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Chapter 13: Problem 46

Calculate the \(\left[\mathrm{H}^{+}\right]\) of each of the following solutions at \(25^{\circ} \mathrm{C}\) Identify each solution as neutral, acidic, or basic. a. \(\left[\mathrm{OH}^{-}\right]=1.5 \mathrm{M}\) b. \(\left[\mathrm{OH}^{-}\right]=3.6 \times 10^{-15} \mathrm{M}\) c. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=7.3 \times 10^{-4} \mathrm{M}\)

Short Answer

Expert verified
The $\left[\mathrm{H}^{+}\right]$ concentrations for each solution are as follows: a. $\left[\mathrm{H}^{+}\right] = 6.67 \times 10^{-15}\ \mathrm{M}$, basic. b. $\left[\mathrm{H}^{+}\right] = 2.78 \times 10^{-9}\ \mathrm{M}$, acidic. c. $\left[\mathrm{H}^{+}\right] = 1.0 \times 10^{-7}\ \mathrm{M}$, neutral. d. $\left[\mathrm{H}^{+}\right] = 1.37 \times 10^{-12}\ \mathrm{M}$, basic.

Step by step solution

01

Calculate the concentration of H⁺ ions

Using the ion product of water, \(K_w = [\mathrm{H}^{+}][\mathrm{OH}^-]\) \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) Plug in the values: \([\mathrm{H}^{+}] = \frac{1.0 \times 10^{-14}}{1.5}\) \([\mathrm{H}^{+}] = 6.67 \times 10^{-15}\ \mathrm{M}\)
02

Determine if the solution is neutral, acidic, or basic

Since the H⁺ ion concentration is less than the OH⁻ ion concentration, the solution is basic. b. \(\left[\mathrm{OH}^{-}\right]=3.6 \times 10^{-15} \mathrm{M}\)
03

Calculate the concentration of H⁺ ions

Using the ion product of water, \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) Plug in the values: \([\mathrm{H}^{+}] = \frac{1.0 \times 10^{-14}}{3.6 \times 10^{-15}}\) \([\mathrm{H}^{+}] = 2.78 \times 10^{-9}\ \mathrm{M}\)
04

Determine if the solution is neutral, acidic, or basic

Since the H⁺ ion concentration is greater than the OH⁻ ion concentration, the solution is acidic. c. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}\)
05

Calculate the concentration of H⁺ ions

Using the ion product of water, \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) Plug in the values: \([\mathrm{H}^{+}] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-7}}\) \([\mathrm{H}^{+}] = 1.0 \times 10^{-7}\ \mathrm{M}\)
06

Determine if the solution is neutral, acidic, or basic

Since the H⁺ ion concentration is equal to the OH⁻ ion concentration, the solution is neutral. d. \(\left[\mathrm{OH}^{-}\right]=7.3 \times 10^{-4} \mathrm{M}\)
07

Calculate the concentration of H⁺ ions

Using the ion product of water, \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) Plug in the values: \([\mathrm{H}^{+}] = \frac{1.0 \times 10^{-14}}{7.3 \times 10^{-4}}\) \([\mathrm{H}^{+}] = 1.37 \times 10^{-12}\ \mathrm{M}\)
08

Determine if the solution is neutral, acidic, or basic

Since the H⁺ ion concentration is less than the OH⁻ ion concentration, the solution is basic.

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Most popular questions from this chapter

Write out the stepwise \(K_{\mathrm{a}}\) reactions for citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) a triprotic acid.

A solution is prepared by dissolving 0.56 g benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}, K_{\mathrm{a}}=6.4 \times 10^{-5}\right)\) in enough water to make \(1.0 \mathrm{L}\) of solution. Calculate \(\left[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\right],\left[\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}\right],\left[\mathrm{H}^{+}\right],\left[\mathrm{OH}^{-}\right]\) and the pH of this solution.

Hemoglobin (abbreviated Hb) is a protein that is responsible for the transport of oxygen in the blood of mammals. Each hemoglobin molecule contains four iron atoms that are the binding sites for \(\mathrm{O}_{2}\) molecules. The oxygen binding is \(\mathrm{pH}\) dependent. The relevant equilibrium reaction is $$\mathrm{HbH}_{4}^{4+}(a q)+4 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Hb}\left(\mathrm{O}_{2}\right)_{4}(a q)+4 \mathrm{H}^{+}(a q)$$ Use Le Châtelier's principle to answer the following. a. What form of hemoglobin, \(\mathrm{HbH}_{4}^{4+}\) or \(\mathrm{Hb}\left(\mathrm{O}_{2}\right)_{4},\) is favored in the lungs? What form is favored in the cells? b. When a person hyperventilates, the concentration of \(\mathrm{CO}_{2}\) in the blood is decreased. How does this affect the oxygenbinding equilibrium? How does breathing into a paper bag help to counteract this effect? (See Exercise 146.) c. When a person has suffered a cardiac arrest, injection of a sodium bicarbonate solution is given. Why is this necessary? (Hint: \(\mathrm{CO}_{2}\) blood levels increase during cardiac arrest.

Calculate the \(\mathrm{pH}\) of each of the following solutions of a strong acid in water. a. \(0.10 \mathrm{M} \mathrm{HCl}\) b. 5.0 M HCl c. \(1.0 \times 10^{-11} \mathrm{M} \mathrm{HCl}\)

The pH of \(1.0 \times 10^{-8} M\) hydrochloric acid is not \(8.00 .\) The correct \(\mathrm{pH}\) can be calculated by considering the relationship between the molarities of the three principal ions in the solution \(\left(\mathrm{H}^{+}, \mathrm{Cl}^{-}, \text {and } \mathrm{OH}^{-}\right) .\) These molarities can be calculated from algebraic equations that can be derived from the considerations given below. a. The solution is electrically neutral. b. The hydrochloric acid can be assumed to be \(100 \%\) ionized. c. The product of the molarities of the hydronium ions and the hydroxide ions must equal \(K_{\mathrm{w}}\) Calculate the \(\mathrm{pH}\) of a \(1.0 \times 10^{-8}-M\) HCl solution.
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