Answer to Question #176465 in General Chemistry for Florence

Question #176465

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.

Expert's answer

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



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

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

Because Ka 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\u00d71\u00d7(-0.0000138)}}{2\u00d71}"

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

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