Problem 11 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

You are handed a bottle labelled 'xylene' (dimethylbenzene). A gas chromatogram gives three peaks corresponding to the \(1,2-,\) the \(1,3-,\) and the 1,4 -isomers with peak areas in the ratio of \(143.1: 9.5: 6.4,\) respectively. Assuming that the detector responds equally to each isomer, calculate the composition of the xylene. (Section 11.3 )

Step-by-Step Solution

Answer

The composition of xylene is approximately 90.0% 1,2-isomer, 6.0% 1,3-isomer, and 4.0% 1,4-isomer.

Step 1: Identify the Ratio of Peak Areas

The given gas chromatogram provides the peak areas of the 1,2-, 1,3-, and 1,4-isomers in the ratio of \(143.1:9.5:6.4\). These values represent the relative abundance of each isomer within the xylene mixture.

Step 2: Calculate Total Area

To find the total area, sum up the peak areas: \(143.1 + 9.5 + 6.4 = 159.0\). This total represents the sum of all isomer contributions in the xylene sample.

Step 3: Determine the Fraction of Each Isomer

Calculate the fraction of each isomer by dividing the peak area of each isomer by the total area. - For 1,2-isomer: \(\frac{143.1}{159.0}\) - For 1,3-isomer: \(\frac{9.5}{159.0}\)- For 1,4-isomer: \(\frac{6.4}{159.0}\)

Step 4: Calculate the Composition Percentage

Multiply each fraction by 100 to convert into a percentage:- For 1,2-isomer: \(\frac{143.1}{159.0} \times 100 \approx 89.97\%\) - For 1,3-isomer: \(\frac{9.5}{159.0} \times 100 \approx 5.97\%\)- For 1,4-isomer: \(\frac{6.4}{159.0} \times 100 \approx 4.03\%\)

Key Concepts

Xylene

Xylene, also known as dimethylbenzene, is a clear, colorless, flammable liquid commonly used as a solvent in the printing, rubber, and leather industries. It is also widely utilized as a precursor in the production of certain chemicals and materials. Xylene consists of a benzene ring with two methyl groups attached, and it exists in three different isomeric forms: ortho-xylene (1,2-dimethylbenzene), meta-xylene (1,3-dimethylbenzene), and para-xylene (1,4-dimethylbenzene). Each form differs by the position of the methyl groups on the benzene ring. These isomers have slightly different chemical properties, affecting how they interact in various industrial and chemical applications, making understanding their composition crucial.

Isomer Analysis

Isomer analysis is pivotal in the study of chemicals that can exist in multiple forms with the same molecular formula but different structural arrangements. In the context of xylene, it involves identifying and quantifying the different isomers. This analysis helps determine the exact makeup and potential uses for a xylene sample. Techniques like gas chromatography (GC) are employed for this purpose, as they can separate the different isomers present in a sample based on their chemical properties. Through isomer analysis, researchers and industry professionals can ensure quality and tailor the properties of chemicals to specific needs, promoting efficiency and efficacy in their applications.

Chromatographic Peak Area

In gas chromatography (GC), the peak area is directly proportional to the concentration of a compound in a mixture. When a sample is analyzed, it generates peaks on a chromatogram, each representing a distinct compound. The size of these peaks (their areas) corresponds to the abundance of the specific compounds present. The chromatographic peak area is particularly useful because it provides a quantitative measure from which the relative abundance of each component, such as xylene isomers, can be deduced. By comparing these areas, one can determine the composition of a mixture, helping to identify which compounds are more prevalent.

Composition Calculation

Composition calculation involves determining the exact percentages of each component within a mixture. After obtaining peak areas via gas chromatography, the process starts with summing up all individual peak areas to find the total area. Next, the fraction of each component is calculated by dividing its peak area by the total area, a process shown in the xylene exercise. Finally, each fraction is multiplied by 100 to convert these values into percentages, revealing the proportional composition of each isomer. This calculation helps in understanding not just what is present in a sample, but in what amounts, thereby influencing product formulation and quality control.