanism requires a polar solvent to stabilize the carbocation. Among the listed solvents, only acetic acid is polar.

4. **Conclusion**:
- Since acetic acid is the only polar solvent among the options, it is the solvent that favors the `S_N^1` mechanism.

### Final Answer:
**Acetic Acid (CH₃COOH)** is the solvent that favors the `S_N^1` mechanism.

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