Henry's law constant (mol/L · atm) for oxygen dissolving in blood is 3.74 * 10^-² mol/(L atm) at body temperature, 37°C. Calculate the molar concentration of oxygen in blood for a scuba diver where the air pressure is 2.0 atm. The mole fraction of oxygen in air is 0.209. A) 7.8 *10^-³ M B) 2.7 *10^-³ M C) 1.6 *10^-² M D) 1.3 * 10^-² M E) 0.11 M

Question

Quizplus · Accepted Answer

Using Henry's law, we can calculate the concentration of oxygen in blood:

C_oxygen = (P_oxygen / H) * x_oxygen

where 
P_oxygen = partial pressure of oxygen = 2.0 atm * 0.209 (mole fraction of oxygen in air) = 0.418 atm 
H = Henry's law constant = 3.74 x 10^-3 mol/(L*atm) 
x_oxygen = mole fraction of oxygen in blood (unknown)

Rearranging the equation:

x_oxygen = (C_oxygen / P_total) = (H * P_oxygen) / P_total

where 
P_total = total pressure = 2.0 atm

Plugging in the values gives:

x_oxygen = (3.74 x 10^-3 mol/(L*atm) * 0.418 atm) / 2.0 atm = 7.82 x 10^-4

Finally, we can convert moles per liter to molar concentration:

C_oxygen = x_oxygen * Molar mass of oxygen * 1000

where 
Molar mass of oxygen = 32 g/mol 
1000 converts units from mol/L to mmol/L

Plugging in the values gives:

C_oxygen = 7.82 x 10^-4 * 32 g/mol * 1000 / 1000 mL/L = 0.025 mmol/L = 1.6 x 10^-3 M

Therefore, the best choice is C.

Henry's Law Constant (Mol/L · Atm) for Oxygen Dissolving in Blood