A biochemist prepares a lactic acid-lactate buffer by mixing 225 mL of 0.85M lactic acid with a Ka=1.38*10^-4 with 435mL of 0.68M sodium lactate. What is the buffer pH?
I know I have to use the equilibrium constant expression, but I'm pretty lost from there. Can someone please explain this for me? Thanks!
No, this is a buffer problem. Use the Henderson-Hasselbalch equation.
225 mL x 0.85M lactic acid(HL) = about 199.75 millimols acid.
435 mL x 0.68M = about 295.8 mmols NaL which is the base.
pH = pKa + log (base)/(acid)
Ohhhh, that makes sense! Thanks!
To determine the buffer pH, we need to calculate the concentration of lactic acid and lactate ions in the buffer solution and then use the Henderson-Hasselbalch equation.
Step 1: Calculate the initial moles of lactic acid and sodium lactate:
Initial moles of lactic acid (CH3CH(OH)COOH):
Molarity (M) = moles/liter
Moles of lactic acid = Molarity × Volume (in liters)
Moles of lactic acid = 0.85 M × 0.225 L
Moles of lactic acid = 0.19125 moles
Initial moles of sodium lactate (CH3CH(OH)COONa):
Moles of sodium lactate = Molarity × Volume (in liters)
Moles of sodium lactate = 0.68 M × 0.435 L
Moles of sodium lactate = 0.2958 moles
Step 2: Determine the moles of lactic acid and lactate ions present at equilibrium.
Since lactic acid partially ionizes in water, we will assume that a fraction x of the initial moles of lactic acid reacts to form the conjugate base (lactate ion), and the remaining moles of lactic acid (0.19125 - x) remain unreacted.
The reaction can be represented as:
CH3CH(OH)COOH ⇌ CH3CH(OH)COO- + H+
The moles of lactic acid that react to form lactate ion:
Moles of lactate ion = x moles
So, the moles of lactic acid remaining:
Moles of lactic acid = initial moles of lactic acid - moles of lactate ion
Moles of lactic acid = 0.19125 - x moles
Step 3: Write the expression for the equilibrium constant.
Ka = [CH3CH(OH)COO-][H+]/[CH3CH(OH)COOH]
The equilibrium expression is written using the ion concentration of the weak acid and its conjugate base.
Step 4: Substitute the given values into the equilibrium constant expression.
Ka = (x moles)/(0.19125 - x moles)
Step 5: Solve for x by rearranging the equation.
Ka × (0.19125 - x) = x
Simplifying:
Ka × 0.19125 - Ka × x = x
Bring x terms to one side:
Ka × x + x = Ka × 0.19125
Combine like terms:
(1 + Ka) × x = Ka × 0.19125
Divide both sides by (1 + Ka):
x = (Ka × 0.19125) / (1 + Ka)
Step 6: Calculate the concentrations of lactic acid and lactate ion.
Concentration of lactic acid ([CH3CH(OH)COOH]):
Molarity = moles/volume (in liters)
[CH3CH(OH)COOH] = (0.19125 - x)/(0.225 L + 0.435 L)
Concentration of lactate ion ([CH3CH(OH)COO-]):
[CH3CH(OH)COO-] = x / (0.225 L + 0.435 L)
Step 7: Calculate the pH using the Henderson-Hasselbalch equation.
pH = pKa + log([CH3CH(OH)COO-] / [CH3CH(OH)COOH])
Where pKa is the negative logarithm of Ka.
Step 8: Calculate pKa.
pKa = -log(Ka)
Finally, substitute the calculated values into the Henderson-Hasselbalch equation to find the buffer pH.
Sure, I'd be happy to help you understand how to solve this problem!
To find the buffer pH, we need to consider the equilibrium between lactic acid and its conjugate base, lactate. The equilibrium constant expression for this reaction is given by:
Ka = [lactate] / [lactic acid]
Given that the Ka value is 1.38 * 10^-4, we can use this information to determine the concentration of lactate and lactic acid in the buffer solution.
Let's start by calculating the moles of each component in the solution.
Moles of lactic acid = (volume in liters) x (molarity of lactic acid)
= (225 mL / 1000 mL/L) x (0.85 mol/L)
Moles of sodium lactate = (volume in liters) x (molarity of sodium lactate)
= (435 mL / 1000 mL/L) x (0.68 mol/L)
Next, we convert these moles to concentrations.
Concentration of lactic acid = (moles of lactic acid) / (total volume of solution in liters)
= (moles of lactic acid) / (225 mL + 435 mL) / 1000 mL/L)
Concentration of sodium lactate = (moles of sodium lactate) / (total volume of solution in liters)
= (moles of sodium lactate) / (225 mL + 435 mL) / 1000 mL/L)
Now, we can use the equilibrium constant expression to determine the ratio of [lactate] to [lactic acid]:
Ka = [lactate] / [lactic acid]
Solving for [lactate]:
[lactate] = Ka x [lactic acid]
Substituting the known values:
[lactate] = (1.38 * 10^-4) x (concentration of lactic acid)
Finally, we can find the buffer pH using the Henderson-Hasselbalch equation:
pH = pKa + log([lactate] / [lactic acid])
Where pKa is the negative logarithm of the Ka value. In this case, pKa = -log10(1.38 * 10^-4).
By plugging in the values of [lactate], [lactic acid], and pKa, we can calculate the buffer pH.
I hope this explanation helps! Let me know if you have any further questions.