What is the PH of a buffer made by adding 8.20 grams of sodium acetate(NaCH3CO2) to 500 ml of 0.10 M acetic acid(CH3CO2H). Ka for acetic acid is 1.8 x 10^-5.
The pH of the buffer is 4.75.
To find the pH of the buffer, we need to apply the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log ([A-]/[HA])
Where:
pH is the pH of the buffer solution
pKa is the negative logarithm of the acid dissociation constant (Ka) for acetic acid
[A-] is the concentration of the conjugate base (sodium acetate)
[HA] is the concentration of the weak acid (acetic acid)
First, let's calculate the number of moles of acetic acid and sodium acetate in the solution.
Step 1: Calculate the moles of acetic acid (CH3CO2H)
Given:
Volume (V) = 500 mL = 500/1000 = 0.5 L
Molarity (M) = 0.10 M
Number of moles (n) of acetic acid = Molarity * Volume
n(CH3CO2H) = 0.10 * 0.5
n(CH3CO2H) = 0.05 moles
Step 2: Calculate the moles of sodium acetate (NaCH3CO2)
Given:
Mass (m) = 8.20 g
Molar mass (M) = atomic mass of Na + atomic mass of C + 3 * atomic mass of H + 2 * atomic mass of O
Molar mass (CH3CO2Na) = 22.99 + 12.01 + 3 * 1.01 + 2 * 16.00
Molar mass (CH3CO2Na) ≈ 82.03 g/mol
Number of moles (n) of sodium acetate = Mass/Molar mass
n(NaCH3CO2) = 8.20 / 82.03
n(NaCH3CO2) ≈ 0.100 moles
Step 3: Calculate the concentrations of acetic acid and sodium acetate
Concentration (C) = moles/volume
Concentration of acetic acid ([HA]) = n(CH3CO2H) / V
[HA] = 0.05 / 0.5
[HA] = 0.10 M
Concentration of sodium acetate ([A-]) = n(NaCH3CO2) / V
[A-] = 0.100 / 0.5
[A-] = 0.20 M
Step 4: Calculate the pKa value
Given:
Ka = 1.8 x 10^-5
pKa = -log(Ka)
pKa = -log(1.8 x 10^-5)
pKa ≈ 4.74
Step 5: Calculate the pH of the buffer solution using the Henderson-Hasselbalch equation
pH = pKa + log ([A-]/[HA])
pH = 4.74 + log(0.20/0.10)
pH ≈ 4.74 + log(2)
pH ≈ 4.74 + 0.30
pH ≈ 5.04
Therefore, the pH of the buffer solution is approximately 5.04.
To determine the pH of the buffer, we need to calculate the concentration of the acetate ion (CH3CO2-) and the acetic acid (CH3CO2H) in the buffer solution.
Step 1: Calculate the moles of sodium acetate (NaCH3CO2):
To find the number of moles, we use the formula: moles = mass / molar mass.
The molar mass of sodium acetate (NaCH3CO2) is:
(1 x atomic mass of Na) + (2 x atomic mass of C) + (2 x atomic mass of H) + (3 x atomic mass of O)
= (1 x 22.99) + (2 x 12.01) + (6 x 1.01) + (2 x 16.00)
= 82.03 g/mol
Therefore, moles of NaCH3CO2 = 8.20 g / 82.03 g/mol
Step 2: Convert the volume of acetic acid (CH3CO2H) to liters:
The volume of acetic acid is given as 500 mL, and we need to convert it to liters since the molarity is specified in moles per liter.
Liters of acetic acid = 500 mL / 1000 mL/L
Step 3: Calculate the moles of acetic acid (CH3CO2H):
Moles of acetic acid = molarity x volume (in liters)
= 0.10 M x (500 mL / 1000 mL/L)
Step 4: Calculate the concentration of acetate ion (CH3CO2-):
The concentration of acetate ion is equal to the moles of sodium acetate divided by the total volume of the solution (in liters).
Concentration of CH3CO2- = moles of NaCH3CO2 / (volume of acetic acid + volume of sodium acetate)
Step 5: Calculate the concentration of acetic acid (CH3CO2H):
The concentration of acetic acid is equal to the moles of acetic acid divided by the total volume of the solution (in liters).
Concentration of CH3CO2H = moles of acetic acid / (volume of acetic acid + volume of sodium acetate)
Step 6: Calculate the pH of the buffer:
The pH of the buffer can be determined using the Henderson-Hasselbalch equation:
pH = pKa + log([concentration of CH3CO2-] / [concentration of CH3CO2H])
where pKa is the negative logarithm of Ka (acid dissociation constant) for acetic acid.
Now, substitute the values we calculated into the Henderson-Hasselbalch equation to find the pH of the buffer.