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Chapter 16: Problem 27

If a neutral solution of water, with \(\mathrm{pH}=7.00,\) is cooled to \(10^{\circ} \mathrm{C},\) the pH rises to \(7.27 .\) Which of the following three statements is correct for the cooled water: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right]\) (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right], \mathrm{or}\) (iii) \(\left[\mathrm{H}^{+}\right]<\left[\mathrm{OH}^{-}\right] ?\)

Short Answer

Expert verified
The correct statement for the cooled water is (iii) \(\left[\mathrm{H}^{+}\right]<\left[\mathrm{OH}^{-}\right]\).

Step by step solution

01

Understand the ion product of water

In a pure water solution, the concentration of hydrogen ions (H+) and hydroxide ions (OH-) are equal, and at 25°C, their product is a constant known as the ion product of water (Kw): \[K_w = [\mathrm{H}^{+}][\mathrm{OH}^{-}] = 1 \times 10^{-14}\]
02

Calculate the concentrations of H+ and OH- ions at the initial temperature

For a neutral solution of water with a pH of 7.00, the concentration of hydrogen ions (H+) is: \([H+] = 10^{-\mathrm{pH}} = 10^{-7.00} = 1 \times10^{-7} M\). Since it is a neutral solution, the concentration of hydroxide ions (OH-) is equal to the concentration of hydrogen ions: \([OH^-] = [H^+] = 1 \times 10^{-7} M\).
03

Calculate the concentrations of H+ and OH- ions in the cooled water

We are given the pH of the cooled water (7.27). To find the concentration of hydrogen ions (H+) in the cooled water, we need to use the same formula we just used: \([H^+] = 10^{-\mathrm{pH}} = 10^{-7.27} M\) We have to find the concentration of OH- ions in the cooled water. To do this, we can use the formula for the ion product of water (Kw): \[K_w = [H^+][OH^-]\] Rearrange the equation to find the concentration of OH- ions: \[ [OH^-] = \frac{K_w}{[H^+]}\]
04

Compare the concentrations of H+ and OH- ions in the cooled water

Plug in the values for Kw and [H+] that we calculated earlier: \[ [OH^-] = \frac{1 \times 10^{-14}}{10^{-7.27}}\] After calculating the value, we get: \([OH^-] = 1.89 \times 10^{-7} M\) Since \([H^+] = 1.89 \times10^{-7} M<{[OH^-]} = 1\times 10^{-7} M\), statement (iii) is correct: \[ \left[\mathrm{H}^{+}\right]<\left[\mathrm{OH}^{-}\right].\]

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Most popular questions from this chapter

If a solution of hydrofluoric acid $\left(\mathrm{HF} ; K_{a}=6.8 \times 10^{-4}\right)\( has a \)\mathrm{pH}$ of 2.12 , calculate the concentration of hydrofluoric acid.

Using data from Appendix \(D\), calculate \(p O H\) and \(p H\) for each (a) \(0.080 M\) potassium hypobromite of the following solutions: \((\mathrm{KBrO}),\) (b) \(0.150 \mathrm{M}\) potassium hydrosulfide \((\mathrm{KHS}),(\mathbf{c})\) a mixture that is \(0.25 \mathrm{M}\) in potassium nitrite \(\left(\mathrm{KNO}_{2}\right)\) and \(0.15 \mathrm{M}\) in magnesium nitrite \(\left(\mathrm{Mg}\left(\mathrm{NO}_{2}\right)_{2}\right)\).

An unknown salt is either \(\mathrm{NaF}, \mathrm{NaCl}\), or \(\mathrm{NaOCl}\). When 0.050 mol of the salt is dissolved in water to form 0.500 L of solution, the pH of the solution is 8.08 . What is the identity of the salt?

(a) Give the conjugate base of the following BrønstedLowry acids: (i) \(\mathrm{H}_{2} \mathrm{SO}_{3},\) (ii) \(\mathrm{HSO}_{3}^{-}\) (b) Give the conjugate acid of the following Bronsted-Lowry bases: (i) $\mathrm{CH}_{3} \mathrm{NH}_{2}$, (ii) \(\mathrm{CH}_{3} \mathrm{COO}^{-}\).

Indicate whether each of the following statements is correct or incorrect. (a) Every Brønsted-Lowry acid is also a Lewis acid. (b) Every Lewis acid is also a Bronsted-Lowry acid. (c) Conjugate acids of weak bases produce more acidic solutions than conjugate acids of strong bases. (d) \(\mathrm{K}^{+}\) ion is acidic in water because it causes hydrating water molecules to become more acidic. (e) The percent ionization of a weak acid in water increases as the concentration of acid decreases.
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