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General Chemistry Principles, Patterns, and Applications, 2011

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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 />

CO2( aq) + H 2O( l) H 2CO3( aq)H2CO3( aq) H + ( aq) + HCO3<br />

-( aq)CO2( aq) + H 2O( l) H + ( aq) + HCO3- ( aq)K ' = 4.0 ´10 - 3 (37°<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 The presence of a gas in the equilibrium constant expression<br />

for a buffer is unusual. According to Henry’s law , [CO2] = kPCO2, where k is the Henry’s law constant<br />

for CO2, which is 3.0 × 10 − 5<br />

M/mmHg at 37°C. (For more information about Henry’s law, seeChapter 13<br />

"Solutions", Section 13.4 "Effects of Temperature <strong>and</strong> Pressure on Solubility".) Substituting this<br />

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 PCO2, with normal pH <strong>and</strong> [HCO3 − ] values indicated by the<br />

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 of PCO2, indicated. Normal values of blood plasma pH <strong>and</strong> [HCO3 − ] are indicated by<br />

dashed lines.<br />

According to Equation 16.65, adding a strong acid to the CO2/HCO3 − system causes [HCO3 − ] to decrease as<br />

HCO3 − is converted to CO2. Excess CO2 is released in the lungs <strong>and</strong> exhaled into the atmosphere, however,<br />

so there is essentially no change in PCO2.Because the change in [HCO3-]/ PCO2 is<br />

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

Saylor.org<br />

1536

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