pH of Weak Acid Solutions

Solving Weak Acid Equilibrium Problems 1.List the major species in the solution. 2.Choose the species that can produce H +, and write balanced equations for the reactions producing H +. 3.Using the values of the equilibrium constants for the reactions you have written, decide which equilibrium will dominate in producing H +. 4.Write the equilibrium expression for the dominant equilibrium. Copyright © Cengage Learning. All rights reserved 2

Solving Weak Acid Equilibrium Problems 5.List the initial concentrations of the species participating in the dominant equilibrium. 6.Define the change needed to achieve equilibrium; that is, define x. 7.Write the equilibrium concentrations in terms of x. 8.Substitute the equilibrium concentrations into the equilibrium expression. Copyright © Cengage Learning. All rights reserved 3

Solving Weak Acid Equilibrium Problems 9.Solve for x the “easy” way, that is, by assuming that [HA] 0 – x about equals [HA] Use the 5% rule to verify whether the approximation is valid. 11.Calculate [H + ] and pH. Copyright © Cengage Learning. All rights reserved 4

Consider a 0.80 M aqueous solution of the weak acid HCN (K a = 6.2 × 10 –10 ). What are the species in solution? HCN, H 2 O, H +, CN What are the major species in solution? Why arent H + or CN – major species? Answer: Because HCN is a weak acid (and so is H 2 O) so they will produce very few ions. Copyright © Cengage Learning. All rights reserved 5 CONCEPT CHECK! 14.5 Solving Weak Acid Equilibrium Problems

Consider This… HCN(aq) + H 2 O(l) H 3 O + (aq) + CN – (aq) K a = 6.2 × H 2 O(l) + H 2 O(l) H 3 O + (aq) + OH – (aq) K w = 1.0 × Which reaction controls the pH? Explain. Copyright © Cengage Learning. All rights reserved 6

Calculate the pH of a 0.50 M aqueous solution of the weak acid, HF. (K a = 7.2 × 10 –4 ) What are the species in solution? HF, H 2 O, H +, F - What are the major species in solution? Why arent H + or CN – major species? Answer: Because HCN is a weak acid (and so is H 2 O) so they will produce very few ions. Copyright © Cengage Learning. All rights reserved 7 EXERCISE! 14.5 Solving Weak Acid Equilibrium Problems

Let’s Think About It… What are the possibilities for the dominant reaction? HF(aq) + H 2 O(l) H 3 O + (aq) + F – (aq) K a =7.2 × H 2 O(l) + H 2 O(l) H 3 O + (aq) + OH – (aq) K w =1.0 × Which reaction controls the pH? Why? Copyright © Cengage Learning. All rights reserved 8

HF(aq) +H2OH2OH 3 O + (aq) + F – (aq) Initial0.50 M~ 0*~ 0 Change–x+x Equilibrium0.50–xxx 0.50xx Steps Toward Solving for pH K a = 7.2 × 10 –4 pH = 1.72 Copyright © Cengage Learning. All rights reserved 9 * Because [H + ] = 1 × 10 –7 Can we make the math easier?

Was the assumption that 0.5-x = 0.5 correct? It is if it meets the 5% rule. x/[HF] × 100 = % difference. If this difference is less than 5%, the assumption was reasonable /0.5 × 100 = 3.78% So, the assumption was reasonable.

Percent Dissociation (Ionization) For a given weak acid, the percent dissociation increases as the acid becomes more dilute. Copyright © Cengage Learning. All rights reserved 11

A solution of 8.00 M formic acid (HCHO 2 ) is 0.47% ionized in water. Calculate the K a value for formic acid. K a = 1.8 × 10 –4 Copyright © Cengage Learning. All rights reserved 12 EXERCISE! Percent Dissociation (Ionization)

Calculate the pH of an 8.00 M solution of formic acid. Use the data from the previous slide to help you solve this problem. pH = 1.42 Copyright © Cengage Learning. All rights reserved 15 EXERCISE!

The value of K a for a 4.00 M formic acid solution should be: higher than lower thanthe same as the value of K a of an 8.00 M formic acid solution. Explain. Copyright © Cengage Learning. All rights reserved 16 EXERCISE!

The percent ionization of a 4.00 M formic acid solution should be: higher than lower thanthe same as the percent ionization of an 8.00 M formic acid solution. Explain. Copyright © Cengage Learning. All rights reserved 17 CONCEPT CHECK!

The pH of a 4.00 M formic acid solution should be: higher than lower thanthe same as the pH of an 8.00 M formic acid solution. Explain. Copyright © Cengage Learning. All rights reserved 18 CONCEPT CHECK!

Calculate the percent ionization of a 4.00 M formic acid solution in water. % Ionization = 0.67% Copyright © Cengage Learning. All rights reserved 19 EXERCISE!

Calculate the pH of a 4.00 M solution of formic acid. pH = 1.57 Copyright © Cengage Learning. All rights reserved 20 EXERCISE!