(b) Calculate the molar mass of a vapor that has a density of 7.135 g>L at 12 °C and 99.06 kPa.

Verified step by step guidance

1. Step 1: Convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = °C + 273.15.
2. Step 2: Convert the pressure from kilopascals to atmospheres. The conversion factor is 1 atm = 101.325 kPa.
3. Step 3: Use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. However, we need to rearrange the equation to solve for molar mass. The molar mass (M) is the mass (m) divided by the number of moles (n), so we can substitute n = m/M into the ideal gas law to get PM = mRT/V.
4. Step 4: We know that density (d) is mass (m) divided by volume (V), so we can substitute m = dV into the equation to get PM = dRT.
5. Step 5: Solve the equation for molar mass (M). The final rearranged equation should be M = dRT/P.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions and is used to derive the molar mass of a gas from its density, pressure, and temperature.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical concept in stoichiometry and helps in converting between the mass of a substance and the number of moles, which is necessary for calculations involving gases and their properties.

Density of Gases

Density is defined as mass per unit volume (g/L for gases). For gases, density can vary with temperature and pressure, and it is used in conjunction with the Ideal Gas Law to calculate molar mass. Understanding how to manipulate density in gas calculations is crucial for solving problems related to vapor properties.