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Ch.16 - Acid-Base Equilibria
Chapter 16, Problem 37

The average pH of normal arterial blood is 7.40. At normal body temperature 137 °C2, Kw = 2.4 * 10-14. Calculate 3H+4, 3OH-4, and pOH for blood at this temperature.

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Identify the given values: pH = 7.40 and Kw = 2.4 \times 10^{-14}.
Use the formula [H^+] = 10^{-pH} to calculate the concentration of hydrogen ions, [H^+].
Use the relationship Kw = [H^+][OH^-] to find the concentration of hydroxide ions, [OH^-].
Calculate pOH using the formula pOH = -\log[OH^-].
Verify the relationship pH + pOH = 14 to ensure consistency with the calculated values.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pH and pOH

pH is a measure of the hydrogen ion concentration in a solution, defined as pH = -log[H+]. A pH of 7.40 indicates a slightly basic environment in arterial blood. pOH, on the other hand, measures the hydroxide ion concentration and is related to pH by the equation pOH = 14 - pH at 25 °C. However, at different temperatures, the relationship changes, necessitating adjustments in calculations.
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Ion Product of Water (Kw)

Kw is the ion product of water, representing the equilibrium constant for the dissociation of water into hydrogen ions (H+) and hydroxide ions (OH-). At 37 °C, Kw is approximately 2.4 x 10^-14, which indicates that the concentrations of H+ and OH- ions in pure water are equal. This value is crucial for calculating the concentrations of H+ and OH- in blood, as it varies with temperature.
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Calculating Ion Concentrations

To find the concentrations of H+ and OH- ions in blood, we can use the relationship between pH, pOH, and Kw. Given the pH, we can calculate [H+] using the formula [H+] = 10^-pH. Subsequently, [OH-] can be determined using the equation [OH-] = Kw / [H+]. This process is essential for understanding the acid-base balance in physiological conditions.
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