The Effect of Carbon Dioxide on pH

Carbon dioxide (CO₂) is an acid anhydride, which means that when it is dissolved in water it lowers the pH of the solution. In fact pure rainwater has a pH of 5.6 because of the 360 ppm atmospheric concentration of CO₂. During World War II, atmospheric concentrations of CO₂ were closer to 330 ppm, but that is not an important difference for the purposes addressed here. One can think of the process as having three steps all of which involve a chemical equilibrium. The first step, is the dissolution of CO₂ in water and its equilibrium constant is the Henry's Law constant of CO₂, K_hc:

CO₂ + H₂O <=> H₂CO₃

The second step is the acid base reaction between carbonic acid and water; its equilibrium constant is denoted here as K_c1:

H₂CO₃ + H₂O <=> H₃O⁺ + HCO₃^-

HCO₃^- + H₂O <=> H₃O⁺ + CO₃^2-

Also, one needs to consider the autoprotolysis of water:

2H₂O <=> H₃O⁺ + OH^-

In aqueous solution, one can treat the concentration of water as a constant and derive a constant for the equilibrium, K_w. These constants and their associated enthalpies are reported in Seinfeld¹. Here is a table of the relevant quantities:

Table II.1: Equilibrium Constants and Associated Enthalpies for the Absorption of Carbon Dioxide by Water.
Constant	Value	Enthalpy at 298 K
		kcal/mole
Khc	3.4 x 10-2	-4.846
Kc1	4.283 x 10-7	1.825
Kc2	4.687 x 10-11	3.55
Kw	1.008 x 10-14	13.345

The slight temperature dependence of these constants can be accounted for by means of the enthalpies given. The pH of a solution is defined as -log[H⁺] where [H⁺] is the concentration of hyronium ions in moles/liter. From the information given it is possible to derive a cubic equation expressing the relationship between [H⁺] and the partial pressure of CO₂, P_CO2. This equation is also presented in Seinfeld:¹

[H⁺]³ - (K_w+K_hcK_c1 P_CO2)[H⁺]-2+K_hcK_c1 K_c2P_CO2=0

Figure II.1

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