Answer:
To calculate the amount of oxygen released from water when the atmospheric pressure changes, we need to consider Henry's Law, which describes the relationship between the partial pressure of a gas and its concentration in a liquid.
Henry's Law is given by the equation:
P = K * C
Where:
P is the partial pressure of the gas above the liquid
K is Henry's law constant for the specific gas and liquid at a given temperature
C is the concentration of the gas in the liquid
In this case, we're interested in the oxygen (O2) dissolved in water. The Henry's law constant for oxygen in water at 298 K is approximately 0.0334 mol/(L * atm).
Let's calculate the initial concentration of oxygen in water when the pressure is 1.00 atm:
P1 = 1.00 atm
K = 0.0334 mol/(L * atm)
C1 = P1 / K
C1 = 1.00 atm / 0.0334 mol/(L * atm)
C1 ≈ 29.94 mol/L
Now, let's calculate the final concentration of oxygen in water when the pressure decreases to 0.891 atm:
P2 = 0.891 atm
C2 = P2 / K
C2 = 0.891 atm / 0.0334 mol/(L * atm)
C2 ≈ 26.68 mol/L
The change in concentration (∆C) can be calculated as the difference between the initial and final concentrations:
∆C = C2 - C1
∆C ≈ 26.68 mol/L - 29.94 mol/L
∆C ≈ -3.26 mol/L
Since the concentration is negative, it means that oxygen will be released from the water.
Now, we can calculate the amount of oxygen released from the 4.20 L of water in the unsealed container. We can use the equation:
Amount of oxygen released = ∆C * V
Where:
∆C is the change in concentration (-3.26 mol/L)
V is the volume of water (4.20 L)
Amount of oxygen released = -3.26 mol/L * 4.20 L
Amount of oxygen released ≈ -13.67 mol
The negative sign indicates that oxygen is being released. However, it's important to note that a negative number of moles doesn't make physical sense in this context. It suggests that the concentration change is unrealistic or that the assumptions made in the calculation are not valid.