91Ó°ÊÓ

At ordinary body temperature and atmospheric pressure, the solubility of Nâ‚‚ is given as 0.015 g/L. We need to convert the mass of Nâ‚‚ into moles. To do that, we can use the molar mass of Nâ‚‚, which is 28 g/mol. Number of moles = (Mass of Nâ‚‚) / (Molar mass of Nâ‚‚) So, Number of moles = \(\frac{0.015 \, \text{g}}{28 \, \text{g/mol}}\)

According to Henry's law, the solubility of a gas is directly proportional to the partial pressure of the gas. Since the pressure increases from 1 atm to 4 atm, the solubility of N₂ will also increase proportionally. Solubility at 4 atm = Solubility at 1 atm × (Pressure at 4 atm / Pressure at 1 atm) So, Solubility at 4 atm = \(\frac{0.015 \, \text{g/L}}{28 \, \text{g/mol}}\) × \(\frac{4 \, \text{atm}}{1 \, \text{atm}}\)

Now we need to calculate the difference in solubility of N₂ at 4 atm and 1 atm to find the amount of N₂ released when the pressure drops. Solubility difference = Solubility at 4 atm - Solubility at 1 atm So, Solubility difference = \(\frac{0.015 \, \text{g/L}}{28 \, \text{g/mol}}\) × \(\frac{4 \, \text{atm}}{1 \, \text{atm}}\) - \(\frac{0.015 \, \text{g/L}}{28 \, \text{g/mol}}\)

Finally, we'll convert the difference in solubility from moles to milliliters of N₂ gas. To do this, we'll use the relationship 1 mole of any gas occupies 22.4 L at standard temperature and pressure (STP). First, convert the difference in moles to millimoles: \[\text{Difference in millimoles of N₂} = \;\text{Solubility difference} \times 1000\] Now, using the relationship mentioned above, convert millimoles to milliliters of N₂ gas: \[\text{Difference in milliliters of N₂ gas} = \;\text{Difference in millimoles}\] × \(\frac{22.4 \, \text{L}}{1000 \, \text{mmol}}\) × 1000\] Once you've calculated the difference in milliliters of N₂ gas, you have the answer - the amount of N₂ released into the bloodstream as tiny bubbles per liter of blood when a scuba diver suddenly surfaces from a depth of 100 ft.