14.3 pH Scale 14.4 pH of Strong Acids

The pH Scale & pH Values of Some Common Substances Copyright © Cengage Learning. All rights reserved

Copyright © Cengage Learning. All rights reserved pH Range pH = 7; neutral pH > 7; basic Higher the pH, more basic. pH < 7; acidic Lower the pH, more acidic. Copyright © Cengage Learning. All rights reserved

Copyright © Cengage Learning. All rights reserved 14.3 – The pH Scale pH = –log[H+] pH changes by 1 for every power of 10 change in [H+]. pH is a quantitative description of solution acidity. pH decreases as [H+] increases. Significant figures: The number of decimal places in the log is equal to the number of significant figures in the original number. Example: If [H+] = 0.010 M or 1.0×10-2M pH = 2.00 Two significant figures! Copyright © Cengage Learning. All rights reserved

Copyright © Cengage Learning. All rights reserved 14.3 – Calculating pH EXERCISE! Calculate the pH for each of the following solutions. 1.0 × 10–4 M H+ pH = -log(1.0 × 10–4) = 4.00 Is this answer reasonable? Yes! Because an acid is present in a low concentration –the pH is a little below 7 b) 0.0400 M H+ pH = -log(0.0400) = 1.398 Yes! Because an acid is present in a higher concentration –the pH is even lower pH = –log[H+] a) pH = –log[H+] = –log(1.0 × 10–4 M) = 4.00 b) Kw = [H+][OH–] = 1.00 × 10–14 = [H+](0.040 M) = 2.5 × 10–13 M H+ pH = –log[H+] = –log(2.5 × 10–13 M) = 12.60 Copyright © Cengage Learning. All rights reserved

14.3 – Calculating concentration from pH EXERCISE! The pH of a solution is 5.85. What is the [H+] for this solution? pH = –log[H+], so [H+] = the inverse log of –pH [H+] = 10–pH [H+] = 10–5.85 = 1.4 × 10–6 M Is this answer reasonable? Yes! The solution is acidic (pH below 7), but not very acidic – it has a low [H+] [H+] = 10^–5.85 = 1.4 × 10–6 M Copyright © Cengage Learning. All rights reserved

14.3 pH and pOH The Acid-Base calculation tool kit: Kw = [H+][OH–] = 1×10-14 –log Kw = –log[H+] – log[OH–] pKw = pH + pOH 14.00 = pH + pOH Copyright © Cengage Learning. All rights reserved

Copyright © Cengage Learning. All rights reserved 14.3 – Calculating pOH EXERCISE! Calculate the pOH for each of the following solutions. 1.0 × 10–4 M H+ pOH = 10.00 –two significant figures Is this reasonable? Yes! Because pH = 4, & pH + pOH = 14 b) 0.0400 M OH– pOH = 1.398 –three significant figures Yes! [OH-] is fairly high = low pOH and high pH = a basic solution is present pH = –log[H+] and pOH = –log[OH–] and 14.00 = pH + pOH a) pH = –log[H+] = –log(1.0 × 10–4 M) = 4.00; So, 14.00 = 4.00 + pOH; pOH = 10.00 b) pOH = –log[OH–] = –log(0.040 M) = 1.40 Copyright © Cengage Learning. All rights reserved

14.3 – Calculating concentration from pOH EXERCISE! The pH of a solution is 5.85. What is the [OH–] for this solution? [H+] = 10–5.85 = 1.4 × 10–6 M [H+][OH–] = 1×10-14 (1.4 × 10–6 M)[OH–] = 1×10-14 [OH–] = 1×10-14 ÷ 1.4 × 10–6 M = 7.1 × 10–9 M Or: 14 – pH = pOH; 14 - 5.85 = pOH = 8.15 [OH-] = 10–8.15 = 7.1 × 10–9 M [OH–] = 7.1 × 10–9 M pH = –log[H+] and pOH = –log[OH–] and 14.00 = pH + pOH 14.00 = 5.85 + pOH; pOH = 8.15 [OH–] = 10^–8.15 = 7.1 × 10–9 M Copyright © Cengage Learning. All rights reserved

Thinking About Acid–Base Problems What are the major species in solution? What is the dominant reaction that will take place? Is it an equilibrium reaction or a reaction that will go essentially to completion? React all major species until you are left with an equilibrium reaction. Solve for the pH if needed. Copyright © Cengage Learning. All rights reserved

YES! Because a strong acid is present in a pretty high concentration! 14.4 – Calculating pH of a Strong Acid CONCEPT CHECK! What is the pH of an aqueous solution of 2.0 × 10–3 M HCl. What are the major species in solution? H+, Cl–, H2O HCl  H+ + Cl– Also: H2O  H+ + OH– pH will be affected by [H+] Main source of [H+]? What is the pH? pH = -log(2.0 × 10–3 ) = 2.70 2.0 × 10–3 M Major Species: H+, Cl-, H2O pH = –log[H+] = –log(2.0 × 10–3 M) = 2.70 pH = 2.70 YES! Because a strong acid is present in a pretty high concentration! Reasonable answer? Copyright © Cengage Learning. All rights reserved

YES! A tiny bit of a strong acid won’t change the pH! 14.4 – Calculating pH of a Strong Acid CONCEPT CHECK! Calculate the pH of a 1.5 × 10–11 M solution of HCl. What are the major species in solution? H+, Cl–, H2O HCl  H+ + Cl– Also: H2O  H+ + OH– Main source of [H+]? What is the pH? pH = -log(1.0 × 10–7 ) = 7.00 1.5 × 10–11 M 1 × 10–7 M NOT! pH = 10.82 Major Species: H+, Cl-, H2O pH = –log[H+] = –log(2.0 × 10–3 M) = 2.70 pH = 2.70 YES! A tiny bit of a strong acid won’t change the pH! Reasonable answer? Copyright © Cengage Learning. All rights reserved

Copyright © Cengage Learning. All rights reserved CONCEPT CHECK! Calculate the pH of a 1.5 × 10–2 M solution of HNO3. Major Species: H+, NO3-, H2O The reaction controlling the pH is: H2O + H2O  H3O+(aq) + OH-(aq) This is because it is the only equilibrium reaction (NO3- is not a base in water). However, the major source for H+ is from the nitric acid, so the pH = -log(1.5 x 10-2) = 1.82. Copyright © Cengage Learning. All rights reserved

Copyright © Cengage Learning. All rights reserved Let’s Think About It… When HNO3 is added to water, a reaction takes place immediately: HNO3 + H2O H3O+ + NO3– Copyright © Cengage Learning. All rights reserved

Copyright © Cengage Learning. All rights reserved Let’s Think About It… Why is this reaction not likely? NO3–(aq) + H2O(l) HNO3(aq) + OH–(aq) Because the K value for HNO3 is very large and HNO3 virtually completely dissociates in solution. Copyright © Cengage Learning. All rights reserved

Copyright © Cengage Learning. All rights reserved Let’s Think About It… What reaction controls the pH? H2O(l) + H2O(l) H3O+(aq) + OH–(aq) In aqueous solutions, this reaction is always taking place. But is water the major contributor of H+ (H3O+)? pH = 1.82 Copyright © Cengage Learning. All rights reserved