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Chapter 17: Problem 29

(a) What is the ratio of \(\mathrm{HCO}_{3}^{-}\) to $\mathrm{H}_{2} \mathrm{CO}_{3}\( in blood of \)\mathrm{pH} 7.4$ ? (b) What is the ratio of \(\mathrm{HCO}_{3}^{-}\) to $\mathrm{H}_{2} \mathrm{CO}_{3}\( in an exhausted marathon runner whose blood \)\mathrm{pH}$ is \(7.1 ?\)

Short Answer

Expert verified
In summary, the ratio of HCO3- to H2CO3 in blood with a pH of 7.4 is approximately 19.95, and the ratio in blood with a pH of 7.1 is 10.

Step by step solution

01

Calculate the ratio of [HCO3-] to [H2CO3] for pH 7.4

Given the blood pH is 7.4, we can use the Henderson-Hasselbalch equation to find the ratio of [HCO3-] to [H2CO3]. The pKa value for the H2CO3/HCO3- buffer system is 6.1, so we plug the values into the equation: \[7.4 = 6.1 + \log{\frac{[HCO_{3}^{-}]}{[H_{2}CO_{3}]}}\] (a)
02

Solve for the ratio of [HCO3-] to [H2CO3]

To find the ratio of [HCO3-] to [H2CO3], we first need to isolate the ratio. Rearrange the equation and solve for the ratio: \[7.4 - 6.1 = \log{\frac{[HCO_{3}^{-}]}{[H_{2}CO_{3}]}}\] \[1.3 = \log{\frac{[HCO_{3}^{-}]}{[H_{2}CO_{3}]}}\] Next, take the inverse logarithm of both sides: \[[HCO_{3}^{-}] : [H_{2}CO_{3}] = 10^{1.3}\] \[[HCO_{3}^{-}] : [H_{2}CO_{3}] \approx 19.95\] So, the ratio of [HCO3-] to [H2CO3] is approximately 19.95 when the blood pH is 7.4. (b)
03

Calculate the ratio of [HCO3-] to [H2CO3] for pH 7.1

Now, we repeat the steps for the blood pH of 7.1 using the Henderson-Hasselbalch equation and the pKa value of 6.1: \[7.1 = 6.1 + \log{\frac{[HCO_{3}^{-}]}{[H_{2}CO_{3}]}}\] (b)
04

Solve for the ratio of [HCO3-] to [H2CO3]

Rearrange and solve for the ratio: \[7.1 - 6.1 = \log{\frac{[HCO_{3}^{-}]}{[H_{2}CO_{3}]}}\] \[1 = \log{\frac{[HCO_{3}^{-}]}{[H_{2}CO_{3}]}}\] Take the inverse logarithm of both sides: \[[HCO_{3}^{-}] : [H_{2}CO_{3}] = 10^1\] \[[HCO_{3}^{-}] : [H_{2}CO_{3}] = 10\] So, the ratio of [HCO3-] to [H2CO3] is 10 when the blood pH is 7.1. In summary, the ratio of HCO3- to H2CO3 in blood with a pH of 7.4 is approximately 19.95, and the ratio in blood with a pH of 7.1 is 10.

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Most popular questions from this chapter

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