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:

HC_{3}H_{5}O_{3} ( weak acid )

C_{3}H_{5}O_{3}^{-} ( conjugate base of HC_{3}H_{5}O_{3} )

Na^{+} ( spectator ion )

H_{2}O ( very weak acid or base )

Determine the equilibrium reaction involved:

HC_{3}H_{5}O_{3} and C_{3}H_{5}O_{3}^{-} will react together to affect the pH of the solution:

HC_{3}H_{5}O_{3} (aq) "\\leftrightarrow" H^{+} (aq) + C_{3}H_{5}O_{3}^{-} (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^{+}][C_{3}H_{5}O_{3}^{-}] / [HC_{3}H_{5}O_{3}] } = { (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:

x^{2} + 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^{-5}M.

Calculate the pH:

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

Learn more about our help with Assignments: Chemistry

## Comments

## Leave a comment