Question

For the monochlorination of hydrocarbons, the following ratio of reactivities has been found: \(3^{\circ}>2^{\circ}>\) \(1^{\circ}, \quad 4.3: 3: 1 . \quad\) How many different monochloro derivatives of 2 -methylbutane are possible, and what percentage of each would you expect to find?

Short answer

There are 5 different possible monochloro derivatives of 2 -methylbutane. The expected percentages are approximately 46.63% for monochlorination on \(\,^1H\), 31.09% on \(\,^2H\), and 22.28% on \(\,^3H\).

Step-by-step solution

Identify possible positions for Chlorine

There are five potential sites for chlorination of 2-methylbutane. Three of these are \(\,^1H\,\) positions, one is a \(\,^2H\,\) position, and one is a \(\,^3H\,\) position.

Consider reactivity ratios and calculate numbers of hydrogen

We're told the reactivity ratios are \(4.3: 3: 1\) for \(\,^3H\), \(\,^2H\), and \(\,^1H\) respectively. Now we can calculate the number of each type of hydrogen: there are 9 \(\,^1H\)'s, 2 \(\,^2H\)'s, and 1 \(\,^3H\).

Calculate the total reactivity

The sum of the total reactivities can be calculated as follows: \( (9 × 1) + (2 × 3) + (1 × 4.3) = 9 + 6 + 4.3 = 19.3 .\) This is the sum of all individual reactivities, which we will use to determine the percentages.

Determine percentages for each type

Divide each individual reactivity by the total reactivity, then multiply the result by 100% to get the percentage. For \(\,^1H\): \( (9 × 1 / 19.3) × 100% = 46.63%\), for \(\,^2H\): \( (2 × 3 /19.3 ) × 100% = 31.09%\), and for \(\,^3H\): \( (1 × 4.3 / 19.3) × 100% = 22.28% \). Remember to perform each step of the mathematical calculation carefully.

Determine the number of different monochloro derivatives and summarize results

The number of different monochloro derivatives of 2-methylbutane is equal to the number of unique sites for chlorination, which is 5. Review the calculations to confirm the percentages for each derivative.

Key concepts

Reactivity ratios

In monochlorination reactions, understanding reactivity ratios is essential for predicting the outcome. Reactivity ratios allow us to compare the likelihood of chlorine atoms reacting with different types of hydrogen atoms in a molecule. In this context, the order of reactivity is tertiary (\(3^{\circ} > 2^{\circ} > 1^{\circ}\)), meaning tertiary hydrogens are most reactive, followed by secondary, and then primary. The specific reactivity ratios given are 4.3:3:1. This means that a chlorine atom is 4.3 times more likely to react with a tertiary hydrogen than with a primary one. These ratios help determine how likely each possible substitution is, influencing both the types and amount of the chlorinated products formed.
Each type of hydrogen in a molecule contributes to its overall chemical behavior. By understanding how each hydrogen type reacts based on these ratios, we can accurately predict the percentages of different chlorinated derivatives formed in a monochlorination reaction.

Chlorination sites

In 2-methylbutane, identifying chlorination sites is the first step to understanding its derivatives. Each carbon-hydrogen bond is a potential site for chlorine to attach during monochlorination. For 2-methylbutane, there are three types of hydrogen: primary, secondary, and tertiary. Primary hydrogens result from carbon atoms that are attached to only one other carbon, secondary from those attached to two, and tertiary from those attached to three.
2-Methylbutane has the following possible chlorination sites:

• Three primary (\(1^{\circ}\)) hydrogens
• Two secondary (\(2^{\circ}\)) hydrogens
• One tertiary (\(3^{\circ}\)) hydrogen

Considering these sites allows chemists to predict the number of distinct monochloro derivatives. Each unique site corresponds to a potential different product, so careful assessment of these sites is crucial for accurate product prediction.

2-methylbutane derivatives

The main focus of understanding the chlorination of 2-methylbutane is identifying its various monochloro derivatives. When 2-methylbutane reacts with chlorine, each distinct type of hydrogen reacts differently, producing unique chlorinated products.
Five possible derivatives exist because of the molecule's structure and the presence of the:

• Three types of primary hydrogens
• Two types of secondary hydrogens
• One type of tertiary hydrogen

Recognizing these different sites helps in predicting the possible outcomes when monochlorinating this hydrocarbon. The interplay between the molecule's structure and the reactivity ratios gives rise to the distinct set of chlorinated derivatives. Therefore, knowing these variants is critical in studying the composition of organic compounds.

Hydrogen reactivity

In determining the expected distribution of monochloro products, the reactivity of hydrogen atoms plays a vital role. The different types of hydrogens (\(1^{\circ}\), \(2^{\circ}\), \(3^{\circ}\)) each exhibit distinct reactivities. These reactivities determine the likelihood that a hydrogen atom in 2-methylbutane will be replaced by a chlorine atom.
The reactivity of each hydrogen type is derived from the following:

• Tertiary hydrogens (\(3^{\circ}\)) are more reactive, leading to a higher likelihood of substitution, with a specific reactivity of 4.3
• Secondary hydrogens (\(2^{\circ}\)) are moderately reactive at 3
• Primary hydrogens (\(1^{\circ}\)) are least reactive at 1

A precise calculation of these reactivities allows for determining the percentage of each monochloro derivative. Calculating the total reactivity helps in quantifying these percentages, making it possible to predict the expected distribution of products within a reaction.