Understanding the pH Scale: Acidity and Basicity of Solutions

1. Chapter 14 Acids and Bases 14.6 The pH Scale

2. pH Scale The pH of a solution • is used to indicate the acidity of a solution • has values that usually range from 0 to 14 • is acidic when the values are less than 7 • is neutral with a pH of 7 • is basic when the values are greater than 7

3. pH of Everyday Substances

4. Learning Check Identify each solution as A) acidic, B) basic, or N) neutral. 1. ___ HCl with a pH = 1.5 2. ___ pancreatic fluid [H3O+] = 1 x 10−8 M 3. ___ soft drink pH = 3.0 4. ___ pH = 7.0 5. ___ [OH−] = 3 x 10−10 M 6. ___ [H3O+ ] = 5 x 10−12

5. Solution 1. A) HCl with a pH = 1.5 2. B) pancreatic fluid [H3O+] = 1 x 10−8 M 3. A) soft drink pH = 3.0 4. N) pH = 7.0 5. A) [OH-] = 3 x 10−10 M 6. B) [H3O+] = 5 x 10−12 M

6. Testing the pH of Solutions The pH of solutions is determined by using • a pH meter, • pH paper, or • indicators that have specific colors at different pH values

7. Calculating pH Mathematically, pH is the negative logarithm (log) of the hydronium ion concentration. pH = -log [H3O+] For a solution with [H3O+] = 1 x 10−4 pH =−log [1 x 104 ] pH = [4.0] pH = 4.0

8. Decimal Places in pH Values When expressing pH values, the number of decimal places is equal to the number of significant figures in the coefficient of [H3O+]. coefficient decimal places [H3O+] = 1 x 104 pH = 4.0 [H3O+] = 8.0 x 106 pH = 5.10 [H3O+] = 2.4 x 108 pH = 7.62

9. Guide to Calculating pH

10. Example of Calculating pH Find the pH of a solution with a [H3O+] of 1.0 x 10−3. STEP 1Enter the [H3O+] value. 1.0 [EE or EXP] 3 [+/] Display: 1−03 or 103 STEP 2Press the log key and change the sign. [log (1 x 10−3)] [+/] = 3 STEP 3 Adjust the number of significant figures on the right of the decimal point to equal the SFs in the coefficient 1.0 x 10−3 3.00 2 SFs2 SFs on the right of the decimal point

11. Learning Check The [H3O+] of tomato juice is 2.2 x 10−4 M. What is the pH of the solution? 1) 3.7 2) 3.66 3) 10.34

12. Solution STEP 1Enter the [H3O+] value. 2.2 [EE or EXP] 4 [+/] Display: 2.2−04or 2.204 STEP 2Press the log key and change the sign. log[2.2−04] [+/] = 3.657577 (Display) STEP 3 Adjust the number of significant figures on the right of the decimal point to equal the SFs in the coefficient 2.2 x 104 3.66 (2) 2 SFs 2 SFs on the right of the decimal point

13. Calculating pH from [OH−] Calculate the pH of a solution with [OH−] of 4.0 x 10−5. STEP 1Enter the [H3O+] value Kw= [H3O+][OH−] = 1.0 x 10−14 = 2.5 x 10 −10 [OH−] [OH−] 4.0 x 10−5 2.5 [EE or EXP] 10 [+/] Display: 2.5−10or 2.5 10 STEP 2 Press the log key and change the sign.  log[2.5−10] = [9.60205] = 9.60205

14. Calculating pH from [OH−] (continued) STEP 3 Adjust the number of significant figures on the right of the decimal point to equal the SFs in the coefficient. 2.5x 10−10 MpH = 9.60 2 SFs 2SFs on the right of the decimal point

15. pOH The pOH of a solution • is analogous to the pH value on the pH scale. • is based on the [OH−] • has high pOH values with low [OH−] and high [H3O+] • is equal to the - log [OH−] pOH = - log [OH−] • added to the pH value is equal to 14.00 pH + pOH = 14.00

16. Example of Calculating pOH Calculate the pOH of a solution that has a pH of 8.35. pH + pOH = 14.00 pOH = 14.0 – pH = 14.00 - 8.35 = 5.65

17. Calculating [H3O+] from pH The [H3O+] can be expressed by using the pH as the negative power of 10. [H3O+] = 10−pH If the pH is 3.0, the [H3O+] = 1 x 10−3 M.

18. Example of Calculating [H3O+] from pH Calculate the [H3O+] for a pH value of 8.0. [H3O+] = 10−pH STEP 1 Enter the pH value and change the sign. 8.0 [+/] Display = –8.0 STEP 2 Convert pH to [H3O+]. Press the secondfunction key and then the 10x key or press the inverse key and then the log key. 1–08

19. Example of Calculating [H3O+] from pH (continued) STEP 3 Adjust the number of significant figures in the coefficient. Because the pH value of 8.0 has one digit on the right of the decimal point, the [H3O+] is written with one significant figure. For pH = 8.0, [H3O+] = 1 x 10−8 M

20. Learning Check What is the [H3O+] of a solution with a pH of 3.80?

21. Solution STEP 1 Enter the pH value and change the sign. 3.80 [+/] Display = –3.80 STEP 2 Convert pH to [H3O+]. Press the second function key and then the 10x key or press the inverse key and then the log key. 3.80 (+/-) inv log (or 10x) Display = 1.5848904 STEP 3 Adjust the number of significant figures in the coefficient. Because the pH value of 3.80 has two digits on the right of the decimal point, the [H3O+] is written with two significant figures in the coefficient. pH 3.80 [H3O+] = 1.6 x 104M

22. pH Range

23. Learning Check What is the pH and the pOH of coffee if the [H3O+] is 1 x 10−5 M? 1) pH = 5.0 pOH =7.0 2) pH = 7.0 pOH = 9.0 3) pH = 5.0 pOH = 9.0

24. Solution STEP 1Enter the [H3O+] value. 1 [EE or EXP] 5 [+/] Display: 1−05or 105 STEP 2 Press the log key and change the sign. pH = –log [1 x 10−5] = –(–5.0) = 5.0

25. Solution (continued) STEP 3 Adjust the number of significant figures on the right of the decimal point to equal the SFs in the coefficient. Because the [H3O+] has one digit in the coefficient, the pH has one digit to the right of the decimal point. pH = 5.0 pH + pOH = 14.00 pOH = 14.00 – pH = 14.00 – 5.0 = 9.0 or [OH−] = 1 x 10−9 pOH = –log [1 x 10−9] = –(–9.0) = 9.0 (3)

26. Learning Check What is the [H3O+] of a solution with a pOH of 11.15? 1) 1.0 x 10−2.85 M 2) 1.4 x 10−3 M 3) 8.5 x 10−2 M

27. Solution STEP 1 Enter the pH value and change the sign. pH = 14.00 – pOH = 14.00 - 11.15 = 2.85 2.85[+/] = 2.85 STEP 2 Convert pH to [H3O+]. Use secondfunction key and then10x key or inverse key and then log key. 102.85 = 1.41253 x 10−03 STEP 3 Adjust the significant figures in the coefficient. In the pH value 2.85, there are two digits on the right of the decimal point; the [H3O+] has two significant figures. pH = 2.85 [H3O+] =1.4 x 10−3 M (2)