Question

Henry’s law states that the solubility of a gas is directly proportional to the partial pressure of the gas if the temperature is constant. Hyperbaric chambers, which provide high pressures (up to 6 atm) of either air or pure oxygen, are used to treat a variety of conditions, ranging from decompression sickness in deep-sea divers to carbon monoxide poisoning. Look up the Henry’s Law Constant (kH) for N2, O2, and CO2 in the textbook.

a) Calculate the solubility (concentration in M) of each gas in water at 1 atm.

b) Explain the trends in relative solubility of these gases.

c) The composition of air is 78% N2, 21% O2, and 1% Argon (along with trace amounts of other compounds). Calculate the partial pressures of Oxygen gas at 760 mmHg.

d) Using the pressure calculated in (c), calculate the solubility (concentration) of Oxygen gas at 25 oC at 760 mmHg (sea-level).

5 e) When air is inhaled, significant amounts of water vapor is introduced to the aveoli of the lungs, and this decreases the partial pressure of the gases available for diffusion into the lungs. The partial pressure of oxygen actually available for diffusion is 100 mmHg. What would the concentration (solubility in M/dL) of dissolved oxygen per dL of blood be, taking in to account the alveolar partial pressure value?

f) If the number of moles of oxygen available in the aveoli is 5.13 x 10-8 moles, what is the volume (in mL/ dL of blood) of dissolved oxygen per dL of blood?

g) If a normal individual has about 5.6 L of blood, calculate the volume in mL of oxygen DISSOLVED in their blood at any given time. Give answer in 2 significant figures.

h) Based on the trends described in (b), the values of volume of oxygen in question (f) and (g), and an understanding of Henry’s Law, explain how elevated pressures and treatment with pure oxygen in a hyperbaric chamber can be used to treat decompression sickness (excess N2).

Answer 1

a) Calculate the solubility (concentration in M) of each gas in water at 1 atm.

From literature Henry's Law constant at 298 K or 25^oC are

k_H,_N2= 1639.34 L.atm/mol; k_H,_O2= 769.23 L.atm/mol; k_H,_CO2= = 29.41 L.atm/mol

Using Henry's Law we get

p_gas = k_H. C_gas

where p_gas = partial pressure of the gas, k_H = Henry's constant at a fixed temperature, C_gas = solubility of the gas

Substituting the value of p_gas = 1 atm and respective k_H, we get

C_N2 = 1/k_H,_N2 = 0.61 mM

Similarly, C_O2 = 1/k_H,_O2 = 1.3 mM

and C_CO2 = 1/k_H,_CO2 = 34 mM

b) Explain the trends in relative solubility of these gases.

Solubility follows the order as: N₂<O₂<CO₂

This can be explained on the basis of dipole-dipole interations between polar C-O and H-O-H that can form Hydrogen bond with water molecule. Thus CO₂ shows highest solubility.

In case of O2 and N2, both are diatomic molecules and are therefore non-polar. However, O₂ has 2 lone pair of electrons on each O atom and are loosely bound as compaired to the bonded pi-electrons. Whereas, in N₂, each N has one loosely bound pair of non-bonding electrons. Theseunpaired of electrons momentarily induce dipoles which interact with polar O-H bond of water and results in their solubility. Therefore, O₂ having more induced dipole will be more soluble than N₂.

c) The composition of air is 78% N2, 21% O2, and 1% Argon (along with trace amounts of other compounds). Calculate the partial pressures of Oxygen gas at 760 mmHg.

According to Dalton's law of partial pressure, each gas in a mixture exerts a pressure independent of other gases. SInce O₂ is 21% of the air, it will exert 21% of the pressure i.e 21% of 760 mmHg

=0.21*760 mmHg=159.6 mmHg

the partial pressures of Oxygen gas at 760 mmHg is 159.6 mmHg

d) Using the pressure calculated in (c), calculate the solubility (concentration) of Oxygen gas at 25 oC at 760 mmHg (sea-level).

Using the Henry's law : k_H,_O2 = 769.23 L.atm/mol at 25^oC, p_O2 = 159.6 mmHg=0.21 atm (using 760 mmHg=1 atm)

we get, C_O2 =p_O2/k_H,_O2 =0.21/769.23=0.273 mM.

Thus solubility of Oxygen gas at 25 ^oC at its partial pressure of 159.6 mmHg is 0.273 mM.