In the following questions, assume that no excess distilled water was added from a wash bottle during the titration of 10.00 mL of vinegar with your standardized solution of NaOH.
A. calculate the pH of vinegar.
B. what was the pH of the solution after 4.00 mL of titrant was added?
C. What was the pH at the equivalence point?
D. Why is the solution basic at the equivalence point?
E. What was the pH of the solution after 35.00 mL of titrant was added?
F. Draw a titration curve for this titration?
See your post above.
A. To calculate the pH of vinegar, we need to know the concentration of acetic acid in vinegar. Assuming vinegar is 5% acetic acid by volume (which is commonly found in household vinegar), we can calculate the molarity of acetic acid.
Molarity (M) = moles/volume (in liters)
Since 5% acetic acid means 5 g of acetic acid in 100 mL of vinegar, we can convert it to grams:
5% of 100 mL = 5 g
Next, we need to calculate the moles of acetic acid:
Moles = mass/molar mass
The molar mass of acetic acid (CH₃COOH) is calculated by multiplying the molar masses of carbon, hydrogen, and oxygen, and then adding the atomic mass of one carbon, two hydrogens, and two oxygens:
(C: 12.01 g/mol, H: 1.008 g/mol, O: 16.00 g/mol)
Molar mass = (12.01 * 2) + (1.008 * 4) + (16.00 * 2) = 60.05 g/mol
Moles of acetic acid = 5 g / 60.05 g/mol = 0.0832 mol
Now, we need to calculate the volume of vinegar in liters:
Volume = 10.00 mL / 1000 mL/L = 0.01000 L
Since acetic acid is a weak acid, we can use the equation for calculating pH of a weak acid:
pH = -log[H+]
To find the [H+], we need to use the equilibrium expression for the dissociation of acetic acid:
CH₃COOH ⇌ CH₃COO- + H+
Assuming that the initial concentration of acetic acid is approximately equal to the concentration of CH₃COOH at equilibrium:
[H+] = √(Ka * [CH₃COOH])
Ka (acid dissociation constant for acetic acid) is approximately 1.8 * 10⁻⁵ at 25°C.
[H+] = √((1.8 * 10⁻⁵) * 0.0832 mol / 0.01000 L) = 8.70 * 10⁻³ M
Finally, we can calculate the pH:
pH = -log(8.70 * 10⁻³) = 2.06
Therefore, the pH of vinegar is approximately 2.06.
B. To find the pH of the solution after adding 4.00 mL of titrant, we need to calculate the moles of NaOH added.
Moles of NaOH = Molarity * Volume (in liters)
Assuming the standardized solution of NaOH has a concentration of 0.1 M:
Moles of NaOH = 0.1 M * (4.00 mL / 1000 mL/L) = 4.00 * 10⁻³ mol
Since NaOH is a strong base and vinegar is a weak acid, we can assume that the reaction between them goes to completion. Therefore, the moles of acetic acid that reacted with NaOH are equal to the moles of NaOH added.
Since the initial concentration of acetic acid was 0.0832 mol and we added 4.00 * 10⁻³ mol of NaOH, we need to calculate the new concentration of acetic acid:
New concentration of acetic acid = (0.0832 mol - 4.00 * 10⁻³ mol) / 0.01000 L
Next, we can calculate the [H+] using the same equilibrium expression as before:
[H+] = √(Ka * [CH₃COOH])
[H+] = √((1.8 * 10⁻⁵) * New concentration of acetic acid)
Finally, we can calculate the pH:
pH = -log([H+])
D. The solution is basic at the equivalence point because the weak acid (acetic acid) has been completely neutralized by the strong base (NaOH). The equivalence point is reached when the moles of acid and base are stoichiometrically balanced, resulting in the formation of the salt of the weak acid (sodium acetate) and water. Sodium acetate is a salt of a weak acid, but it does not undergo hydrolysis to a significant extent, meaning no additional acid or base will be produced. Therefore, the solution remains basic at the equivalence point.
E. To find the pH of the solution after adding 35.00 mL of titrant, we need to follow the same process as in part B. Calculate the moles of NaOH added, subtract them from the initial moles of acetic acid, calculate the new concentration of acetic acid, find the [H+], and then calculate the pH.
F. Unfortunately, I cannot draw a titration curve as an AI text-based assistant, but you can find a titration curve for this titration by searching online or referring to textbooks or educational resources.
A. To calculate the pH of vinegar, you need to know the concentration of acetic acid (the main component of vinegar) in the solution. Acetic acid is a weak acid, so you can use the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log([A-]/[HA])
Where pKa is the negative logarithm of the acid dissociation constant (Ka) of acetic acid, [A-] is the concentration of the acetate ion (CH3COO-), and [HA] is the concentration of acetic acid (CH3COOH).
B. To determine the pH of the solution after adding 4.00 mL of titrant, you need to know the volume and concentration of the titrant (NaOH) used in the titration. With this information, you can calculate the number of moles of NaOH that reacted with the acetic acid in the vinegar, and subsequently determine the concentration of acetic acid remaining in the solution. Again, you can use the Henderson-Hasselbalch equation mentioned above to calculate the pH with the new acetic acid concentration.
C. The equivalence point in a titration is the point at which the stoichiometrically equivalent amounts of acid and base have reacted. In this case, it would be the point at which all the acetic acid in the vinegar has reacted with the NaOH titrant. At the equivalence point, the pH depends on the nature of the reactants. Since NaOH is a strong base and acetic acid is a weak acid, the pH at the equivalence point is basic. However, without knowing the concentration of acetic acid and NaOH used in the titration, it is difficult to give an exact pH value.
D. The solution is basic at the equivalence point because the reaction between the strong base (NaOH) and the weak acid (acetic acid) produces the acetate ion (CH3COO-), which is the conjugate base of acetic acid. The acetate ion can accept a proton, increasing the hydroxide ion concentration in the solution and making it basic.
E. Similar to question B, you need to know the volume and concentration of the titrant (NaOH) used in the titration, as well as the volume of titrant added (35.00 mL) to determine the pH of the solution. Calculate the number of moles of NaOH reacted and the concentration of acetic acid remaining, then use the Henderson-Hasselbalch equation to calculate the pH.
F. To draw a titration curve, you need to plot the pH of the solution on the y-axis against the volume of titrant added on the x-axis. Start by plotting the initial pH of the vinegar (answer from question A) at the beginning of the x-axis (0 mL). Then, plot the pH at different points throughout the titration:
- Before the equivalence point, the pH will gradually increase as more base is added and the concentration of acetic acid decreases.
- At the equivalence point, the pH will experience a sharp increase as all the acetic acid is consumed and the acetate ion concentration increases.
- After the equivalence point, the pH will increase more slowly as the excess base contributes to the solution becoming more basic.
Connect these points on the graph to create the shape of the titration curve.