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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
(a) The ratio of HCO3- to H2CO3 at pH 7.4 is approximately 19.95:1. (b) The ratio of HCO3- to H2CO3 at pH 7.1 is approximately 10:1.

Step by step solution

01

Recall the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is given by: \[pH = pK_a + \log \frac{[A^-]}{[HA]}\] In this exercise, \([A^-]\) represents the concentration of bicarbonate ion (HCO3-), and \([HA]\) represents the concentration of carbonic acid (H2CO3).
02

Find pKa for carbonic acid

In order to plug in our pH values into the equation, we need to know the pKa value of carbonic acid. The pKa value for carbonic acid is approximately 6.1.
03

Solve for the ratio at pH 7.4 (Part a)

Plug the pH value of 7.4 and the pKa value of 6.1 into the Henderson-Hasselbalch equation: \[7.4 = 6.1 + \log \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] Now, solve for the ratio \(\frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\): \[7.4 - 6.1 = \log \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] \[1.3 = \log \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] To get rid of the logarithm, take 10 to the power of both sides: \[10^{1.3} = \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] \[19.95 \approx \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] The ratio of HCO3- to H2CO3 at pH 7.4 is approximately 19.95:1.
04

Solve for the ratio at pH 7.1 (Part b)

Plug the pH value of 7.1 and the pKa value of 6.1 into the Henderson-Hasselbalch equation: \[7.1 = 6.1 + \log \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] Now, solve for the ratio \(\frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\): \[7.1 - 6.1 = \log \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] \[1.0 = \log \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] To get rid of the logarithm, take 10 to the power of both sides: \[10^{1.0} = \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] \[10 \approx \frac{[\mathrm{HCO}_3^-]}{[\mathrm{H}_2 \mathrm{CO}_3]}\] The ratio of HCO3- to H2CO3 at pH 7.1 is approximately 10:1.

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Most popular questions from this chapter

A solution contains three anions with the following concentrations: \(0.20 \mathrm{M} \mathrm{CrO}_{4}^{2-}, 0.10 \mathrm{M} \mathrm{CO}_{3}^{2-},\) and \(0.010 \mathrm{M} \mathrm{Cl}^{-}\). If a dilute \(\mathrm{AgNO}_{3}\) solution is slowly added to the solution, what is the first compound to precipitate: \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) \(\left(K_{s p}=1.2 \times 10^{-12}\right), \mathrm{Ag}_{2} \mathrm{CO}_{3}\left(K_{s p}=8.1 \times 10^{-12}\right),\) or \(\mathrm{AgCl}\) \(\left(K_{s p}=1.8 \times 10^{-10}\right) ?\)

Suggest how the cations in each of the following solution mixtures can be separated: (a) \(\mathrm{Na}^{+}\) and \(\mathrm{Cd}^{2+},(\mathbf{b}) \mathrm{Cu}^{2+}\) and \(\mathrm{Mg}^{2+}\), (c) \(\mathrm{Pb}^{2+}\) and \(\mathrm{Al}^{3+},(\mathbf{d}) \mathrm{Ag}^{+}\) and \(\mathrm{Hg}^{2+}\).

A sample of \(0.1687 \mathrm{~g}\) of an unknown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\) of water and titrated with \(0.1150 \mathrm{M} \mathrm{NaOH}\). The acid required \(15.5 \mathrm{~mL}\) of base to reach the equivalence point. (a) What is the molecular weight of the acid? (b) After \(7.25 \mathrm{~mL}\) of base had been added in the titration, the \(\mathrm{pH}\) was found to be 2.85 . What is the \(K_{a}\) for the unknown acid?

Assume that \(30.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M}\) solution of a weak base \(\mathrm{B}\) that accepts one proton is titrated with a \(0.10 \mathrm{M}\) solution of the monoprotic strong acid HX. (a) How many moles of \(\mathrm{HX}\) have been added at the equivalence point? (b) What is the predominant form of \(\mathrm{B}\) at the equivalence point? (c) What factor determines the \(\mathrm{pH}\) at the equivalence point? (d) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?

Predict whether the equivalence point of each of the following titrations is below, above, or at \(\mathrm{pH}\) 7: (a) \(\mathrm{NaHCO}_{3}\) titrated with \(\mathrm{NaOH},\) (b) \(\mathrm{NH}_{3}\) titrated with \(\mathrm{HCl}\) (c) KOH titrated with HBr.
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