USING RESPONSE FACTORS In a gas chromatogram, the peak areas are related to the relative percentages of the components in the mixture being analyzed. However, the detector is not equally sensitive to all the compounds eluted. So, the areas under the peaks may not reflect accurate percentages_ Thus, it is necessary to correct the measured areas using response factor. Although it is possible to determine response factors experimentally for different compounds, approximate values are published in the gas chromatography literature. Additionally, response factors can be classified as weigh factors or mole factors. As their names indicate, weight factors enable quantitative analysis of the mixture by weight; whereas mole factors enable analysis of the mol percentages of the components Once the response factor is known; the peak area for each component can be divided by its response factor to obtain a corrected area. This area can then be used to obtain a more accurate estimate of the percentage composition of the mixture: A sample containing ethanol, heptane, benzene, and ethyl acetate was run on mass chromatograph and vielded 4 peaks with the areas (A) shown on the table: The mole factors (M;) for each compound are also given: Based on this information, fill in the missing entries (vellow boxes) in the table: 2 points per box: Total: 30 points: Area (A) Uncorrected % Mole factor Corrected Area (mm?) to one decimal M; to one decimal Compound Mol % Ethanol 44.0 1.39 Heptane 78.0 0.70 Benzene 23.2 1.00 Ethyl acetate 61.9 0.89 Total 207.1
The Correct Answer and Explanation is:
To solve this, we’ll compute the corrected area for each compound using the formula:
Corrected Area=Area (A)Mole factor (Mₙ)\text{Corrected Area} = \frac{\text{Area (A)}}{\text{Mole factor (Mₙ)}}
Then, we calculate the mol % for each component:
\text{Mol %} = \left( \frac{\text{Corrected Area}}{\text{Sum of Corrected Areas}} \right) \times 100
Step-by-step table completion:
| Compound | Area (A) | Mole Factor (Mₙ) | Corrected Area (A/Mₙ) | Mol % (to 1 decimal) |
|---|---|---|---|---|
| Ethanol | 44.0 | 1.39 | 31.7 | 14.5 |
| Heptane | 78.0 | 0.70 | 111.4 | 51.1 |
| Benzene | 23.2 | 1.00 | 23.2 | 10.6 |
| Ethyl acetate | 61.9 | 0.89 | 69.5 | 23.8 |
| Total | 207.1 | — | 235.8 | 100.0 |
Explanation (no em dashes):
In gas chromatography, detectors vary in sensitivity to different chemical compounds. The resulting peak areas do not always accurately reflect the proportions of those compounds in a mixture. That is where response factors come into play. A mole factor is a type of response factor that normalizes detector response per mole of compound.
The corrected area of each peak is computed by dividing the measured area by its mole factor. This corrects for differences in detector response. Once we compute each corrected area, we sum them up to determine the total corrected signal. Each compound’s mol percent is then calculated by expressing its corrected area as a proportion of the total corrected area.
For instance, ethanol’s uncorrected area of 44.0 is divided by its mole factor of 1.39, giving a corrected area of 31.7. Its mol percent is then computed by dividing 31.7 by the total corrected area (235.8) and multiplying by 100, yielding approximately 14.5 percent.
By this method, we ensure that the final composition reflects the true molar distribution of each compound, accounting for the differences in detector sensitivity.
