Chemistry
pH and pOH
pH and pOH are measures of the acidity and basicity of a solution, respectively. pH is the negative logarithm of the hydrogen ion concentration, while pOH is the negative logarithm of the hydroxide ion concentration. Both pH and pOH are used to quantify the strength of acids and bases in a solution, with lower values indicating higher acidity or basicity.
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eBook - PDFAnalytical Chemistry
A Toolkit for Scientists and Laboratory Technicians
- Bryan M. Ham, Aihui MaHam(Authors)
- 2024(Publication Date)
- Wiley(Publisher)
The pH scale in general is defined as: If the solution pH is 7.0, the solution is neutral. If the solution pH is <7.0, the solution is acidic. If the solution pH is >7.0, the solution is basic. The pOH in Figure 9.4 is the negative log of the molar [OH − ] concentration. pOH = − log[OH − ] (9.61) A useful relationship exists between pH, pOH, and the ion product for water, K w : pH + pOH = pK w (9.62) MEASURING THE PH 171 Acidic pH Basic pH pH Scale 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pH [H + ] [OH – ] pOH 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 × 10 –14 1 × 10 0 1 × 10 –13 1 × 10 –12 1 × 10 –11 1 × 10 –10 1 × 10 –9 1 × 10 –8 1 × 10 –7 1 × 10 –6 1 × 10 –5 1 × 10 –4 1 × 10 –3 1 × 10 –2 1 × 10 –1 1 × 10 0 1 × 10 –14 1 × 10 –1 1 × 10 –2 1 × 10 –3 1 × 10 –4 1 × 10 –5 1 × 10 –6 1 × 10 –7 1 × 10 –8 1 × 10 –9 1 × 10 –10 1 × 10 –11 1 × 10 –12 1 × 10 –13 Ammonia solution Baking soda Milk Blood Rain water Coffee Stomach fluid Soft drink Fresh egg Lemons Tomatoes Calcium carbonate Milk of magnesia FIGURE 9.4 The pH scale, the hydrogen ion concentration [H + ], the hydroxide ion concentration [OH − ], the pOH, and the pH of some common solutions and substances. If we know the pH of a solution, then we can calculate the pOH from the relationship in Equation 9.12. Suppose a solution has a pH of 5.9. The value of pK w is −log(1 × 10 −14 ) = 14, thus: 5.9 + pOH = 14 (9.63) pOH = 8.1 (9.64) 9.13 MEASURING THE pH The laboratory technician and chemical analyst will often mea- sure the pH of a solution or of a substance dissolved in water. The pH is not usually calculated from a determination of the hy- drogen ion [H + ] molar concentration by any wet chemical anal- yses such as titration, but typically by a pH meter, or sometimes as an approximate estimation by pH paper or strips as depicted in Figure 9.2. An example of a typical pH meter is depicted in Figure 9.5. The pH meter system consists of a pH-sensing elec- trode and a readout screen.
eBook - PDFChemistry
Structure and Dynamics
- James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
He therefore introduced the symbol p to indicate the negative of the logarithm of a number. Thus, pH is the negative of the logarithm of the H 3 O ion concentration. Similarly, pOH is the negative of the logarithm of the OH ion concentration. It should be noted that the equations for pH and pOH are valid only for dilute solutions of acid or base in pure water. Most solutions used in the labora- tory do not meet this criterion, so the above equations can only be used to approx- imate the pH and pOH of real solutions. Since values from these calculations are approximations, they are normally reported to no more than two digits after the decimal. A pH meter, however, can accurately determine the pH of a solution to two digits after the decimal. If the pH is given, the H 3 O ion concentration can be calculated with the following equation. [H 3 O + ] = 10 - pH pOH = - log[OH - ] pH = - log[H 3 O + ] log(10 - 7 ) = - 7 478 CHAPTER 11 / ACIDS AND BASES ➤ CHECKPOINT When an acid is added to water, the equilibrium between neutral water mol- ecules and their ions shifts to the left, decreasing the amount of H 3 O from the dissociation of water. Does K w still equal 1.0 10 14 ? 2 H 2 O(l) uv H 3 O + (aq) + OH - (aq) The advantage of the pH scale is illustrated in Figure 11.5, which shows the possible combinations of H 3 O ion and OH concentrations in an aqueous solu- tion. In Figure 11.5a, the concentration of the OH ion is plotted on the vertical axis, and the concentration of the H 3 O ion is plotted on the horizontal axis. For the plot to be a reasonable size, it has to be restricted to only 1 order of magni- tude of concentration. The concept of pH compresses the range of H 3 O concentrations onto a scale that is much easier to handle. As the H 3 O concentration decreases from roughly 1 M to 10 14 M, the pH of the solution increases from 0 to 14.
eBook - PDFChemistry
The Molecular Nature of Matter
- James E. Brady, Neil D. Jespersen, Alison Hyslop(Authors)
- 2014(Publication Date)
- Wiley(Publisher)
According to the color code, the pH of the solution is closer to 3 than to the color for pH 5. Andy Washnik 806 Chapter 16 | Acid–Base Equilibria in Aqueous Solutions | Summary Organized by Learning Objective Define pH and explain the use of “p” notation Water reacts with itself to produce small amounts of H 3 O + (often abbreviated H + ) and OH - ions. The concentrations of these ions, both in pure water and dilute aqueous solutions, are related by the expression 3 H + 4 3 OH - 4 = K w = 1.0 Ž 10 -14 (at 25 °C) K w is the ion product constant of water. In pure water 3 H + 4 = 3 OH - 4 = 1.0 Ž 10 -7 The pH of a solution is defined by the equation, pH = -log[H + ]. As the pH decreases, the acidity, or [H + ], increases. The compa- rable term, pOH (= -log[OH - ]), is used to describe a solution that is basic. A solution is acidic if the hydrogen ion concentration exceeds 1.0 Ž 10 -7 or the pH is less than 7.00. Similarly, a solution is basic if the hydroxide ion concentration exceeds 1.0 Ž 10 -7 or if the pH is greater than 7.00. Explain how to determine the pH of strong acids or bases in aqueous solution When calculating the pH of strong acids or strong bases, we assume that they are 100% ionized. Write expressions for the acid ionization constant, K a , and base ionization constant, K b , and explain how they are related to each other A weak acid H A ionizes according to the general equation H A + H 2 O m H 3 O + + A - or more simply, H A mH + + A - The equilibrium constant is called the acid ionization con- stant, K a : K a = 3 H 3 O + 4 3 A - 4 3 H A 4 A weak base B ionizes by the general equation B + H 2 O mBH + + OH - The equilibrium constant is called the base ionization con- stant, K b : K b = 3 BH + 4 3 OH - 4 3 B 4 The smaller the values of K a (or K b ), the weaker are the sub- stances as Brønsted acids (or bases).
eBook - PDF- Douglas P. Heller, Carl H. Snyder(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
[H 3 O + ] [H 3 O + ] A basic solution has a pH greater than 7. 10 –14 10 –13 10 –12 10 –11 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 10 –14 10 –13 10 –12 10 –11 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 Low concentration High concentration Low concentration High concentration pH = 3 Here, [H 3 O + ] = 10 –3 , so pH = 3. [H 3 O + ] [H 3 O + ] [OH – ] An acidic solution has a pH less than 7. 10 –14 10 –13 10 –12 10 –11 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 10 –14 10 –13 10 –12 10 –11 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 Low concentration High concentration Low concentration High concentration [OH – ] Any increase in the hydronium ion concentration above 10 −7 (with an associated decrease in the hydroxide ion concentration) produces an acidic solution: Any decrease in the hydronium ion concentration below 10 −7 (with an associated increase in the hydroxide ion concentration) produces a basic solution: The pH Scale 245 increases [OH − ] and lowers [H 3 O + ]. We can see this see- saw effect and its relation to pH in Figure 8.11 In Words, Math, and Pictures. To summarize, at 25°C: • The pH of a neutral solution equals 7. • The pH of an acidic solution is less than 7. • The pH of a basic solution is greater than 7. We can see the relationship between hydronium ion con- centration and pH in Figure 8.12. We can increase the H 3 O + concentration of a solution by adding acid, such as HCl. Conversely, we can increase the OH − concentration by adding base, such as NaOH. Furthermore, the value obtained by multiplying the hy- dronium ion concentration of a solution, [H 3 O + ], by its hydroxide ion concentration, [OH − ], is always constant, regardless of the addition of acid or base to the water. Since the value of this product remains fixed at any spe- cific temperature, adding acid not only increases [H 3 O + ] but lowers [OH − ] as well.
eBook - PDF- Gary D. Christian, Purnendu K. Dasgupta, Kevin A. Schug(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
2 This is because at these high concentrations, the activity coefficient is less than unity (although at still higher concentrations the activity coefficient may become greater than unity—see Chapter 6). Nevertheless, there is mathematically no basis for not having a negative pH (or a negative pOH), although it may be rarely encountered in situations relevant to analytical chemistry. If the concentration of an acid or base is much less than 10 −7 M, then its contribution to the acidity or basicity will be negligible compared with the contribution The pH of 10 −9 M HCl is not 9! from water. The pH of a 10 −8 M sodium hydroxide solution would therefore not differ significantly from 7. If the concentration of the acid or base is around 10 −7 M, then its contribution is not negligible and neither is that from water; hence the sum of the two contributions must be taken. Example 7.6 Calculate the pH and pOH of a 1.0 × 10 −7 M solution of HCl. Solution Equilibria: HCl → H + + Cl − H 2 O H + + OH − [H + ][OH − ] = 1.0 × 10 −14 [H + ] H 2 Odiss. = [OH − ] H 2 Odiss. = x Since the hydrogen ions contributed from the ionization of water are not negligible compared to the HCl added, [H + ] = C HCl + [H + ] H 2 Odiss. Then, ([H + ] HCl + x)(x) = 1.0 × 10 −14 (1.00 × 10 −7 + x)(x) = 1.0 × 10 −14 x 2 + 1.00 × 10 −7 x − 1.0 × 10 −14 = 0 Using the quadratic equation to solve [see Appendix B] or the use of Excel Goal Seek (Section 6.11), x = −1.00 × 10 −7 ± 1.0 × 10 −14 + 4(1.0 × 10 −14 ) 2 = 6.2 × 10 −8 M 2 As will be seen in Chapter 13, it is also difficult to measure the pH of a solution having a negative pH or pOH because high concentrations of acids or bases tend to introduce an error in the measurement by adding a significant and unknown liquid-junction potential in the measurements.
- Peter V. Hobbs(Author)
- 2000(Publication Date)
- Cambridge University Press(Publisher)
We see from definition (5.14) that (1) the greater the hydrogen ion concentration (i.e., the more acidic the solution) the smaller is the pH value of the solution, and (2) a change in the hydrogen ion concentration by a factor of ten (e.g., from 10 1 to 10~ 2 M) changes the pH value by unity. At the beginning of this section we defined a solution as being neutral if [H + (aq)] = [OH(aq)]. Pure water is neutral; therefore, from Eqs. (5.12) and (5.13) [H 3 O + (aq)][OH-(aq)] = l(r 14 or, [H 3 O + (aq)] 2 =10-Therefore, for pure water [H 3 O + (aq)] = [H + (aq)] = 10 7 M Hence, the pH of pure water is -log(10~ 7 ) = 7. It follows that acidic solu-tions have pH < 7 and basic solutions have pH > 7. Observed pH values in nature are generally between 4 and 9. Seawater normally has a pH between 8.1 and 8.3. Streams in wet climates generally have a pH between 5 and 6.5 and in dry climates between 7 and 8. Soil water in the presence of abundant decaying vegetation may have a pH of 4 or lower. The pH of rainwater can range from quite acidic (around 4.0) in industrial regions to about 5.6 in very clean regions. We will discuss the acidity of rainwater in some detail at the end of this chapter, but the following exercise illustrates why even clean rainwater does not have a pH of 7. Exercise 5.2. The pH of natural rainwater is about 5.6. Assum-ing that all of this acidity is due to the absorption of CO 2 by the rain, determine how many moles of CO 2 would have to be absorbed in 1L of rainwater. Solution. Since the pH of rainwater is 5.6, the concentration of H 3 O + (aq) in natural rainwater is given by pH = 5.6 = -log[H 3 O + (aq)] Therefore, [H 3 O + (aq)] = 0.25xl0-5 M 90 Acids and bases The main source of H 3 O + (aq) when CO 2 dissolves in water is CO 2 (g) + H 2 O(l)+±H 2 CO 3 (aq) (5.15a) H 2 CO 3 (aq) + H 2 O(1) ?± HCO 3 -(aq) + H 3 O + (aq) (5.15b) We see from Reactions (5.15) that for every mole of CO 2 that is absorbed in water, one mole of H 3 O + (aq) is produced.
eBook - PDF- William R. Robinson, Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
18. Calculate the pH and 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 HNO 3 (d) 0.0031 M Ca(OH) 2 19. Calculate the pH and the pOH of each of the following solutions at 25 °C for which the substances ionize completely: (a) 0.000259 M HClO 4 (b) 0.21 M NaOH (c) 0.000071 M Ba(OH) 2 (d) 2.5 M KOH 20. What are the pH and pOH of a solution of 2.0 M HCl, which ionizes completely? 21. What are the hydronium and hydroxide ion concentrations in a solution whose pH is 6.52? 22. Calculate the hydrogen ion concentration and the hydroxide ion concentration in wine from its pH. See Figure 14.2 for useful information. 794 Chapter 14 | Acid-Base Equilibria This OpenStax book is available for free at http://cnx.org/content/col12012/1.7 23. Calculate the hydronium ion concentration and the hydroxide ion concentration in lime juice from its pH. See Figure 14.2 for useful information. 24. The hydronium ion concentration in a sample of rainwater is found to be 1.7 × 10 −6 M at 25 °C. What is the concentration of hydroxide ions in the rainwater? 25. 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? 14.3 Relative Strengths of Acids and Bases 26. Explain why the neutralization reaction of a strong acid and a weak base gives a weakly acidic solution. 27. Explain why the neutralization reaction of a weak acid and a strong base gives a weakly basic solution. 28. Use this list of important industrial compounds (and Figure 14.8) to answer the following questions regarding: CaO, Ca(OH) 2 , CH 3 CO 2 H, CO 2, HCl, H 2 CO 3 , HF, HNO 2 , HNO 3 , H 3 PO 4 , H 2 SO 4 , NH 3 , NaOH, Na 2 CO 3 . (a) Identify the strong Brønsted-Lowry acids and strong Brønsted-Lowry bases. (b) List those compounds in (a) that can behave as Brønsted-Lowry acids with strengths lying between those of H 3 O + and H 2 O.
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2015(Publication Date)
- Openstax(Publisher)
18. Calculate the pH and 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 HNO 3 (d) 0.0031 M Ca(OH) 2 19. Calculate the pH and the pOH of each of the following solutions at 25 °C for which the substances ionize completely: (a) 0.000259 M HClO 4 (b) 0.21 M NaOH (c) 0.000071 M Ba(OH) 2 (d) 2.5 M KOH 20. What are the pH and pOH of a solution of 2.0 M HCl, which ionizes completely? 21. What are the hydronium and hydroxide ion concentrations in a solution whose pH is 6.52? 22. Calculate the hydrogen ion concentration and the hydroxide ion concentration in wine from its pH. See Figure 14.2 for useful information. 828 Chapter 14 | Acid-Base Equilibria This OpenStax book is available for free at http://cnx.org/content/col11760/1.9 23. Calculate the hydronium ion concentration and the hydroxide ion concentration in lime juice from its pH. See Figure 14.2 for useful information. 24. The hydronium ion concentration in a sample of rainwater is found to be 1.7 × 10 −6 M at 25 °C. What is the concentration of hydroxide ions in the rainwater? 25. 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? 14.3 Relative Strengths of Acids and Bases 26. Explain why the neutralization reaction of a strong acid and a weak base gives a weakly acidic solution. 27. Explain why the neutralization reaction of a weak acid and a strong base gives a weakly basic solution. 28. Use this list of important industrial compounds (and Figure 14.8) to answer the following questions regarding: CaO, Ca(OH) 2 , CH 3 CO 2 H, CO 2, HCl, H 2 CO 3 , HF, HNO 2 , HNO 3 , H 3 PO 4 , H 2 SO 4 , NH 3 , NaOH, Na 2 CO 3 . (a) Identify the strong Brønsted-Lowry acids and strong Brønsted-Lowry bases. (b) List those compounds in (a) that can behave as Brønsted-Lowry acids with strengths lying between those of H 3 O + and H 2 O.
eBook - PDFGeneral, Organic, and Biological Chemistry
An Integrated Approach
- Kenneth W. Raymond(Author)
- 2012(Publication Date)
- Wiley(Publisher)
7.6 The pH Scale 253 SOLUTION a. [H 3 O + ] = 10 - pH = 10 - 6 = 1 * 10 - 6 M (acidic) b. [H 3 O + ] = 10 - pH = 10 - 6.5 = 3 * 10 - 7 M (acidic) c. [H 3 O + ] = 10 - pH = 10 - 1.2 = 6 * 10 - 2 M (acidic) Solving part a does not require a calculator. All three answers are reported with one signifi- cant figure (Math Support—Logs and Antilogs). PRACTICE PROBLEM 7.8 What is [OH - ] in the following solutions? Indicate whether each is acidic, neutral, or basic. a. pH = 7.2 b. pH = 9.1 c. pH = 3.3 MATH SUPPORT—LOGS AND ANTILOGS On your scientific calculator you should be able to calculate logarithms (logs). If you try a few calculations, you will see that log 100 = 2 log 1000 = 3 log 0.0001 = -4 Converting these three numbers (100, 1000, and 0.0001) into scientific notation (Section 1.4) should help explain what the log or logarithm of a number is. log 100 = log 10 2 = 2 log 1000 = log 10 3 = 3 log 0.0001 = log 10 -4 = -4 The log of a number is the power to which ten must be raised to equal the number (log 10 n = n). The log of 100 is 2, because 10 2 equals 100 and the log of 0.0001 is -4 because 10 -4 = 0.0001. When a number has the value 1 * 10 n , where n is an integer (-2, 5, etc.), its log can be determined without using a calculator. In these cases, the log is equal to the value of n. log 1 * 10 -2 = -2 log 1 * 10 5 = 5 In all other cases (7.9 * 10 2 , 2.2 * 10 -5 , etc.), a calculator will be required. log 7.9 * 10 2 = 2.90 log 2.2 * 10 -5 = -4.66 Reversing this process gives the antilog or antilogarithm of a number (antilog n = 10 n ). log of 10 2 = 2, so antilog 2 = 10 2 log of 10 -8 = -8, so antilog -8 = 10 -8 When n is an integer (2, -8, etc.), its antilog can be determined without using a calculator, because the antilog is equal to 10 n (see the two examples directly above). At other times (3.5, -1.3, etc.) a calculator must be used.
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
To obtain this ideal result, selecting an appropriate indicator requires foresight. We will understand this better by studying how the pH of the solution being titrated changes with the addition of titrant. When the pH of a solution at different stages of a titration is plotted against the volume of titrant added, we obtain a titration curve. The values of pH in these plots can be exper- imentally measured using a pH meter during the titration, or they can be calculated by the procedures we will describe below. We will use the calculation method, and also demonstrate that all titration curves can be described by four calculations. Two calculations describe single points on the curve, the start- ing point and the equivalence point. The other two calculations are simple limiting reactant calculations for (a) mixtures between the start and the equivalence point and for (b) after the equivalence point. Strong Acid–Strong Base Titrations The titration of HCl(aq) with a standardized NaOH solution illustrates the titration of a strong acid by a strong base. The molecular and net ionic equations are HCl (aq) + NaOH (aq) ⟶ NaCl (aq) + H 2 O H + (aq) + OH − (aq) ⟶ H 2 O Let’s consider what happens to the pH of a solution, initially 25.00 mL of 0.2000 M HCl, as small amounts of the titrant, 0.2000 M NaOH, are added. We will calculate the pH of the resulting solution at various stages of the titration, retaining only two decimal places, and plot the values against the volume of titrant. At the start, before any titrant has been added, the receiving flask contains only 0.2000 M HCl. Because this is a strong acid, we know that [H + ] = [HCl] = 0.2000 M So the initial pH is pH = − log ( 0.2000 ) = 0.70 After the start but before the equivalence point we need to determine the concentration of the excess reactant in a simple limiting reactant problem. Let’s first calculate the amount of HCl initially present in 25.00 mL of 0.2000 M HCl.
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