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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° C is always 14.

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Most popular questions from this chapter

Classify these following oxides as acidic, basic, amphoteric, or neutral: (a) \(\mathrm{CO}_{2},\) (b) \(\mathrm{K}_{2} \mathrm{O},\) (c) \(\mathrm{CaO}\) (d) \(\mathrm{N}_{2} \mathrm{O}_{5},(\mathrm{e}) \mathrm{CO},(\mathrm{f}) \mathrm{NO}\) \((\mathrm{g}) \mathrm{SnO}_{2},(\mathrm{~h}) \mathrm{SO}_{3},(\mathrm{i}) \mathrm{Al}_{2} \mathrm{O}_{3}\) (j) \(\mathrm{BaO}\).

Most of the hydrides of Group \(1 \mathrm{~A}\) and Group \(2 \mathrm{~A}\) metals are ionic (the exceptions are \(\mathrm{BeH}_{2}\) and \(\mathrm{MgH}_{2}\), which are covalent compounds). (a) Describe the reaction between the hydride ion \(\left(\mathrm{H}^{-}\right)\) and water in terms of a Bronsted acid-base reaction. (b) The same reaction can also be classified as a redox reaction. Identify the oxidizing and reducing agents.

Compare the strengths of the following pairs of acids: (a) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and \(\mathrm{H}_{2} \mathrm{SeO}_{4},\) (b) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) and \(\mathrm{H}_{3} \mathrm{AsO}_{4}\).

Why do we normally not quote \(K_{\mathrm{a}}\) values for strong acids such as \(\mathrm{HCl}\) and \(\mathrm{HNO}_{3}\) ? Why is it necessary to specify temperature when giving \(K_{\mathrm{a}}\) values?

In terms of orbitals and electron arrangements, what must be present for a molecule or an ion to act as a Lewis acid (use \(\mathrm{H}^{+}\) and \(\mathrm{BF}_{3}\) as examples)? What must be present for a molecule or ion to act as a Lewis base (use \(\mathrm{OH}^{-}\) and \(\mathrm{NH}_{3}\) as examples)?
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