Calculate the PH of a buffer solution by mixing 74ml of 1.0M lactic acid and 25ml of 1.0 sodium lactate having a Pka of 3.86 lactic acid
Let's save some typing time (and space) by using HL for lactic acid and NaL for sodium lactate. Then L^- will be the lactate ion.
millimols Lactic acid = mL x M = 74 mL x 1.0 M = 74 or 0.074 mols.
millimols sodium lactate = 25 mL x 1.0 M NaL = 25 or 0.025 mols.
(HL) = the acid = mols/L = 0.074/0.099 = ?
(NaL) = the base = mols/L = 0.025/0.099 = ?
Then plug into the Henderson-Hasslebalch equation of
pH = pKa + log [(base)/(acid)]
Post your work if you get stuck. You should get approximately 3.7 or so.
3.38
To calculate the pH of a buffer solution, you need to take into account the Henderson-Hasselbalch equation, which relates the concentrations of the acid and conjugate base in the solution to the pH.
The Henderson-Hasselbalch equation is given as:
pH = pKa + log ([conjugate base]/[acid])
In this case, the acid is lactic acid and the conjugate base is sodium lactate. You have been given the pKa value for lactic acid, which is 3.86.
First, let's calculate the concentrations of lactic acid and sodium lactate in the solution.
Given:
Volume of lactic acid (V1) = 74 mL
Concentration of lactic acid (C1) = 1.0 M
Using the formula c = n/V, we can calculate the number of moles of lactic acid (n1):
n1 = C1 * V1
= 1.0 M * 0.074 L
= 0.074 mol
Next, let's calculate the concentration of sodium lactate.
Given:
Volume of sodium lactate (V2) = 25 mL
Concentration of sodium lactate (C2) = 1.0 M
Using the same formula, we can calculate the number of moles of sodium lactate (n2):
n2 = C2 * V2
= 1.0 M * 0.025 L
= 0.025 mol
Next, let's calculate the concentration of lactic acid and sodium lactate after mixing:
Total volume of the buffer solution (V_total) = V1 + V2 = 0.074 L + 0.025 L = 0.099 L
Concentration of lactic acid after mixing (C1_intermediate) = n1/V_total
= 0.074 mol / 0.099 L
= 0.747 M
Concentration of sodium lactate after mixing (C2_intermediate) = n2/V_total
= 0.025 mol / 0.099 L
= 0.253 M
Now, we can substitute the values into the Henderson-Hasselbalch equation:
pH = pKa + log ([C2_intermediate]/[C1_intermediate])
= 3.86 + log (0.253 M / 0.747 M)
Using logarithmic properties, we can simplify the equation:
pH = 3.86 - log (0.747 M / 0.253 M)
Finally, calculate the pH using a calculator:
pH = 3.86 - log (0.747 / 0.253)
= 3.86 - log (2.951)
The pH will depend on the evaluation of this logarithm. Using a calculator or software, you can get the value of the logarithm and calculate the final pH.