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Which value for the first dissociation constant of carbonic acid should be used in biological work?
1Department of Physiology and Biophysics, Wright State University School of Medicine, Dayton, Ohio 45435.
Insights
Understanding carbonic acid dissociation constants is crucial for accurate biochemical calculations. Using the activity-based constant (K'1) ensures precise derivation of bicarbonate concentration from blood gas measurements.
Area of Science:
- Biochemistry
- Physical Chemistry
- Analytical Chemistry
Background:
- The apparent first dissociation constant of carbonic acid (H2CO3) is defined variably in scientific literature.
- Existing definitions include those based on molality (Ks) and H ion activity (K'1).
Purpose of the Study:
- To clarify the distinction between different definitions of the apparent first dissociation constant of carbonic acid.
- To emphasize the importance of using the correct constant for accurate calculations in biological and chemical systems.
Main Methods:
- Comparison of two established definitions: Harned and co-workers' molality-based Ks and Hastings and Sendroy's activity-based K'1.
- Analysis of the mathematical relationship between Ks and K'1, highlighting the role of the H ion activity coefficient (gamma H).
Main Results:
- The two constants, Ks and K'1, differ by a factor of gamma H.
- The logarithmic form of the activity-based constant, pK'1, is greater than pKs by -log gamma H (approximately 0.1 at ionic strength mu = 0.16 M).
Conclusions:
- Accurate computation of biological and chemical quantities requires the correct apparent dissociation constant.
- For deriving bicarbonate concentration from partial pressure of carbon dioxide (PCO2) and pH (-log aH), the activity-based constant (pK'1) must be used, not the molality-based pKs.
Abstract:
The apparent first dissociation constant of carbonic acid has been defined in different ways in the literature. Harned and co-workers (8-10) have defined it in terms of molalities of the participating species, including H ions: Ks = mHmHCO3/mCO2. In contrast, Hastings and Sendroy have defined an apparent constant in which acidity is expressed as H ion activity: K'1 = aHmHCO3/mCO2. These constants differ by a factor gamma H, the activity coefficient of H ions at the prevailing ionic strength. Therefore, pK'1 is greater than pKs by an amount equal to -log gamma H, which, at mu = 0.16 M, is approximately 0.1. It is important that the correct value for the apparent dissociation constant or its logarithmic form be entered in the mass action expression or in the Henderson-Hasselbalch equation in order to prevent significant errors in the computation by means of these equations of quantities that cannot be directly measured. Specifically, for the derivation of bicarbonate concentration from PCO2 and pH (-log aH), pK'1 is to be used and not an uncorrected pKs.