91Ó°ÊÓ

To determine the molar mass of a compound, we need to know the molar masses of the individual elements that make up the compound. Each element has its own unique molar mass, measured in grams per mole (g/mol), which reflects the mass of one mole of atoms of that element.

For example, ethyl mercaptan, represented as \( C_{2}H_{6}S \), consists of carbon (C), hydrogen (H), and sulfur (S). The molar masses are approximately:

• Carbon (C): \(12\, \text{g/mol}\)
• Hydrogen (H): \(1\, \text{g/mol}\)
• Sulfur (S): \(32\, \text{g/mol}\)

To calculate the molar mass of ethyl mercaptan, multiply the molar mass of each element by the number of atoms of that element in the compound, and then sum these values. Thus, the molar mass of ethyl mercaptan is computed as:\[ (2 \times 12\, \text{g/mol}) + (6 \times 1\, \text{g/mol}) + (1 \times 32\, \text{g/mol}) = 62\, \text{g/mol}\]This calculation gives the total mass of one mole of ethyl mercaptan, an important step in converting quantities between moles and grams.

Parts per billion (ppb) is a unit of measurement used to express the concentration of a substance in a solution. It represents one part of the substance per billion parts of the entire mixture, often using grams for convenience in such calculations.

Understanding units like ppb is crucial when dealing with extremely small concentrations, such as detecting trace amounts of ethyl mercaptan in air. In this exercise, we converted from grams per liter (\( g/L \)) to parts per billion, building on how concentration relates to both mass and volume. To achieve this, we first used the known detectability limit of ethyl mercaptan in \( \mu mol/m^{3} \).

To convert this detectability into grams, the molar mass was used. Then, converting cubic meters to liters allowed us to find the measurement in \( g/L \).

Finally, to convert \( g/L \) of ethyl mercaptan to ppb, we account for the density of air by multiplying \( 5.58 \times 10^{-5} \ g/L \) by the standard conversion factor of a billion (as there's no unit change in mass), resulting in \( 67.4 \ ppb \). This unit helps us understand trace concentrations in environmental or laboratory settings.

The concept of density is essential in many scientific and engineering calculations. Density is defined as mass per unit volume, commonly expressed as grams per liter (\( g/L \)) when referring to gases like air. In the context of gases, density can vary with changes in temperature or pressure.

For everyday conditions, we typically use a standardized value which approximates the density of air at room temperature and standard atmospheric pressure. This density is approximately \( 1.2\, \text{g/L} \), a value that simplifies calculations when working with air.

When converting concentrations from grams per cubic meter (\( g/m^3 \)) to parts per billion (ppb), understanding the density of air is a keystone concept. This density factor allows us to bridge the gap between volume-based measures (like liters) and mass-based measures (like grams).

Thus, when converting \(5.58 \times 10^{-5} \ g/L \) to ppb, knowing the density of air as \( 1.2\, \text{g/L} \), helps us precisely express ethyl mercaptan's detectability in air, ensuring our calculations accurately represent real-world conditions.