Trace organic compounds in the atmosphere are first concentrated and then measured by gas chromatography. In the concentration step, several liters of air are pumped through a tube containing a porous substance that traps organic compounds. The tube is then connected to a gas chromatograph and heated to release the trapped compounds. The organic compounds are separated in the column and the amounts are measured. In an analysis for benzene and toluene in air, a \(3.00-\mathrm{L}\) sample of air at \(748\) torr and \(23^{\circ} \mathrm{C}\) was passed through the trap. The gas chromatography analysis showed that this air sample contained \(89.6\) ng benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) and \(153 \mathrm{ng}\) toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right) .\) Calculate the mixing ratio (see Exercise 121 ) and number of molecules per cubic centimeter for both benzene and toluene.

The ideal gas law, expressed as the equation PV = nRT, is a pivotal concept in chemistry that describes the behavior of an ideal gas under varying conditions of pressure (P), volume (V), temperature (T), and amount in moles (n). It hinges on the notion that these four properties are interrelated. For instance, as demonstrated in the exercise solution, the ideal gas law allows us to calculate the number of moles of air in a given volume at a known temperature and pressure. This is essential in atmospheric analysis, such as when assessing the concentration of pollutants using gas chromatography.
By converting known units of pressure to atmospheres (atm) and temperature to Kelvin (K), the ideal gas constant (R), which is 0.0821 L⋅atm⋅K⁻¹⋅mol⁻¹, facilitates the computation of moles of gas present. This step is fundamental for accurate mixing ratio calculations, ensuring precise measurements when analyzing atmospheric samples.

The concept of a mixing ratio is integral in environmental science, particularly when quantifying the concentration of a substance within a mixture. The mixing ratio is defined as the amount of a particular compound relative to the total amount of air in a sample. This can be expressed using the mole ratio, which is the number of moles of the compound divided by the number of moles of air.

Applying the Mixing Ratio in Practice

In the context of atmospheric analysis through gas chromatography, precise mixing ratio calculations can reveal the level of pollutants, like benzene and toluene, within an air sample. After calculating the moles of air with the ideal gas law, as detailed in the original solution, the subsequent step is to determine the moles of the pollutants. The ratio of these respective moles then yields the mixing ratios, pivotal for ascertaining atmospheric pollution levels. Understanding this calculation fosters greater insight into environmental monitoring and the effectiveness of pollutant mitigation strategies.

Avogadro's number (6.022 × 10²³) is a fundamental constant that represents the number of atoms or molecules in one mole of a substance. This immense number plays a critical role in converting between the macroscopic scale of substances we can handle and measure and the microscopic scale of atoms and molecules.

Converting Moles to Molecules

When conducting atmospheric analyses with tools like gas chromatography, Avogadro's number allows us to transition from moles of a substance, which is a rather abstract concept, to something more tangible like the number of molecules present in a given volume. By multiplying the number of moles of a substance, for instance benzene or toluene as shown in the exercise, by Avogadro's number, we can estimate the number of individual molecules in any sample size, providing a microscopic view of chemical quantities.