calculate the mass of water contained in 4.021 m^3
of saturated air at
27 ºCgiven that the saturate
d vapour pressure of water at 27 ºC is 3.53 kPa.
(RMM of water is 18.02, R = 8.314 J K-1 mol^-1
Use PV = nRT and solve for n = number of mols. You must convert cubic meters to L. Then n = grams/molar mass. You know molar mass and n, solve for grams.
To calculate the mass of water contained in the given volume of saturated air at a certain temperature, we need to determine the amount of water vapor in the air, and then convert it to mass.
1. Determine the partial pressure of water vapor:
The partial pressure of water vapor can be calculated using the saturation vapor pressure at the given temperature. In this case, the saturation vapor pressure of water at 27 ºC is given as 3.53 kPa.
2. Use the ideal gas law to find the amount of water vapor:
The ideal gas law equation is: PV = nRT, where P is the pressure, V is the volume, n is the amount of gas in moles, R is the gas constant, and T is the temperature in Kelvin.
Rearranging the equation to solve for n, we get: n = PV / RT.
Substituting the values:
n = (3.53 kPa) * (4.021 m^3) / [(8.314 J K-1 mol^-1) * (27 ºC + 273.15 K)]. (Note that we added 273.15 to convert Celsius to Kelvin)
Calculating this expression will give us the amount of water vapor in moles.
3. Convert moles of water vapor to mass:
To convert moles to mass, we need to use the molar mass of water, which is 18.02 g/mol.
So, mass of water = (amount of water vapor in moles) * (molar mass of water).
Finally, calculate the mass of water using the values obtained from the previous steps.