In an experiment, a mixture of two gases occupies a volume of 3.00 L at a temperature of 22.5 degree centigrade. The mixture contains 14.0 g of water, 11.5 g of oxygen, and 37.3 g of nitrogen. Calculate the total pressure and the partial pressure of each gas?
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Do we assume the H2O is liquid and it occupies no volume. Convert grams of each gas to mols (mols = grams/molar mass) and use PV = nRT to calculate pressure of each gas. Sum of the partial pressures will give Ptotal.
To calculate the total pressure and the partial pressure of each gas in the mixture, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
The first step is to calculate the number of moles for each gas. We can do this by dividing the mass of each gas by its molar mass.
For water (H₂O):
Molar mass of H₂O = 2(1.008 g/mol) + 16.00 g/mol = 18.016 g/mol
Number of moles of H₂O = mass / molar mass = 14.0 g / 18.016 g/mol
For oxygen (O₂):
Molar mass of O₂ = 2(16.00 g/mol) = 32.00 g/mol
Number of moles of O₂ = mass / molar mass = 11.5 g / 32.00 g/mol
For nitrogen (N₂):
Molar mass of N₂ = 2(14.01 g/mol) = 28.02 g/mol
Number of moles of N₂ = mass / molar mass = 37.3 g / 28.02 g/mol
Next, we can calculate the total number of moles for all the gases by summing up the moles of each gas.
Total moles = moles of H₂O + moles of O₂ + moles of N₂
Once we have the total moles, we can use the ideal gas law equation to calculate the total pressure.
Total pressure = (Total moles * R * T) / V
Now, to find the partial pressure of each gas, we can use the mole fraction of each gas, which is the ratio of the moles of each gas to the total moles.
Mole fraction = moles of a particular gas / total moles
Partial pressure of a gas = mole fraction * total pressure
Finally, plug in the values and solve the equation to get the total pressure and the partial pressure of each gas in the mixture.