Question

Lake Titicaca is located high in the Andes Mountains between Peru and Bolivia. Its surface is 3811 m above sea level, where the average atmospheric pressure is 0.636 atm. During the summer, the average temperature of the water’s surface rarely exceeds 15°C. What is the solubility of oxygen in Lake Titicaca at that temperature? Express your answer in molarity and mg/L.

Answer 1

Henry's constant for water at 15 deg.c =36,400 atm/mole fraction =P/x

P= partial pressure of oxygen = mole fraction of oxygen in the gas phase* total pressure

x= mole fraction of oxygen in the solution

x= P/36400

Air contains 21% O2 and 79% N2, P= 0.21*0.636 atm=0.13356

x= 0.13356/36400=3.7*10-6 moles/ mole solution

Basis : 1 mole of solution, moles of Oxygen= 3.7*10-6 moles, mass of oxygen =moles* molar mass= 3.7*10^-6*32 gm, in terms of mg, this becomes = 3.7*10^-6*32*10³ mg=0.1184 mg

moles of water= 1-3.7*10^-6 = 0.9999963 , mass of water= 0.9999963*18= 17.99993395 gm

mass of the solution = 17.99993395+0.1184*10^-3 gm =18 gm

Density of water can be considered as close to 1 g/cc or 1000g/ml (1000cc= 1L)

volume of solution = mass/density= 18/1000 ml =0.018 ml= 0.018*10^-3 L

Molarity = moles of oxygen/L of solution = 3.7*10^-6 moles/(0.018*10^-3L)=0.2055 M

concentration in mg/L= 0.1184/(0.018*10^-3 L)=6300 mg/L= 6300/1000 mg/ml= 6.3 ppm ( mg/L= ppm)