Calculate the mass of oxygen (in mg) dissolved in a 5.00 L bucket of water exposed to a pressure of 1.13 atm of air. Assume the mole fraction of oxygen in air to be 0.21 given that kH for O2 is 1.3×10-3 M/ atm at this temperature
To calculate the mass of oxygen dissolved in water, we can use Henry's law equation:
C = kH * P
Where:
C is the concentration of dissolved gas in terms of moles per liter (M)
kH is the Henry's law constant (M/atm)
P is the partial pressure of the gas (atm)
First, we need to calculate the partial pressure of oxygen (O2) in the air. Since the mole fraction is given as 0.21, we can determine the partial pressure using the ideal gas law:
PV = nRT
Where:
P is the pressure (atm)
V is the volume (L)
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature (in K)
Rearranging the equation to solve for n, we have:
n = PV / RT
n = (1.13 atm)(0.21)(5.00 L) / (0.0821 L·atm/mol·K)(298 K)
n ≈ 0.4979 mol
Next, we can calculate the concentration of dissolved oxygen using the Henry's law equation:
C = kH * P
C = (1.3 × 10^-3 M/atm)(0.4979 mol)
C ≈ 6.4747 × 10^-4 M
Finally, we can calculate the mass of oxygen dissolved in the water:
mass = concentration × volume × molar mass
mass = (6.4747 × 10^-4 M)(5.00 L)(32 g/mol)(10^-3 g/mg)
mass ≈ 1.0373 mg
Therefore, the mass of oxygen dissolved in the 5.00 L bucket of water is approximately 1.0373 mg.