Calculate the K_a of a weak acid given the pH and other concentration data (not molarity)

Return to Acid Base Menu

Return to a listing of many types of acid base problems and their solutions

Example #1: A student prepared a solution of salicylic acid (a monoprotic weak acid, MW = 138.123 g mol¯¹) and measured the pH of the solution to be 2.430. Then, she evaporated 100.0 mL of the solution and collected 0.220 g of dry salicylic acid. What is the K_a of salicylic acid?

Solution:

1) Write the dissociation equation for salicylic acid, HSal:

HSal ---> H⁺ + Sal¯

2) Write the K_a expression for HSal:

K_a = ([H⁺] [Sal¯]) / [HSal]

3) Use the pH to determine [H⁺] and [Sal¯]:

[H⁺] = 10¯^pH = 10¯^2.20 = 3.71535 x 10¯³ M (some guard digits)

4) Determine molarity of HSal:

0.220 g / 138.123 g mol¯¹ = 1.59278 x 10¯³ mol

1.59278 x 10¯³ mol / 0.100 L = 1.59278 x 10¯² M

K_a = [(3.71535 x 10¯³) (3.71535 x 10¯³)] / 1.59278 x 10¯²

K_a = 8.67 x 10¯⁴

Comment: I did some Internet searching on the K_a of salicylic acid and found some striking differences in reported values. For example, I found "Quantitative Chemical Analysis" (by Daniel C. Harris) on Google Books. On page 183, he reports the pK_a of salicylic acid to be 2.97; from that we see the K_a to be 1.07 x 10¯³, almost a 20% difference.

This is not to say any one number is wrong, just that various sources give different values for the K_a of salicylic acid. I just haven't fond an authoritative source for the value. Yet!

Example #2: An aqueuous solution containing 8.40 g/L of Cyanoacetic acid (abbreviated HCya), CH₂CNCOOH has a pH of 1.77. What is the value of the K_a?

Solution:

1) Write the dissociation equation for HCya:

HCya ---> H⁺ + Cya¯

2) Write the K_a expression for HCya:

K_a = ([H⁺] [Cya¯]) / [HCya]

3) Use the pH to determine [H⁺] and [Cya¯]:

[H⁺] = 10¯^pH = 10¯^1.77 = 1.69824 x 10¯² M (I kept some guard digits)

4) Determine molarity of HCya:

8.40 g / 85.0618 g mol¯¹ = 9.875 x 10¯² mol

1.59278 x 10¯³ mol / 1.00 L = 9.875 x 10¯² M

K_a = [(1.69824 x 10¯²) (1.69824 x 10¯²] / 9.875 x 10¯²

K_a = 2.92 x 10¯³

Return to a listing of many types of acid base problems and their solutions

Return to Acid Base Menu