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Chapter 16: Problem 30

Calculate \(\left[\mathrm{OH}^{-}\right]\) for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: (a) $\left[\mathrm{H}^{+}\right]=0.00010 \mathrm{M} ;(\mathbf{b})\left[\mathrm{H}^{+}\right]=7.3 \times 10^{-14} \mathrm{M} ;(\mathbf{c})\( a solution in which \)\left[\mathrm{OH}^{-}\right]$ is 100 times greater than \(\left[\mathrm{H}^{+}\right]\).

Short Answer

Expert verified
Answer: (a) \([\mathrm{OH}^{-}]\) = \(1.0 \times 10^{-10} \mathrm{M}\), acidic (b) \([\mathrm{OH}^{-}]\) ≈ \(1.37 \times 10^{-1} \mathrm{M}\), basic (c) \([\mathrm{OH}^{-}]\) = \(1.0 \times 10^{-6} \mathrm{M}\), basic

Step by step solution

01

Calculate \([\mathrm{OH}^{-}]\)

Using the ion-product constant for water, \(K_w = \left[\mathrm{H}^{+}\right] \cdot \left[\mathrm{OH}^{-}\right] = 1.0 \times 10^{-14}\), solve for \([\mathrm{OH}^{-}]\): \[\left[\mathrm{OH}^{-}\right] = \frac{K_w}{\left[\mathrm{H}^{+}\right]} = \frac{1.0 \times 10^{-14}}{0.0001 \mathrm{M}} = 1.0 \times 10^{-10} \mathrm{M}\]
02

Compare \([\mathrm{H}^{+}]\) and \([\mathrm{OH}^{-}]\)

In this case, \[\left[\mathrm{H}^{+}\right] = 0.0001 \mathrm{M} > \left[\mathrm{OH}^{-}\right] = 1.0 \times 10^{-10} \mathrm{M}\]
03

Classify the solution

Since the hydrogen ion concentration is greater than the hydroxide ion concentration, the solution is acidic. (b) \[\left[\mathrm{H}^{+}\right] = 7.3 \times 10^{-14} \mathrm{M}\]
04

Calculate \([\mathrm{OH}^{-}]\)

Using the ion-product constant for water, solve for \([\mathrm{OH}^{-}]\): \[\left[\mathrm{OH}^{-}\right] = \frac{K_w}{\left[\mathrm{H}^{+}\right]} = \frac{1.0 \times 10^{-14}}{7.3 \times 10^{-14} \mathrm{M}} \approx 1.37 \times 10^{-1} \mathrm{M}\]
05

Compare \([\mathrm{H}^{+}]\) and \([\mathrm{OH}^{-}]\)

In this case, \[\left[\mathrm{H}^{+}\right] = 7.3 \times 10^{-14} \mathrm{M} < \left[\mathrm{OH}^{-}\right] \approx 1.37 \times 10^{-1} \mathrm{M}\]
06

Classify the solution

Since the hydrogen ion concentration is smaller than the hydroxide ion concentration, the solution is basic. (c) \[\left[\mathrm{OH}^{-}\right] = 100\left[\mathrm{H}^{+}\right]\]
07

Calculate \([\mathrm{OH}^{-}]\)

Again, using the ion-product constant for water, solve for \([\mathrm{OH}^{-}]\): \[\left[\mathrm{H}^{+}\right] \cdot \left[\mathrm{OH}^{-}\right] = K_w\] \[\left[\mathrm{H}^{+}\right] \cdot (100\left[\mathrm{H}^{+}\right]) = 1.0 \times 10^{-14}\] \[100\left[\mathrm{H}^{+}\right]^2 = 1.0 \times 10^{-14}\] \[\left[\mathrm{H}^{+}\right]^2 = 1.0 \times 10^{-16}\] \[\left[\mathrm{H}^{+}\right] = 1.0 \times 10^{-8} \mathrm{M}\] Now we can calculate \(\left[\mathrm{OH}^{-}\right]\): \[\left[\mathrm{OH}^{-}\right] = 100\left[\mathrm{H}^{+}\right] = 100(1.0 \times 10^{-8} \mathrm{M}) = 1.0 \times 10^{-6} \mathrm{M}\]
08

Compare \([\mathrm{H}^{+}]\) and \([\mathrm{OH}^{-}]\)

In this case, \[\left[\mathrm{H}^{+}\right] = 1.0 \times 10^{-8} \mathrm{M} < \left[\mathrm{OH}^{-}\right] = 1.0 \times 10^{-6} \mathrm{M}\]
09

Classify the solution

Since the hydrogen ion concentration is smaller than the hydroxide ion concentration, the solution is basic.

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Most popular questions from this chapter

(a) Give the conjugate base of the following Brønsted Lowry acids: (i) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-},\) (ii) HBr. (b) Give the conjugate acid of the following Bronsted-Lowry bases: (i) \(\mathrm{CN}^{-},\) (ii) \(\mathrm{HSO}_{4}^{-}\).

Ammonia, \(\mathrm{NH}_{3}\), acts as an Arrhenius base, a Brønsted-Lowry base, and a Lewis base, in aqueous solution. Write out the reaction \(\mathrm{NH}_{3}\) undergoes with water and explain what properties of ammonia correspond to each of the three definitions of "base."

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.

Consider two solutions, solution A and solution B. [H \(\left.^{+}\right]\) in solution A is 25 times greater than that in solution \(B\). What is the difference in the pH values of the two solutions?

Identify the Brønsted-Lowry acid and the BrønstedLowry base on the left side of each equation, and also identify the conjugate acid and conjugate base of each on the right side. $$ \begin{array}{l} \text { (a) } \mathrm{HBrO}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{BrO}^{-}(a q) \\\ \text { (b) } \mathrm{HSO}_{4}^{-}(a q)+\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons \mathrm{SO}_{4}^{2-}(a q)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q) \\ \text { (c) } \mathrm{HSO}_{3}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \end{array} $$
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