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General Chemistry Principles, Patterns, and Applications, 2011

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with K′ = 4.0 × 10 − 3<br />

at 37°C. The true pKa of carbonic acid at 37°C is therefore 3.70, not 6.35,<br />

corresponding to a Ka of 2.0 × 10 − 4 , which makes it a much stronger acid thanEquation 16.63 suggests.<br />

Adding Equation 16.63 <strong>and</strong> Equation 16.64 <strong>and</strong> canceling H2CO3 from both sides give the following overall<br />

equation for the reaction of CO2 with water to give a proton <strong>and</strong> the bicarbonate ion:<br />

Equation 16.65<br />

C)Ka = 2.0 ´10 - 4 (37°CK = 8.0 ´10 - 7 (37°C)<br />

The K value for the reaction in Equation 16.65 is the product of the true ionization constant for carbonic<br />

acid (Ka) <strong>and</strong> the equilibrium constant (K) for the reaction of CO2(aq) with water to give carbonic acid. The<br />

equilibrium equation for the reaction of CO2 with water to give bicarbonate <strong>and</strong> a proton is therefore<br />

Equation 16.66<br />

K = [H+][HCO3-][CO2] = 8.0 ´10 - 7<br />

The presence of a gas in the equilibrium constant expression for a buffer is unusual. According to Henry’s<br />

law, [CO2] = kPCO2, where k is the Henry’s law constant for CO2, which is 3.0 × 10 − 5<br />

M/mmHg at<br />

37°C. (For more information about Henry’s law, seeChapter 13 "Solutions", Section 13.4 "Effects of<br />

Temperature <strong>and</strong> Pressure on Solubility".) Substituting this expression for [CO2] in Equation 16.66,<br />

Equation 16.67<br />

K = [H+][HCO3-](3.0 ´10 - 5 M / mmHg)(PCO2)<br />

where PCO2 is in mmHg. Taking the negative logarithm of both sides <strong>and</strong> rearranging,<br />

Equation 16.68<br />

pH = 6.10 + log[HCO3-](3.0 ´10 - 5 M / mm Hg)(PCO2)<br />

Thus the pH of the solution depends on both the CO2 pressure over the solution <strong>and</strong> [HCO3 − ]. Figure 16.29<br />

"Buffering in Blood: pH versus [HCO" plots the relationship between pH <strong>and</strong> [HCO3 − ] under physiological<br />

conditions for several different values of<br />

PCO2, with<br />

normal pH <strong>and</strong> [HCO3 − ] values indicated by the dashed lines.<br />

Only those combinations of pH <strong>and</strong> [HCO3 − ] that lie on a given line are allowed for the particular<br />

value f PCO indicated. Normal values of blood plasma pH <strong>and</strong> [HCO3 − ] are indicated by dashed<br />

lines.<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

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