Question

The number of ethoxy groups \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O}-\right)\) in an organic compound is determined by the following two reactions. $$ \begin{array}{c} \mathrm{R}\left(O \mathrm{CH}_{2} \mathrm{CH}_{3}\right)_{x}+x \mathrm{HI} \longrightarrow \mathrm{R}(\mathrm{OH})_{x}+x \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{I} \\ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{I}+\mathrm{Ag}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{AgI}(s)+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} \end{array} $$ A 36.92 -mg sample of an organic compound with an approximate molecular weight of 176 is treated in this fashion, yielding \(0.1478 \mathrm{~g}\) of \(\mathrm{AgI}\). How many ethoxy groups are there in each molecule of the compound?

Short answer

There are approximately 3 ethoxy groups per molecule of the compound.

Step-by-step solution

Understanding the Problem

We are trying to determine the number of ethoxy groups in a compound using two chemical reactions. These reactions indicate that for each ethoxy group, one mole of silver iodide (AgI) is formed.

Calculate Moles of Silver Iodide

First, calculate the number of moles of AgI formed. Using the given mass of AgI (0.1478 g) and the molar mass of AgI (234.77 g/mol), we calculate the moles of AgI produced. \[ \text{Moles of AgI} = \frac{0.1478 \text{ g}}{234.77 \text{ g/mol}} \approx 6.293 \times 10^{-4} \text{ moles} \]

Determine Moles of Ethoxy Groups

Since each ethoxy group leads to the formation of one mole of AgI, the moles of AgI calculated are equal to the moles of ethoxy groups in the 36.92 mg of the compound. Thus, the moles of ethoxy groups are approximately \(6.293 \times 10^{-4}\).

Find Number of Ethoxy Groups in One Molecule

First, calculate the number of moles of the organic compound in the 36.92 mg sample: \[ \text{Moles of compound} = \frac{36.92 \text{ mg}}{176 \text{ g/mol}} = \frac{36.92 \times 10^{-3} \text{ g}}{176 \text{ g/mol}} \approx 2.098 \times 10^{-4} \text{ moles} \]Since these moles contain \(6.293 \times 10^{-4}\) moles of ethoxy groups, calculate the number of ethoxy groups per molecule by dividing moles of ethoxy groups by moles of compound:\[ \text{Number of ethoxy groups per molecule} = \frac{6.293 \times 10^{-4}}{2.098 \times 10^{-4}} \approx 3 \]

Conclusion

We have determined that there are approximately 3 ethoxy groups per molecule of the compound.

Key concepts

Ethoxy Groups Determination

Determining ethoxy groups in an organic compound involves finding out how many ethoxy groups (\(\mathrm{CH}_{3} \mathrm{CH}_{2}\mathrm{O}-\)) are present in each molecule. This is crucial in understanding the compound's composition and functionality. The procedure typically involves using chemical reactions to encourage the release or transformation of ethoxy groups into a measurable product.
In the provided problem, a sample compound reacts to form silver iodide (AgI) whenever an ethoxy group is displaced. Hence, by measuring the amount of AgI produced, it becomes possible to reverse-calculate the number of ethoxy groups. Such quantitative analysis is invaluable in both research and industry for accurate compound characterization.

Chemical Reactions in Organic Compounds

Analyzing organic compounds involves using specific chemical reactions to dissect complex molecules into measurable parts. Two key reactions help in determining ethoxy groups:

• First Reaction: \(\mathrm{R}(\mathrm{OCH}_2\mathrm{CH}_3)_x + x \mathrm{HI} \to \mathrm{R}(\mathrm{OH})_x + x \mathrm{CH}_3\mathrm{CH}_2\mathrm{I} \)
  Here, iodine from HI replaces the ethoxy group, converting it to ethyl iodide (\(\mathrm{CH}_3\mathrm{CH}_2\mathrm{I}\)).
• Second Reaction: \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{I} + \mathrm{Ag}^+ + \mathrm{H}_2 \mathrm{O} \to \mathrm{AgI}(s) + \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH} \)
  This reaction further pushes the transformation, with silver ions (\(\mathrm{Ag}^+\)) aiding in precipitating silver iodide as a solid for quantitative analysis.

This systematic use of reactions highlights the precision with which reactions manipulate and reveal structured details of organic compounds.

Mole Calculations

Using mole calculations allows chemists to link measurable masses to atomic levels, bridging macroscopic and molecular scales. Moles give a count of particles based on their atomic or molecular weights, expressing them in terms compatible with macroscopic observations.
For the silver iodide formed: \[ \text{Moles of AgI} = \frac{0.1478 \text{ g}}{234.77 \text{ g/mol}} \approx 6.293 \times 10^{-4} \text{ moles} \]
These moles directly correspond to the number of moles of ethoxy groups in the compound since every ethoxy group leads to an equivalent mole of AgI formed.

Molecular Weight in Analysis

Molecular weight plays a crucial role in quantitative analysis. It serves as the bridge linking molecular structure to measurable mass. With molecular weight, one can determine the moles of a substance when its mass is known. This is crucial for calculations in analytical chemistry.
For example, in our compound sample with a molecular weight of 176 g/mol, it is possible to calculate how many moles exist in a known mass:\[ \text{Moles of compound} = \frac{36.92 \text{ mg}}{176 \text{ g/mol}} = \frac{36.92 \times 10^{-3} \text{ g}}{176 \text{ g/mol}} \approx 2.098 \times 10^{-4} \text{ moles} \]
With moles calculated, we determine molecular composition, such as how many functional groups per molecule are present. This is essential for understanding chemical reactivity and properties.