Explain the characterization of aqueous solutions as acidic, basic, or neutralExpress hydronium and hydroxide ion concentrations on the pH and pOH scalesPerform calculations relating pH and pOH

As discussed earlier, hydronium và hydroxide ions are present both in pure water & in all aqueous solutions, and their concentrations are inversely proportional as determined by the ion hàng hóa of water (Kw). The concentrations of these ions in a solution are often critical determinants of the solution’s properties & the chemical behaviors of its other solutes, và specific vocabulary has been developed lớn describe these concentrations in relative terms. A solution is neutral if it contains equal concentrations of hydronium và hydroxide ions; acidic if it contains a greater concentration of hydronium ions than hydroxide ions; and basic if it contains a lesser concentration of hydronium ions than hydroxide ions.

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A common means of expressing quantities, the values of which may span many orders of magnitude, is lớn use a logarithmic scale. One such scale that is very popular for chemical concentrations and equilibrium constants is based on the p-function, defined as shown where “X” is the quantity of interest & “log” is the base-10 logarithm:

The pH of a solution is therefore defined as shown here, where is the molar concentration of hydronium ion in the solution:

Finally, the relation between these two ion concentration expressed as p-functions is easily derived from the Kw expression:

- extlog;K_ extw = - extlog(< extOH^->) = - extlog;+;- extlog
extpK_ extw = extpH;+; extpOH

At 25 °C, the value of Kw is 1.0 × 10−14, và so:

14.00 = extpH;+; extpOH

As was shown in Example 1 in Chapter 14.1 Brønsted-Lowry Acids & Bases, the hydronium ion molarity in pure water (or any neutral solution) is 1.0 × 10−7M at 25 °C. The pH and pOH of a neutral solution at this temperature are therefore:

And so, at this temperature, acidic solutions are those with hydronium ion molarities greater than 1.0 × 10−7M và hydroxide ion molarities less than 1.0 × 10−7M (corresponding khổng lồ pH values less than 7.00 & pOH values greater than 7.00). Basic solutions are those with hydronium ion molarities less than 1.0 × 10−7M and hydroxide ion molarities greater than 1.0 × 10−7M (corresponding khổng lồ pH values greater than 7.00 and pOH values less than 7.00).

Since the autoionization constant Kw is temperature dependent, these correlations between pH values and the acidic/neutral/basic adjectives will be different at temperatures other than 25 °C. For example, the “Check Your Learning” exercise accompanying Example 1 in Chapter 14.1 Brønsted-Lowry Acids và Bases showed the hydronium molarity of pure water at 80 °C is 4.9 × 10−7M, which corresponds khổng lồ pH and pOH values of:

At this temperature, then, neutral solutions exhibit pH = pOH = 6.31, acidic solutions exhibit pH less than 6.31 and pOH greater than 6.31, whereas basic solutions exhibit pH greater than 6.31 và pOH less than 6.31. This distinction can be important when studying certain processes that occur at nonstandard temperatures, such as enzyme reactions in warm-blooded organisms. Unless otherwise noted, references to lớn pH values are presumed to lớn be those at standard temperature (25 °C) (Table 1).

ClassificationRelative Ion ConcentrationspH at 25 °C
acidic > pH 3O+> = pH = 7
basic −>pH > 7
Table 1. Summary of Relations for Acidic, Basic và Neutral Solutions

Figure 1 shows the relationships between , , pH, và pOH, & gives values for these properties at standard temperatures for some common substances.

Figure 1. The pH và pOH scales represent concentrations of và OH−, respectively. The pH and pOH values of some common substances at standard temperature (25 °C) are shown in this chart.

### Example 1

Calculation of pH from What is the pH of stomach acid, a solution of HCl with a hydronium ion concentration of 1.2 × 10−3M?

Solution

extpH = - extlog
= - extlog(1.2; imes;10^-3)
= -(-2.92) =2.92

(The use of logarithms is explained in Appendix B. Recall that, as we have done here, when taking the log of a value, keep as many decimal places in the result as there are significant figures in the value.)

Check Your LearningWater exposed to air contains carbonic acid, H2CO3, due lớn the reaction between carbon dioxide and water:

extCO_2(aq);+; extH_2 extO(l);leftrightharpoons; extH_2 extCO_3(aq)

Air-saturated water has a hydronium ion concentration caused by the dissolved CO2 of 2.0 × 10−6M, about 20-times larger than that of pure water. Calculate the pH of the solution at 25 °C.

### Example 2

Calculation of Hydronium Ion Concentration from pHCalculate the hydronium ion concentration of blood, the pH of which is 7.3 (slightly alkaline).

Solution

< extH_3 extO^+> = 10^-7.3; extor;< extH_3 extO^+> = extantilog;of;;-7.3

(On a calculator take the antilog, or the “inverse” log, of −7.3, or calculate 10−7.3.)

Check Your LearningCalculate the hydronium ion concentration of a solution with a pH of −1.07.

### Environmental Science

Normal rainwater has a pH between 5 và 6 due lớn the presence of dissolved CO2 which forms carbonic acid:

extH_2 extO(l);+; extCO_2(g);longrightarrow; extH_2 extCO_3(aq)
extH_2 extCO_3(aq); ightleftharpoons; extH^+(aq);+; extHCO_3^;;-(aq)

Acid rain is rainwater that has a pH of less than 5, due to a variety of nonmetal oxides, including CO2, SO2, SO3, NO, and NO2 being dissolved in the water & reacting with it to size not only carbonic acid, but sulfuric acid và nitric acid. The formation và subsequent ionization of sulfuric acid are shown here:

extH_2 extO(l);+; extSO_3(g);longrightarrow; extH_2 extSO_4(aq)
extH_2 extSO_4(aq);longrightarrow; extH^+(aq);+; extHSO_4^;;-(aq)

Carbon dioxide is naturally present in the atmosphere because we & most other organisms produce it as a waste hàng hóa of metabolism. Carbon dioxide is also formed when fires release carbon stored in vegetation or when we burn wood or fossil fuels. Sulfur trioxide in the atmosphere is naturally produced by volcanic activity, but it also stems from burning fossil fuels, which have traces of sulfur, và from the process of “roasting” ores of metal sulfides in metal-refining processes. Oxides of nitrogen are formed in internal combustion engines where the high temperatures make it possible for the nitrogen & oxygen in air to chemically combine.

Acid rain is a particular problem in industrial areas where the products of combustion & smelting are released into the air without being stripped of sulfur and nitrogen oxides. In North America và Europe until the 1980s, it was responsible for the destruction of forests and freshwater lakes, when the acidity of the rain actually killed trees, damaged soil, and made lakes uninhabitable for all but the most acid-tolerant species. Acid rain also corrodes statuary and building facades that are made of marble và limestone (Figure 2). Regulations limiting the amount of sulfur & nitrogen oxides that can be released into the atmosphere by industry & automobiles have reduced the severity of acid damage to both natural và manmade environments in North America and Europe. It is now a growing problem in industrial areas of đài loan trung quốc and India.

For further information on acid rain, visit this website hosted by the US Environmental Protection Agency.

Figure 2. (a) Acid rain makes trees more susceptible lớn drought and insect infestation, & depletes nutrients in the soil. (b) It also is corrodes statues that are carved from marble or limestone. (credit a: modification of work by Chris M Morris; credit b: modification of work by “Eden, Janine and Jim”/Flickr)

### Example 3

Calculation of pOHWhat are the pOH and the pH of a 0.0125-M solution of potassium hydroxide, KOH?

SolutionPotassium hydroxide is a highly soluble ionic compound & completely dissociates when dissolved in dilute solution, yielding = 0.0125 M:

Check Your LearningThe hydronium ion concentration of vinegar is approximately 4 × 10−3M. What are the corresponding values of pOH and pH?

The acidity of a solution is typically assessed experimentally by measurement of its pH. The pOH of a solution is not usually measured, as it is easily calculated from an experimentally determined pH value. The pH of a solution can be directly measured using a pH meter (Figure 3).

Figure 3. (a) A research-grade pH meter used in a laboratory can have a resolution of 0.001 pH units, an accuracy of ± 0.002 pH units, và may cost in excess of \$1000. (b) A portable pH meter has lower resolution (0.01 pH units), lower accuracy (± 0.2 pH units), & a far lower price tag. (credit b: modification of work by Jacopo Werther)

The pH of a solution may also be visually estimated using colored indicators (Figure 4).

Figure 4.

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(a) A universal indicator assumes a different màu sắc in solutions of different pH values. Thus, it can be added lớn a solution to lớn determine the pH of the solution. The eight vials each contain a universal indicator and 0.1-M solutions of progressively weaker acids: HCl (pH = l), CH3CO2H (pH = 3), and NH4Cl (pH = 5), deionized water, a neutral substance (pH = 7); và 0.1-M solutions of the progressively stronger bases: KCl (pH = 7), aniline, C6H5NH2 (pH = 9), NH3 (pH = 11), & NaOH (pH = 13). (b) pH paper contains a mixture of indicators that give different colors in solutions of differing pH values. (credit: modification of work by Sahar Atwa)Key Concepts & Summary

The concentration of hydronium ion in a solution of an acid in water is greater than 1.0 × 10−7M at 25 °C. The concentration of hydroxide ion in a solution of a base in water is greater than 1.0 × 10−7M at 25 °C. The concentration of extH_3 extO^+ in a solution can be expressed as the pH of the solution; extpH = - extlog. The concentration of OH− can be expressed as the pOH of the solution: pOH = −log. In pure water, pH = 7.00 và pOH = 7.00

Key Equations extpH = - extlogpOH = −log = 10−pH = 10−pOHpH + pOH = pKw = 14.00 at 25 °C

### Chemistry end of Chapter Exercises

Explain why a sample of pure water at 40 °C is neutral even though = 1.7 × 10−7M. Kw is 2.9 × 10−14 at 40 °C.The ionization constant for water (Kw) is 2.9 × 10−14 at 40 °C. Calculate , , pH, & pOH for pure water at 40 °C.The ionization constant for water (Kw) is 9.311 × 10−14 at 60 °C. Calculate , , pH, & pOH for pure water at 60 °C.Calculate the pH và the pOH of each of the following solutions at 25 °C for which the substances ionize completely:

(a) 0.200 M HCl

(b) 0.0143 M NaOH

(c) 3.0 M HNO3

(d) 0.0031 M Ca(OH)2

Calculate the pH & the pOH of each of the following solutions at 25 °C for which the substances ionize completely:

(a) 0.000259 M HClO4

(b) 0.21 M NaOH

(c) 0.000071 M Ba(OH)2

(d) 2.5 M KOH

What are the pH and pOH of a solution of 2.0 M HCl, which ionizes completely?What are the hydronium và hydroxide ion concentrations in a solution whose pH is 6.52?The hydronium ion concentration in a sample of rainwater is found lớn be 1.7 × 10−6 M at 25 °C. What is the concentration of hydroxide ions in the rainwater?The hydroxide ion concentration in household ammonia is 3.2 × 10−3 M at 25 °C. What is the concentration of hydronium ions in the solution?

## Glossary

acidicdescribes a solution in which > basicdescribes a solution in which −>neutraldescribes a solution in which = pHlogarithmic measure of the concentration of hydronium ions in a solutionpOHlogarithmic measure of the concentration of hydroxide ions in a solution

### Solutions

Answers to Chemistry kết thúc of Chapter Exercises

1. In a neutral solution = . At 40 °C, = = (2.910−14)1/2 = 1.7 × 10−7.

3. x = 3.051 × 10−7M = = pH = −log3.051 × 10−7 = −(−6.5156) = 6.5156pOH = pH = 6.5156

5. (a) pH = 3.587; pOH = 10.413; (b) pH = 0.68; pOH = 13.32; (c) pOH = 3.85; pH = 10.15; (d) pH = −0.40; pOH = 14.4