A student titrates 25.0 mL of a 0.100 M solution of acetic acid with a 0.100 solution of sodium hydroxide. Calculate the pH at the equivalence point.
OH- + HC2H3O2 --> H20 + C2H3O2-
0.0025 mol 0.0025 mol - 0
-0.0025 -0.0025 - +0.0025
0 0 - 0.0025
0.0025 mol/0.050 L = 0.050 M
C2H3O2- + H20 <--> HC2H3O2 + OH-
0.050 M - 0 0
-x - +x +x
0.050-x - x x
Kb = 10^(-14)/(1.8x10^(-5) = 5.56x10^(-8)
= x^2/(0.050-x)
x = 5.27x10^(-6)
pOH = -log(x)
= 5.28
pH = 14 - 5.28 = 8.72
Is that correct? The answer key says that the answer is 2.87, but that doesn't seem logical to me either.
I think 8.72 is the correct answer.
To calculate the pH at the equivalence point of an acid-base titration, we need to determine the moles of acid and base present at that point. The equivalence point occurs when an equal number of moles of acid and base have reacted.
1. Begin by calculating the number of moles of acetic acid used in the titration. Since the volume of the acetic acid solution is given in milliliters (mL), we need to convert it to liters (L):
Volume of acetic acid = 25.0 mL = 25.0 mL * (1 L / 1000 mL) = 0.025 L
Moles of acetic acid = concentration * volume
Moles of acetic acid = 0.100 M * 0.025 L = 0.0025 mol
2. Since it is a 1:1 stoichiometric reaction between acetic acid and sodium hydroxide, the number of moles of sodium hydroxide at the equivalence point is also 0.0025 mol.
3. To find the concentration of the sodium hydroxide solution at the equivalence point, use the number of moles and the volume of the sodium hydroxide solution:
Moles of sodium hydroxide = concentration * volume
Concentration of sodium hydroxide = Moles of sodium hydroxide / volume
Since the volume of sodium hydroxide is not given, we will assume it is also 25.0 mL and convert it to liters:
Volume of sodium hydroxide = 25.0 mL = 25.0 mL * (1 L / 1000 mL) = 0.025 L
Concentration of sodium hydroxide = 0.0025 mol / 0.025 L = 0.100 M
4. At the equivalence point, acetic acid and sodium hydroxide react completely to form water and sodium acetate, which is a salt of a weak acid and a strong base. Sodium acetate is the conjugate base of acetic acid, and it undergoes hydrolysis in water to form hydroxide ions and acetate ions.
Since the concentration of sodium hydroxide at the equivalence point is 0.100 M, the concentration of hydroxide ions is also 0.100 M.
5. To determine the pH at the equivalence point, we need to calculate the pOH using the concentration of hydroxide ions:
pOH = -log[OH-]
pOH = -log(0.100)
pOH ≈ 1.00
6. Finally, we can calculate the pH:
pH = 14 - pOH
pH ≈ 14 - 1.00
pH ≈ 13.00
Therefore, the pH at the equivalence point of this titration is approximately 13.00.
To calculate the pH at the equivalence point, we need to determine the moles of acetic acid and sodium hydroxide at the equivalence point, and then use that information to find the concentration of the resulting solution.
1. Determine the moles of acetic acid:
- The given volume of acetic acid is 25.0 mL, which is equivalent to 0.0250 L.
- The concentration of acetic acid is 0.100 M, which means it contains 0.100 moles of acetic acid per liter.
- Therefore, the moles of acetic acid can be calculated as:
moles = concentration x volume
= 0.100 mol/L x 0.0250 L
= 0.00250 moles
2. Determine the moles of sodium hydroxide:
- At the equivalence point, the number of moles of sodium hydroxide is equal to the number of moles of acetic acid.
- Therefore, the moles of sodium hydroxide can also be calculated as 0.00250 moles.
3. Calculate the concentration of the resulting solution:
- Since the volumes of acetic acid and sodium hydroxide are equal, the final volume of the resulting solution will be twice the initial volume of either solution.
- Therefore, the final volume is 2 x 25.0 mL = 50.0 mL = 0.0500 L.
- The total moles of acetic acid and sodium hydroxide in the resulting solution is the sum of their individual moles, which is 2 x 0.00250 moles = 0.00500 moles.
- The concentration of the resulting solution is then calculated as:
concentration = moles / volume
= 0.00500 moles / 0.0500 L
= 0.100 M.
4. Calculate the pH of the resulting solution:
- At the equivalence point, acetic acid (a weak acid) reacts completely with sodium hydroxide (a strong base) to form water and sodium acetate, which is the conjugate base of acetic acid.
- Sodium acetate is a salt of a weak acid and a strong base, so it hydrolyzes in water to produce hydroxide ions.
- The concentration of hydroxide ions can be determined from the concentration of sodium acetate.
- The pH of a basic solution can be calculated using the pOH formula:
pOH = -log10(OH- concentration)
- Since the solution is at the equivalence point, the concentration of hydroxide ions is the same as the concentration of sodium acetate, which is 0.100 M.
- Therefore, the pOH can be calculated as:
pOH = -log10(0.100)
= 1.00 (rounded to two decimal places)
- Finally, the pH can be calculated by subtracting the pOH from 14:
pH = 14 - pOH
= 14 - 1.00
= 13.00 (rounded to two decimal places)
Therefore, the pH at the equivalence point is 13.00.