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Chapter 16: Problem 29

Calculate \(\left[\mathrm{H}^{+}\right]\) for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: (a) \(\left[\mathrm{OH}^{-}\right]=0.00045 M ;\) (b) \(\left[\mathrm{OH}^{-}\right]=8.8 \times 10^{-9} \mathrm{M} ;\) (c) a solution in which \(\left[\mathrm{OH}^{-}\right]\) is 100 times greater than \(\left[\mathrm{H}^{+}\right]\) .

Short Answer

Expert verified
For the given solutions: (a) \([\mathrm{H}^{+}] = 2.22 \times 10^{-12}\,\text{M}\) and the solution is basic; (b) \([\mathrm{H}^{+}] = 1.14 \times 10^{-6}\,\text{M}\) and the solution is acidic; (c) \([\mathrm{H}^{+}] = 1.0 \times 10^{-7}\,\text{M}\) and the solution is neutral.

Step by step solution

01

Find \([\mathrm{H}^{+}]\)

Given that \([\mathrm{OH}^{-}] = 0.00045\,\text{M}\), we can find \([\mathrm{H}^{+}]\) using the K_w expression: \[\left[\mathrm{H}^{+}\right]=\frac{K_\text{w}}{\left[\mathrm{OH}^{-}\right]}=\frac{1.0\times10^{-14}}{0.00045}\]
02

Calculate \([\mathrm{H}^{+}]\) and determine the solution type

Calculating the concentration of hydrogen ions: \[\left[\mathrm{H}^{+}\right] = 2.22 \times 10^{-12}\,\text{M}\] Since \([\mathrm{H}^{+}] < [\mathrm{OH}^{-}]\), the solution is basic. #Case (b):#
03

Find \([\mathrm{H}^{+}]\)

Given that \([\mathrm{OH}^{-}]=8.8\times10^{-9}\,\text{M}\), we can find \([\mathrm{H}^{+}]\) using the K_w expression: \[\left[\mathrm{H}^{+}\right]=\frac{K_\text{w}}{\left[\mathrm{OH}^{-}\right]}=\frac{1.0\times10^{-14}}{8.8\times10^{-9}}\]
04

Calculate \([\mathrm{H}^{+}]\) and determine the solution type

Calculating the concentration of hydrogen ions: \[\left[\mathrm{H}^{+}\right] = 1.14 \times 10^{-6}\,\text{M}\] Since \([\mathrm{H}^{+}] > [\mathrm{OH}^{-}]\), the solution is acidic. #Case (c):#
05

Write the given relation

We are given that \([\mathrm{OH}^{-}]\) is 100 times greater than \([\mathrm{H}^{+}]\): \[\left[\mathrm{OH}^{-}\right] = 100\left[\mathrm{H}^{+}\right]\]
06

Find \([\mathrm{H}^{+}]\) using the K_w expression

Using the K_w expression and substituting the given relation: \[\left[\mathrm{H}^{+}\right]\left(100\left[\mathrm{H}^{+}\right]\right) = 1.0 \times 10^{-14}\]
07

Solve for \([\mathrm{H}^{+}]\) and determine the solution type

Solving the equation for \([\mathrm{H}^{+}]\) we get: \[\left[\mathrm{H}^{+}\right] = 1.0 \times 10^{-7}\,\text{M}\] Since \([\mathrm{H}^{+}] = [\mathrm{OH}^{-}]\) (given their ratio is 100), the solution is neutral.

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Most popular questions from this chapter

(a) Write a chemical equation that illustrates the auto-ionization of water. (b) Write the expression for the ion-product constant for water \(K_{w}\) . (c) If a solution is described as basic, which of the following is true: (i) \(\left[\mathrm{H}^{+}\right]>\left[\mathrm{OH}^{-}\right],\) (ii) \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{OH}^{-}\right],\) or (iii) \(\left[\mathrm{H}^{+}\right]<\left[\mathrm{OH}^{-}\right] ?\)

\(\mathrm{NH}_{3}(g)\) and \(\mathrm{HCl}(g)\) react to form the ionic solid \(\mathrm{NH}_{4} \mathrm{Cl}(s) .\) Which substance is the Bronsted-Lowry acid in this reaction? Which is the Bronsted-Lowry base?

Carbon dioxide in the atmosphere dissolves in raindrops to produce carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right),\) causing the pH of clean, unpolluted rain to range from about 5.2 to 5.6. What are the ranges of \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in the raindrops?

Based on their compositions and structures and on conjugate acid-base relationships, select the stronger base in each of the following pairs: (a) \(\mathrm{BrO}^{-}\) or \(\mathrm{ClO}^{-},(\mathbf{b}) \mathrm{BrO}^{-}\) or \(\mathrm{BrO}_{2}^{-}\) (c) \(\mathrm{HPO}_{4}^{2-}\) or \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}.\)

The fluoride ion reacts with water to produce HF. (a) Write out the chemical equation for this reaction. (b) Will a concentrated solution of NaF in water be acidic, basic, or neutral? (c) Is fluoride acting as a Lewis acid or as a Lewis base when reacting with water?
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