Final answer:
The molar mass of a vapor is calculated using the Ideal Gas Law, converting given conditions to proper units, then using density, temperature, and pressure to find the number of moles, which is then used to compute the molar mass.
Step-by-step explanation:
The molar mass of a vapor can be calculated using the Ideal Gas Law equation, which relates the pressure, volume, temperature, and moles of a gas. The equation is PV = nRT, where P is pressure, V is volume, n is the amount in moles, R is the gas constant, and T is the temperature in Kelvin.
To find the molar mass (M), we need to rearrange the Ideal Gas Law to solve for n (moles) first and then use the relation n = mass (m) / Molar mass (M). The steps are as follows:
- Convert all measurements to the correct units: temperature to Kelvin and pressure to atmospheres.
- Use the Ideal Gas Law to solve for the number of moles of gas.
- Divide the mass of the gas by the number of moles to determine the molar mass.
Using the given conditions (density = 7.135 g/L, temperature = 12°C = 285.15 K, and pressure = 743 torr = 0.978 atm), we can calculate the molar mass by applying the conversion of density to mass (since density = mass/volume), and then using the Ideal Gas Law:
Molar mass (M) = (mass of the gas, m) / (number of moles, n)
m = density × volume = 7.135 g/L × 1 L = 7.135 g
n = PV / RT = (0.978 atm × 1 L) / (0.08206 L·atm/K·mol × 285.15 K)
M = 7.135 g / n
From the above steps, we can calculate the moles and then determine the molar mass of the vapor.