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Ch.17 - Applications of Aqueous Equilibria
Chapter 17, Problem 73

What is the Henderson–Hasselbalch equation to calculate the ratio of HCO3- and H2CO3 in blood with a pH of 7.40, given that the value of Ka for carbonic acid at body temperature (37 degrees Celsius) is 7.9 x 10^-7?

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1
Identify the Henderson–Hasselbalch equation: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the base form (HCO3-) and \([\text{HA}]\) is the concentration of the acid form (H2CO3).
Calculate the pKa from the given Ka value using the formula \( \text{pKa} = -\log(\text{Ka}) \).
Substitute the given pH value (7.40) and the calculated pKa into the Henderson–Hasselbalch equation.
Rearrange the equation to solve for the ratio \( \frac{[\text{HCO}_3^-]}{[\text{H}_2\text{CO}_3]} \).
Use the properties of logarithms to express the ratio in terms of powers of 10, if needed, to simplify the interpretation of the result.