Final answer:
To calculate the mass and volume of N₂ gas released as a diver surfaces, we can use the ideal gas law equation. Given the initial conditions and the partial pressure of N₂, we can calculate the final pressure. Using this final pressure, we can find the final number of moles of N₂ and then calculate the mass of the released gas. However, in this scenario, there is no N₂ gas released, resulting in a mass of 0 g and a volume of 0 L.
Step-by-step explanation:
To calculate the mass and volume of N₂ gas released by a diver as they surface, we need to use the ideal gas law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Given the initial conditions:
P(initial) = 4.0 atm
V = 5.0 L
n(initial) = 0.00056 mol/L * 5.0 L = 0.0028 mol
T = 37 °C + 273.15 = 310.15 K
We can rearrange the ideal gas law equation to solve for n:
n(final) = (P(final) * V) / (R * T)
Where P(final) is the final pressure when the diver surfaces.
Now, we can calculate the final pressure using the given partial pressure of N₂ at atmospheric pressure:
P(final) = P(N2) * P(atm)
Plugging in the values:
P(final) = 0.80 atm * 4.0 atm = 3.20 atm
Finally, we can calculate the final number of moles of N₂ :
n(final) = (3.20 atm * 5.0 L) / (0.0821 L·atm/mol·K * 310.15 K) ≈ 0.062 mol
The mass of the N₂ gas released is calculated as the difference between the initial and final number of moles:
Mass = (n(initial) - n(final)) * molar mass of N₂
Substituting the values:
Mass = (0.0028 mol - 0.062 mol) * 28.0134 g/mol ≈ -1.664 g
Since the mass cannot be negative, we can conclude that there was no N₂ gas released as the diver surfaced. Therefore, the volume of N₂ gas released is 0 L.