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?
a. 0.015g/L x (1 molN2/28 gN2) = about 0.5.36E-4 M
b. calculate k. k = p/c
XN2 = 0.78 atm from the problem.
XN2 = pN2/Ptotal
0.78 x 1 atm = pN2 = 0.78 atm
k = p/c = 0.78/5.36E-4 = about 1450 or so. You need to do it more accurately.
At 100 ft the Ptotal = 4.0 atm.
Then pN2 = XN2 x Ptotal = 0.78*4.0 atm = 3.12 atm.
c = pN2/k = 3.12/1450 = about 2E-3 M.
c. Take the difference in moles in a liter at the two parts of the problem.
5.36E-4 - 2E-3 = about 0.0016 or so moles N2 for each liter.
The problem asks for mL, I would use PV = nRT, plug in n, R, T(37 + 273), and P (1 atm) and solve for volume, then convert to mL. I came out with about 41 mL N2 per liter of blood.
But isn't the K (Henry's constant) suppose to be mol/(L x atm)???
To calculate the number of moles of N2 dissolved per liter of blood, we need to use the given solubility of N2 in water at ordinary body temperature (37 °C) and atmospheric pressure (1.0 atm).
a) First, we need to convert the given solubility of N2 from grams per liter (g/L) to moles per liter (mol/L). The molar mass of N2 is approximately 28.0134 g/mol.
Given:
Solubility of N2 in water = 0.015 g/L
Molar mass of N2 = 28.0134 g/mol
To calculate the number of moles of N2 dissolved per liter of water, we'll use the formula:
Number of moles = Mass / Molar mass
Number of moles of N2 = 0.015 g / 28.0134 g/mol
b) To calculate the solubility of N2 from air in blood at a pressure of 4.0 atm, we need to use Henry's Law. Henry's Law states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the liquid.
The equation for Henry's Law is: C = k * P
Where:
C is the concentration of the gas in the liquid (mol/L)
k is the Henry's Law constant (mol/(L * atm))
P is the partial pressure of the gas above the liquid (atm)
Given:
Partial pressure of N2 in air at ordinary atmospheric pressure = 1.0 atm
Partial pressure of N2 in air at a depth of 100 ft = 4.0 atm
We can set up the equation using the ratio of the partial pressures:
C1 / P1 = C2 / P2
C1 is the initial concentration (moles of N2 per liter of blood) at P1 (1.0 atm)
C2 is the solubility at P2 (4.0 atm)
To find C2, we rearrange the equation:
C2 = (C1 * P2) / P1
c) To calculate the amount of N2 gas released into the bloodstream from each liter of blood when a scuba diver surfaces from a depth of 100 ft, we need to find the difference between the amount of N2 dissolved at 100 ft (4.0 atm) and that at atmospheric pressure (1.0 atm).
The amount of N2 released = C2 - C1
Given:
C1 is the concentration at 1.0 atm (from part a)
C2 is the concentration at 4.0 atm (from part b)
Finally, to calculate the amount of N2 gas released in milliliters (mL), we can convert from moles to mL by using the ideal gas law:
1 mole of gas occupies 22.4 L (at 1 atm and 273 K)
1 mL = 0.001 L
Hope this helps!