What is the pH of a solution when 1ml of 0.10M NaOH is added to 100ml of buffer containing 0.1M acetic acid and 0.1M sodium acetate?
100 mL x 0.1M HAc = 10 mmoles.
100 mL x 0.1M NaAc = 10 mmols.
1 mL x 0.1M NaOH = 0.1 mmol.
-----------------------
......HAc + OH^- ==> Ac^- + H2O
I.....10.....0.......10
add........0.1..............
C...-0.1..-0.1.......+0.1
E.....9.9...0........10.1
Substitute the equilibrium values into the Henderson-Hasselbalch equation and solve for pH.
To find the pH of a solution, we need to consider the equation for an acid-base reaction and the principles of buffer solutions.
The reaction between acetic acid (CH3COOH) and sodium acetate (CH3COONa) can be represented as follows:
CH3COOH + OH- → CH3COO- + H2O
In this reaction, sodium hydroxide (NaOH) acts as a base, while acetic acid acts as an acid.
Since the initial solution is a buffer solution, it contains a weak acid (acetic acid) and its conjugate base (sodium acetate). Buffers are resistant to changes in pH because they can neutralize small amounts of acid or base added to them.
To determine the pH after adding 1 mL of 0.10 M NaOH to the 100 mL buffer solution, we need to calculate the new concentrations of acetic acid and sodium acetate.
First, we need to determine the amount of moles of NaOH added:
moles of NaOH = volume (L) x concentration (mol/L)
= 0.001 L x 0.10 mol/L
= 0.0001 mol
The stoichiometry of the reaction tells us that one mole of NaOH reacts with one mole of acetic acid, producing one mole of sodium acetate.
Considering the initial concentration of acetic acid, we can determine the remaining concentration:
concentration of acetic acid = initial concentration - moles of NaOH added / total volume in liters
= 0.10 M - 0.0001 mol / 0.101 L
= 0.099 M
Now, we need to calculate the concentration of sodium acetate formed:
concentration of sodium acetate = moles of NaOH added / total volume in liters
= 0.0001 mol / 0.101 L
= 0.00099 M
At equilibrium, a buffer solution can be described using the Henderson-Hasselbalch equation:
pH = pKa + log([A-] / [HA])
where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.
Since acetic acid is a weak acid, we can use the pKa value for acetic acid, which is estimated to be around 4.75.
Using the Henderson-Hasselbalch equation, we can now calculate the pH:
pH = 4.75 + log(0.00099 M / 0.099 M)
= 4.75 + log(0.01)
= 4.75 + (-2)
= 2.75
Therefore, the pH of the solution after adding 1 mL of 0.10 M NaOH to the buffer is approximately 2.75.