Wet air containing 4.0 mole% water vapor is passed through a column of calcium chloride pellets. The pellets adsorb 97.0% of the water and none of the other constituents of the air. The column packing was initially dry and had a mass of 3.40kg. Following 5.0 hours of operation, the pellets are reweighed and found to have a mass of3.54kg.
(a)Calculate the molar flow rate (mol/h) of the feed gas and the mole fraction of water vapor in the product gas
fgfe
I want to know how it can be calculated
To solve this problem, we can use the mass balance equation for the water vapor in the feed and product gas.
(a) The mass of water vapor adsorbed by the pellets can be calculated as follows:
Initial mass of pellets = 3.40 kg
Final mass of pellets = 3.54 kg
Mass of water vapor adsorbed = Initial mass - Final mass = 3.40 kg - 3.54 kg = -0.14 kg
Since the pellets adsorb 97.0% of the water vapor, the mass of water vapor in the feed gas is given by:
Mass of water vapor in feed gas = -0.14 kg / 0.97 = -0.1443 kg
Next, we can calculate the number of moles of water vapor in the feed gas using the molecular weight of water (18 g/mol):
Moles of water vapor in feed gas = Mass of water vapor / Molecular weight of water = -0.1443 kg / 0.018 kg/mol = -8.0167 mol
However, the negative sign indicates a loss of water vapor, so we take the absolute value:
Moles of water vapor in feed gas = 8.0167 mol
Now, we can calculate the moles of dry air in the feed gas:
Mole fraction of water vapor = 4.0 mole% = 0.04
Moles of dry air in feed gas = (1 - Mole fraction of water vapor) * Moles of feed gas = (1 - 0.04) * 8.0167 mol = 7.694 mol
Therefore, the molar flow rate of the feed gas is 7.694 mol/h.
The mole fraction of water vapor in the product gas can be calculated using the mass balance for the water vapor:
Mass of water vapor in product gas = Mass of water vapor in feed gas - Mass of water vapor adsorbed = -0.1443 kg - (-0.14 kg) = -0.0043 kg
Again, we take the absolute value due to the negative sign:
Mass of water vapor in product gas = 0.0043 kg
Moles of water vapor in product gas = Mass of water vapor / Molecular weight of water = 0.0043 kg / 0.018 kg/mol = 0.2390 mol
Mole fraction of water vapor in product gas = Moles of water vapor / (Moles of water vapor + Moles of dry air) = 0.2390 mol / (0.2390 mol + 7.694 mol) = 0.0305
Therefore, the mole fraction of water vapor in the product gas is 0.0305.
To solve this problem, we need to use the conservation of mass principle to determine the molar flow rate of the feed gas and the mole fraction of water vapor in the product gas. Here's how you can do it:
Step 1: Calculate the mass of water vapor adsorbed by the calcium chloride pellets:
Initial mass of the column packing = 3.40 kg
Final mass of the column packing = 3.54 kg
Mass of water vapor adsorbed = Initial mass - Final mass
Mass of water vapor adsorbed = 3.40 kg - 3.54 kg
Mass of water vapor adsorbed = -0.14 kg
Step 2: Calculate the number of moles of water vapor adsorbed:
Molar mass of water (H2O) = 18.02 g/mol
Number of moles of water vapor adsorbed = Mass of water vapor adsorbed / Molar mass of water
Number of moles of water vapor adsorbed = (-0.14 kg) / (18.02 g/mol)
Number of moles of water vapor adsorbed = -7.77 x 10^-3 mol
Note: The negative sign indicates that the mass of the column packing increased after adsorption due to the adsorption of water vapor.
Step 3: Calculate the number of moles of water vapor in the original feed gas:
Mole fraction of water vapor in feed gas = 4.0 mole%
Number of moles of water vapor in feed gas = Mole fraction of water vapor in feed gas * Total moles in feed gas
Number of moles of water vapor in feed gas = (4.0/100) * Total moles in feed gas
Step 4: Calculate the molar flow rate of the feed gas:
Since we know that the pellets adsorbed 97.0% of the water vapor, the remaining 3% stayed in the product gas.
Molar flow rate of feed gas = Number of moles of water vapor in feed gas / (1 - 0.03)
Step 5: Calculate the mole fraction of water vapor in the product gas:
Mole fraction of water vapor in product gas = Number of moles of water vapor adsorbed / Total moles in product gas
Now you can plug in the values and calculate the molar flow rate of the feed gas and the mole fraction of water vapor in the product gas.