A concentration of \(8.00 \times 10^{2}\) ppm by volume of \(\mathrm{CO}\) is considered lethal to humans. Calculate the minimum mass of CO in grams that would become a lethal concentration in a closed room \(17.6 \mathrm{~m}\) long, \(8.80 \mathrm{~m}\) wide, and \(2.64 \mathrm{~m}\) high. The temperature and pressure are \(20.0^{\circ} \mathrm{C}\) and \(756 \mathrm{mmHg}\), respectively.

Understanding parts per million (ppm) concentration is essential when dealing with dilute substances, such as pollutants in the air or solutes in a solution. PPM is a unit of measurement that describes the number of parts of a substance found within a million parts of a particular medium, typically used when the concentrations are very low.

For instance, a concentration of 800 ppm indicates that for every million parts of air, there are 800 parts of carbon monoxide (CO). When calculating the mass of CO to determine a lethal concentration, we multiply the total volume of air by the ppm value divided by a million to find the volume of CO. This step is crucial because it allows us to link the ppm concentration to the volume measurements we have, which can then be converted into a mass using the molar mass of the substance.

The ideal gas law, represented by the equation \(PV = nRT\), where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles of gas, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin, is a fundamental equation in chemistry. It relates the physical properties of an ideal gas in a closed system.

In this calculation, we are using the ideal gas law to determine the number of moles of air (\