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Chapter 16: Problem 33

At the freezing point of water \(\left(0^{\circ} \mathrm{C}\right), K_{w}=1.2 \times 10^{-15}\). Calculate \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) for a neutral solution at this temperature.

Short Answer

Expert verified
In a neutral solution at 0掳C, the concentration of H+ ions and OH- ions is given by: \[[\mathrm{H}^+] = [\mathrm{OH}^-] = 1.09 \times 10^{-8} \, \mathrm{M}\]

Step by step solution

01

Write down the formula for Kw

The formula for Kw is given by: \[K_w = [\mathrm{H}^+][\mathrm{OH}^-]\] where \(K_w\) is the ionization constant for water, and [H+] and [OH-] are the hydrogen and hydroxide ion concentrations respectively.
02

Insert the given value of Kw and neutrality condition

We are given that at 0掳C, \(K_w = 1.2 \times 10^{-15}\), and for a neutral solution, the concentration of H+ ions is equal to the concentration of OH- ions. Let's denote this concentration as x. Therefore: \[1.2 \times 10^{-15} = x^2\]
03

Solve for x

To find the concentration of H+ and OH- ions, we can solve for x. \begin{align*} x^2 &= 1.2 \times 10^{-15} \\ x &= \sqrt{1.2 \times 10^{-15}} \\ x &= 1.09 \times 10^{-8} \end{align*} Since x represents the concentration of both H+ and OH- ions in a neutral solution: \[[\mathrm{H}^+] = [\mathrm{OH}^-] = 1.09 \times 10^{-8} \, \mathrm{M}\]
04

Write the answer

In a neutral solution at 0掳C, the concentration of H+ ions and OH- ions is: \[[\mathrm{H}^+] = [\mathrm{OH}^-] = 1.09 \times 10^{-8} \, \mathrm{M}\]

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Most popular questions from this chapter

(a) Which of the following is the stronger BronstedLowry acid, \(\mathrm{HNO}_{3}\) or \(\mathrm{HNO}_{2} ?\) (b) Which is the stronger Br酶nsted- Lowry base, \(\mathrm{NH}_{3}\) or \(\mathrm{H}_{2} \mathrm{O}\) ? Briefly explain your choices.

In many reactions the addition of \(\mathrm{AlCl}_{3}\) produces the same effect as the addition of \(\mathrm{H}^{+}\). (a) Draw a Lewis structure for \(\mathrm{AlCl}_{3}\) in which no atoms carry formal charges, and determine its structure using the VSEPR method. (b) What characteristic is notable about the structure in part (a) that helps us understand the acidic character of \(\mathrm{AlCl}_{3} ?(\mathrm{c})\) Predict the result of the reaction between \(\mathrm{AlCl}_{3}\) and \(\mathrm{NH}_{3}\) in a solvent that does not participate as a reactant. (d) Which acid-base theory is most suitable for discussing the similarities between \(\mathrm{AlCl}_{3}\) and \(\mathrm{H}^{+}\) ?

An unknown salt is either \(\mathrm{KBr}, \mathrm{NH}_{4} \mathrm{Cl}, \mathrm{KCN}\), or \(\mathrm{K}_{2} \mathrm{CO}_{3}\) If a \(0.100 \mathrm{M}\) solution of the salt is neutral, what is the identity of the salt?

How does the acid strength of an oxyacid depend on (a) the electronegativity of the central atom; (b) the number of nonprotonated oxygen atoms in the molecule?

Identify the Lewis acid and Lewis base among the reactants in each of the following reactions: (a) \(\mathrm{Fe}\left(\mathrm{ClO}_{4}\right)_{3}(s)+6 \mathrm{H}_{2} \mathrm{O}(I) \rightleftharpoons\) \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}(a q)+3 \mathrm{ClO}_{4}^{-}(a q)\) (b) \(\mathrm{CN}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HCN}(a q)+\mathrm{OH}^{-}(a q)\) (c) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}(\mathrm{~g})+\mathrm{BF}_{3}(g) \rightleftharpoons\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NBF}_{3}(\mathrm{~s})\) (d) \(\mathrm{HIO}(\mathrm{lq})+\mathrm{NH}_{2}^{-(l q)} \rightleftharpoons \mathrm{NH}_{3}(l q)+\mathrm{IO}^{-}(l q)\) (Iq denotes liquid ammonia as solvent)
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