Answer to Question #176465 in General Chemistry for Florence

Question

Calculate the pH of a buffer solution prepared by mixing 25ml of 0.1M lactic acid and 75ml of 1.0 sodium lactate.the ka for lactic acid is 1.38*10^-4. Chemical formula for lactic acid is C3H6O3. Molecular weight 90.08g/mol.

Answer 1

Identify the major species in solution:

HC₃H₅O₃ ( weak acid )

C₃H₅O₃^- ( conjugate base of HC₃H₅O₃ )

Na⁺ ( spectator ion )

H₂O ( very weak acid or base )

Determine the equilibrium reaction involved:

HC₃H₅O₃ and C₃H₅O₃^- will react together to affect the pH of the solution:

HC₃H₅O₃ (aq) $\leftrightarrow$   H⁺ (aq) + C₃H₅O₃^- (aq)

0.1M __________0_________1.0M

-x_______________+x___________+x

(0.1-x)_______x___________(1.0+x)

Substitute equilibrium concentrations into the equilibriuum constant expression, then simplify and solve the expression:

K_a = { [H⁺][C₃H₅O₃^-] / [HC₃H₅O₃] } = { (x)(1 + x) / (0.1 - x) } = 1.38 x 10^-4

Because K_a x 1000 is larger than both 0.100 and 1, simplification is not possible. Thus, to reach the solution, it is necessary to use the quadratic formula to solve. Rearrangement gives:

x² + 1.000138x - 0.0000138 = 0

x = $\frac{-b+\sqrt{b^2-4ac}}{2a}$

x = $\frac{-1.000138+\sqrt{4×1×(-0.0000138)}}{2×1}$

x =[H⁺] 1.37×10^-5 M and --1.0M

Because we cannot have a negative concentration of H⁺ ions,

x = [H⁺] = 1.37 x 10^-5M.

Calculate the pH:

pH = - log[H⁺] = - log( 1.37 x 10^-5 ) = 4.86