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.

검증된 단계별 안내

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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주요 개념

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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.

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.

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.