Question

Following is a structural formula for the tert-butyl cation. (We discuss the formation, stability, and reactions of cations such as this one in Chapter 6.) (a) Predict all \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in this cation. (b) What is the hybridization of the carbon bearing the positive charge? (c) Write a balanced equation to show its reaction as a Lewis acid with water. (d) Write a balanced equation to show its reaction as a Brønsted-Lowry acid with water.

Short answer

Answer: The hybridization of the positively charged carbon in the tert-butyl cation is sp². It can react with water as a Lewis acid, forming a bond with an oxygen atom in water, or as a Brønsted-Lowry acid by transferring a proton (H⁺) from one of the neighboring carbon atoms to the oxygen of the water molecule. The balanced equations for these reactions are: 1. As a Lewis acid: \(\mathrm{C}_{\mathrm{4}} \mathrm{H}_{9}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H} \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{O}^{+}\) 2. As a Brønsted-Lowry acid: \(\mathrm{C}_{\mathrm{4}} \mathrm{H}_{9}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{C}_{\mathrm{4}} \mathrm{H}_{8}\)

Step-by-step solution

1. Identify the tert-butyl cation structure

The tert-butyl cation has the following structure: a central carbon atom (C1) bearing a positive charge, which is bonded to three other carbon atoms (C2, C3, and C4), each of which is bonded to three hydrogen atoms. We can represent the structure as follows: ``` H H \ / H - C2 | H - C1(+) | H - C3 / \ H H ```

2. Predict the C-C-C bond angles

In the given structure, there is one bond angle to be determined: the one between C1, C2, and C3 (or C4). The central carbon atom (C1) has three bonding regions and no lone pairs, so the electronic geometry should be "trigonal planar". According to the Valence Shell Electron Pair Repulsion (VSEPR) theory, the bond angle in a trigonal planar structure is 120 degrees. Therefore, the C-C-C bond angle in the tert-butyl cation is 120 degrees.

3. Determine the hybridization of the positively charged carbon

The positively charged carbon atom (C1) is bonded to three other carbon atoms and has no lone pairs. It has an sp² hybridization, which corresponds to the trigonal planar geometry.

4. Write a balanced equation for its reaction as a Lewis acid with water

As a Lewis acid, the tert-butyl cation will accept an electron pair from water, forming a bond with an oxygen atom. In this reaction, the water molecule acts as a Lewis base. The balanced equation for this reaction is: \(\mathrm{C}_{\mathrm{4}} \mathrm{H}_{9}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H} \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{O}^{+}\)

5. Write a balanced equation for its reaction as a Brønsted-Lowry acid with water

As a Brønsted-Lowry acid, the tert-butyl cation will donate a proton (H⁺) to water, which acts as a Brønsted-Lowry base in this reaction. Since the cation has no hydrogen atoms directly attached to it, a hydrogen atom will be transferred from one of the neighboring carbon atoms (C2, C3, or C4) to the oxygen of the water molecule. The balanced equation for this reaction is: \(\mathrm{C}_{\mathrm{4}} \mathrm{H}_{9}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{C}_{\mathrm{4}} \mathrm{H}_{8}\)