At ordinary body temperature (37 C) the solubility of N2 in water in contact with air at ordinary atmospheric pressure (1.0 atm) is 0.015 g/l. Air is approximately 78 mol % N2.
a)Calculate the number of moles of N_2 dissolved per liter of blood, which is essentially an aqueous solution.
b)t a depth of 100ft in water, the pressure is 4.0 atm. What is the solubility of N_2 from air in blood at this pressure?
c)If a scuba diver suddenly surfaces from this depth, how many milliliters of N_2 gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood?
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To solve these questions, we need to use Henry's Law, which states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
a) The first question asks us to calculate the number of moles of N2 dissolved per liter of blood. Given that the solubility of N2 at 37°C and 1.0 atm is 0.015 g/L, we can use the molar mass of N2 (28 g/mol) to find the moles.
First, convert the grams to moles using the molar mass:
0.015 g/L * (1 mol/28 g) = 0.000536 mol/L
Therefore, the number of moles of N2 dissolved per liter of blood is approximately 0.000536 mol/L.
b) At a depth of 100 ft in water, the pressure is 4.0 atm. We need to calculate the solubility of N2 from air in blood at this pressure.
Using Henry's Law, we can set up the equation:
P1 / S1 = P2 / S2
P1 is the initial pressure (1.0 atm), S1 is the initial solubility (0.015 g/L), P2 is the new pressure (4.0 atm), and S2 is what we want to find (the new solubility).
Plug in the values:
1.0 atm / 0.015 g/L = 4.0 atm / S2
Cross-multiply and solve for S2:
S2 = (0.015 g/L) * (4.0 atm / 1.0 atm) = 0.06 g/L
Therefore, the solubility of N2 from air in blood at a pressure of 4.0 atm is 0.06 g/L.
c) If a scuba diver suddenly surfaces from this depth, we need to calculate how many milliliters of N2 gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood.
To do this, we need to calculate the change in pressure from 4.0 atm to atmospheric pressure (1.0 atm). The change in pressure represents the gas released from the solution.
Using Henry's Law again, we can set up the equation:
P1 / S1 = P2 / S2
P1 is the initial pressure (4.0 atm), S1 is the initial solubility (0.06 g/L), P2 is the final pressure (1.0 atm), and S2 is what we want to find (the gas released).
Plug in the values:
4.0 atm / 0.06 g/L = 1.0 atm / S2
Cross-multiply and solve for S2:
S2 = (0.06 g/L) * (1.0 atm / 4.0 atm) = 0.015 g/L
Therefore, the solubility of N2 gas released from each liter of blood is 0.015 g/L.
To convert this to milliliters, we need to take into account that 1 liter is equal to 1000 milliliters:
0.015 g/L * 1000 mL/L = 15 mL/L
Therefore, approximately 15 milliliters of N2 gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood when a scuba diver suddenly surfaces from a depth of 100 ft.