In a titration of 50 mL 1 Molar HC2H3O2 with 1 Molar NaOH, a student used bromcresol green as an indicator (Ka = 1 X 10^-5). About how many mL of NaOH would it take to reach the end point with this indicator? What would be a better indicator for this titration; why?
I would use the Henderson-Hasselbalch equation here. Have you had that in your course?
pH = pKa + log[(base)/(acid)]
Substitute pH = 5 (the middle point of where the indicator turns color) and calculate (base)/(acid). pKa for acetic acid (which I will call HAc) is 4.74.
I found about 2 but that's approximate and you need to do the calculation and be more exact about it. Let's just assume 2 is the number for the moment.
B/A = 2 and that means
(base) = 2*(acid).
We know that we have 50 x 1M or 50 mmoles HAc to neutralize and as we add NaOH, we will take away from th HAc and add to acetate (Ac^-); therefore,
HAc + Ac^- = 50 mmoles or
A for acid + B for base = 50
Then we can substitute the ratio from above.
A + 2*A = 50
3A = 50 and A = about 17 and B = about 33. Since the solutions are 1 M and since the volume for the acid and the base are the same (because they are in the same solution), these numbers are millimoles BUT they are the same as mL. You know that the equivalence point is at 50 mL of the NaOH; therefore, something in the neighborhood of 33 mL or so for NaOH doesn't even come close to matching the end point with the equivalence point. The end point comes out far short of the equivalence point. Phenolphthalein indicator (which turns between 8 and 10--midpoint about 9) would be a much better indicator. You can calculate the pH at the equivalence point from the hydrolysis of the salt.
Ac^- + HOH ==> HAc + OH^-
Set up an ICE chart and substitute into the Kb expression for the hydrolysis.
Kb = Kw/Ka and the pH should be about 9 for the equivalence point.
To determine how many mL of NaOH would be needed to reach the end point with bromcresol green as the indicator, we need to understand the principles of acid-base titrations and indicators.
In an acid-base titration, a measured volume of acid is titrated with a base solution of known concentration until the stoichiometric equivalence point is reached. At this point, the moles of acid and base are chemically equivalent, and any additional base added will result in excess base.
An indicator is a substance that undergoes a color change at a specific pH range. It is used to visually detect the end point of a titration, which is when the indicator changes color indicating that the stoichiometric equivalence point has been reached.
To estimate the volume of NaOH required to reach the end point with bromcresol green, we need to know the pKa of the indicator. The pKa is the negative logarithm (base 10) of the acid dissociation constant (Ka). In this case, the pKa of bromcresol green is given as 5.
Now, let's calculate the approximate volume of NaOH required to reach the end point:
1. Convert the volume of HC2H3O2 to moles:
Moles of HC2I3O2 = Volume (in liters) x Concentration (in M)
Moles of HC2H3O2 = 0.050 L x 1 M = 0.050 mol
2. Since the stoichiometric equation between HC2H3O2 and NaOH is 1:1, the moles of NaOH required is also 0.050 mol.
3. To neutralize the moles of NaOH, the moles of H3O+ formed from HC2H3O2 must be equal to the moles of OH- from NaOH. In this case, they are at a 1:1 ratio.
4. The pKa of the bromcresol green indicates its transition range. In general, indicators are most effective when they change color within a pH range that matches the equivalence point. For bromcresol green, the color transition occurs around pH 4 - 5.
5. In an ideal situation, when the pH equals the pKa of the indicator, the moles of HA and A- are equal. In this case, the moles of HC2H3O2 and C2H3O2- (from the dissociation of HC2H3O2) are at a 1:1 ratio when the pH equals the pKa.
6. Since the pKa of bromcresol green is 5 and the equivalence point occurs around pH 7 (neutral), the indicator is not at the optimal pH when the reaction reaches its stoichiometric equivalence point.
Given this, it would be better to choose an indicator that changes color in the pH range close to the expected pH at the equivalence point, such as phenolphthalein (pKa = 9) or methyl orange (pKa = 3.7).
To reiterate:
- The approximate volume of NaOH required to reach the end point with bromcresol green can be estimated based on stoichiometry, assuming the indicator changes color slightly before or after the stoichiometric equivalence point.
- However, since bromcresol green's pKa doesn't match the expected pH at the equivalence point, it is not the optimal indicator choice for this titration.
- More suitable indicators for this titration could include phenolphthalein or methyl orange, as their pKa values are closer to the expected pH at the equivalence point.