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Chapter 15: Problem 51

Carbonate buffers are important in regulating the pH of blood at \(7.40 .\) If the carbonic acid concentration in a sample of blood is 0.0012 M, determine the bicarbonate ion concentration required to buffer the pH of blood at pH \(=7.40\) $$ \mathrm{H}_{2} \mathrm{CO}_{3}(a q) \rightleftharpoons \mathrm{HCO}_{3}^{-}(a q)+\mathrm{H}^{+}(a q) \quad K_{\mathrm{a}}=4.3 \times 10^{-7} $$

Short Answer

Expert verified
The bicarbonate ion concentration (HCO₃⁻) required to buffer the pH of blood at pH = 7.40 is approximately 0.0021 M, calculated using the Henderson-Hasselbalch equation and given the carbonic acid concentration and Ka value.

Step by step solution

01

Calculate pKa

To calculate the pKa, use the following equation: pKa = -log(Ka). We're given the Ka value for carbonic acid, which is 4.3 x 10⁻⁷. Therefore: pKa = -log(4.3 x 10⁻⁷) Now, calculate the pKa value: pKa ≈ 6.37
02

Use the Henderson-Hasselbalch equation

Now that we have the pKa value, we can use the Henderson-Hasselbalch equation to solve for the bicarbonate ion concentration: pH = pKa + log([A⁻]/[HA]) We are given the pH (7.40) and the concentration of carbonic acid ([HA]) which is 0.0012 M. Plug in these values into the equation: 7.40 = 6.37 + log([HCO₃⁻]/0.0012)
03

Solve for bicarbonate ion concentration [HCO₃⁻]

Now, solve for the [HCO₃⁻] concentration: 7.40 - 6.37 = log([HCO₃⁻]/0.0012) 1.03 = log([HCO₃⁻]/0.0012) To undo the logarithm, raise 10 in power of both sides: 10^1.03 = [HCO₃⁻]/0.0012 Now, simply solve for [HCO₃⁻]: [HCO₃⁻] = 0.0012 x 10^1.03 [HCO₃⁻] ≈ 0.0021 M The bicarbonate ion concentration required to buffer the pH of blood at pH = 7.40 is approximately 0.0021 M.

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Most popular questions from this chapter

Sketch two pH curves, one for the titration of a weak acid with a strong base and one for a strong acid with a strong base. How are they similar? How are they different? Account for the similarities and the differences

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Acid-base indicators mark the end point of titrations by "magically" turning a different color. Explain the "magic" behind acid-base indicators.

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