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J. W. Hill, R. H. Petrucci, T. W. McCreary, & S. S. Perry General Chemistry 4th edition

Problem 15.133

Normal rainfall is made slightly acidic from the dissolving of atmospheric CO2 in the rainwater and ionization of the resulting carbonic acid, H2CO3. At a CO2(g) partial pressure of 1 atm and a temperature of 25 oC, the solubility of CO2(g) in water is 0.759 mL CO2 at STP per mL H2O. Given that air contains 0.036% CO2 by volume, estimate the pH of rainwater that is saturated with CO2(g). (Hint: Recall Henry's law [Equation (12.5)], and assume that the dissolved CO2 is present as carbonic acid.)




Answer:

First, determine the molar concentration of CO2 in saturated water using Henry's law.

Change the volume solubility of CO2 in water to a molar solubility using the ideal gas law:

One of the assumptions in the problem is that all of the dissolved CO2 reacts with water to form carbonic acid, i.e.

CO2(aq) + H2O(l) H2CO3(aq)

Now the problem becomes a typical weak acid equilibrium:
H2CO3(aq)
+
H2O(l)
H3O+(aq)
+
HCO3 (aq)
Initial
1.1×10–5
0
0
Change
– x
+ x
+ x
Equilibrium
1.1×10–5 – x
x
x

Approximate? 1.1×10–5/4.4×10–7 = 25 <100, so no.

Using the quadratic equation gives

x = 2.0×10–6, –2.4×10–6

Only the positive value makes sense, so

x = [H3O+] = 2.0×10–6 M

pH = – log[H3O+] = – log[2.0×10–6] = 5.70