Question

2-Methylpropane (containing traces of 2-methylpropene) is converted by a large excess of deuteriosulfuric acid \(\left(\mathrm{D}_{2} \mathrm{SO}_{4}\right)\) rather rapidly to 2 -methylpropane with only nine deuteriums. a. Write a polar mechanism for this hydrogen-exchange reaction that is in harmony with the known chemical properties of sulfuric acid and that predicts exchange of no more than nine of the ten hydrogens of 2 -methylpropane. b. Explain how 2-methylpropane-D \(_{9}\) can be formed more rapidly than 2 -methylpropane- \(\mathrm{D}_{n}\) with \(n<9\) in the early stages of the reaction.

Short answer

The reaction exchanges nine hydrogens due to carbocation-mediated deuterium exchange, with rapid conversion in an excess of \( D_2SO_4 \).

Step-by-step solution

Understanding Structure and Reactivity

2-Methylpropane (isobutane) has the formula \( C_4H_{10} \). The molecule contains 9 hydrogen atoms on the three methyl groups and 1 hydrogen on the central methine carbon. Traces of 2-methylpropene could enhance reactivity in the presence of acids due to the alkene's ability to form carbocations.

Polar Mechanism Initiation

In the presence of deuteriosulfuric acid \( \left( D_2SO_4 \right) \), sulfuric acid can donate a \( D^+ \) (deuteron) to form a carbocation \((CH_3)_3C^+ \) from 2-methylpropene. The carbocation is a highly reactive intermediate that can lead to hydrogen (or deuterium in this case) exchange.

Deuterium Exchange Process

The carbocation \((CH_3)_3C^+ \) formed interacts with the deuterated acid causing hydrogen atoms at the methyl groups to undergo sequential deuterium exchange involving reversible deuterium uptake and hydronium release by the repeated addition-elimination through the formation and stabilization of alkenes.

Limitation to Nine Deuteriums

Only the methyl hydrogens (9 in total) are involved in this exchange due to their position in the transition states and their ability to stabilize carbocations during deuterium exchange. The center carbon holding one hydrogen is sterically hindered and less reactive to interconversion during the reaction.

Kinetic Preference for Rapid Formation

Initially, in the presence of an excess of deuteriosulfuric acid, 2-methylpropane-D \(_9\) is formed more rapidly because the carbocation formation and subsequent deuterium exchange processes are fast and localized to the 9 exchangeable hydrogens. The rapid reaction in early stages ensures more hydrogens are replaced quickly, saturating the possible sites before other slower processes equilibrate.

Key concepts

Hydrogen-Deuterium Exchange

Hydrogen-deuterium exchange is a fascinating reaction mechanism frequently observed in organic chemistry. It involves the replacement of hydrogen atoms in a molecule with their heavier isotope, deuterium. In the case of 2-methylpropane, deuteriosulfuric acid \( (D_2SO_4) \) provides a source of deuterons \( (D^+) \) that replace the hydrogen atoms.

• The key step involves the formation of a reactive intermediate known as a carbocation.
• This is initiated when a deuteron is added to form a transient carbocation, facilitating subsequent deuterium incorporation.

Only nine out of the ten hydrogens in 2-methylpropane are replaceable due to their location on the methyl groups which can stabilize the carbocation. The hydrogen on the central methine carbon is not exchanged due to steric hindrance, making it less accessible. This results in a limited exchange pattern, emphasizing the molecule's selective reactivity.

Carbocation Reactions

Carbocations are positively charged carbon species that play a central role in many organic reactions, especially in hydrogen-deuterium exchange. When a molecule like 2-methylpropene forms a carbocation through the action of an acid, it becomes highly reactive. This process:

• Occurs when the double bond of the alkene donates electrons to the incoming deuterium, forming the carbocation.
• Sets up the molecule for a sequence of transformations where hydrogen atoms can be swapped with deuterium.

The stability of the carbocation determines the reaction path and efficiency. In this scenario, the tertiary structure of \((CH_3)_3C^+\) carbocation is notably stable, facilitating fast deuterium exchange primarily at the methyl hydrogens while leaving the central methine hydrogen unchanged. This alteration often results in a more rapid incorporation of deuterium into positions that stabilize the carbocation.

Sulfuric Acid Reactivity

Sulfuric acid, especially in its deuterated form \((D_2SO_4)\), is a potent acid used in facilitating the hydrogen-deuterium exchange reaction. Its role in the reaction is multifaceted:

• It acts as a source of \(D^+\) ions, or deuterons, that are necessary for initiating exchange.
• It helps stabilize carbocations formed during the reaction by its ability to donate deuterons and subsequently partake in protonation-deprotonation cycles.

The presence of sulfuric acid greatly influences the kinetics and outcome of the reaction by ensuring that the exchange can proceed quickly and efficiently. By providing a robust acidic environment, the reaction drives towards rapid exchange of the nine accessible methyl hydrogens.

Alkane Reactivity

Understanding alkane reactivity, as seen in 2-methylpropane, helps clarify why only specific hydrogens are exchanged in a hydrogen-deuterium exchange. Alkanes are typically quite stable, lacking a functional group that participates easily in reactions under normal conditions. However, when an acid such as deuteriosulfuric acid is introduced:

• The normally unreactive alkane (2-methylpropane) becomes susceptible to deuterium exchange at its more reactive sites, such as the methyl group hydrogens.
• The selective reactivity is influenced by the molecule's ability to form and stabilize a carbocation, which is crucial for the exchange to take place.

This specific reactivity pattern underlines that only hydrogens capable of stabilizing charge during the transition state, such as those on the methyl groups, participate in the exchange process, leaving the central methine hydrogen largely untouched by the reaction dynamics.