Question

The water in a lake has a pH of 6. The water is in equilibrium with atmospheric carbon dioxide which has a pressure of P_CO²= 10^-3.5.

What is the concentration of the carbonate ion (CO₃^2-) in the water?

The Henrys Constant for carbon dioxide is KH = 10^-1.5 atm•L/mol

Other Info:

R= 0.08206 atm•L/mole•K = 1.987 cal/mole•K = 8.314 J/mole•K

1 Joule = Newton • Meter

1 atm = 1.013 X 10⁵ N/m² = 1.013 X 10⁵ Pa

1 gallon = 3.785 L

Answer 1

Given data:

The pH of lake water = 6, i.e. [H⁺] = 10^-6

Partial pressure of CO₂, i.e. P_CO2 = 10^-3.5 atm.

Henry's constant for CO2, i.e. K_H = 10^-1.5 atm.L/mol

According to Henry's law, the mass of a gas dissolved in water (i.e. the concentration of a gas in water) is directly proportional to its partial pressure in the gas phase, i.e.

P_CO2 = K_H*[H₂CO₃]

K_H = P_CO2/[H₂CO₃]

Therefore, [H₂CO₃] = 10^-3.5/10^-1.5, i.e. 10^-2 mol/L

The carbonic acid (weak acid) dissociates as follows:

H₂CO₃ 2H⁺ + CO₃^2-; K = 4.3*10^-7, where K is the dissociation constant for H₂CO₃.

Here, K = [H⁺]²[CO₃^2-]/[H₂CO₃]

Therefore, [CO₃^2-] = (4.3*10^-7)*10^-2/(10^-6)².

= 4.3*10³ mol/L