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Chapter 16: Problem 10

Write an equation relating \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in solution at \(25^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The equation relating \([H^{+}]\) and \([OH^{-}]\) in solution at 25 degrees Celsius is \(pH + pOH = 14\).

Step by step solution

01

Understand the Concept of Auto-ionization of Water

Water can auto-ionize or self-ionize, meaning water molecules have the ability to donate and accept protons, resulting in the formation of hydrogen ions \(\left[\mathrm{H}^{+}\right]\) and hydroxide ions \(\left[\mathrm{OH}^{-}\right]\). This can be represented by the equation \(\mathrm{H}_{2}\mathrm{O}\rightleftharpoons\mathrm{H}^{+}+\mathrm{OH}^{-}\). Ion concentrations in this case are determined by the equilibrium constant for water (Kw).
02

Understand the Concept of Equilibrium Constant (pKw)

At 25 degrees Celsius, the ion product for water, Kw, equals \(1.0 \times 10^{-14}\). This product, also known as the equilibrium constant for water, is defined as \(Kw= [\mathrm{H^{+}}][\mathrm{OH^{-}}]\). Taking the logarithm base 10 and multiplying by -1 gives pKw, where \(pKw = -log_{10}([H^{+}][OH^{-}])\). At 25 degrees Celsius, pKw is 14. Therefore, the equation relating \([H^{+}]\) and \([OH^{-}]\) in solution at 25 degrees Celsius is \(pH + pOH = pKw = 14 \).
03

Final Equation for Relation

Combining the relationships, we get the equation relating [H+] and [OH-] in solution at 25 degrees Celsius: \(pH + pOH = 14\). This equation indicates that the sum of the pH and pOH of a solution at 25掳 C is always 14.

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Most popular questions from this chapter

List four factors that affect the strength of an acid.

To which of the following would the addition of an equal volume of \(0.60 \mathrm{M} \mathrm{NaOH}\) lead to a solution having a lower \(\mathrm{pH} ?\) (a) water, (b) \(0.30 \mathrm{M} \mathrm{HCl}\), (c) \(0.70 \mathrm{M} \mathrm{KOH}\) (d) \(0.40 \mathrm{M} \mathrm{NaNO}_{3}\).

A typical reaction between an antacid and the hydrochloric acid in gastric juice is \(\mathrm{NaHCO}_{3}(a q)+\mathrm{HCl}(a q) \longrightarrow\) $$\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)$$ Calculate the volume (in liters) of \(\mathrm{CO}_{2}\) generated from \(0.350 \mathrm{~g}\) of \(\mathrm{NaHCO}_{3}\) and excess gastric juice at \(1.00 \mathrm{~atm}\) and \(37.0^{\circ} \mathrm{C}\).

Prove the statement that when the concentration of a weak acid HA decreases by a factor of 10 , its percent ionization increases by a factor of \(\sqrt{10}\). State any assumptions.

Define pOH. Write an equation relating pH and pOH.
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