To calculate the hydrogen ion concentration of the buffer solution, we need to determine the amount of acid and the amount of conjugate base in the solution.
First, we can calculate the amount of acetic acid added:
0.10 L * 2.0 mol/L = 0.20 mol acetic acid
Next, we can calculate the amount of sodium hydroxide added. Since sodium hydroxide is a strong base, it completely dissociates in water to form sodium ions and hydroxide ions:
0.10 L * 1.0 mol/L = 0.10 mol sodium hydroxide
The hydroxide ions will react with the acetic acid to form acetate ions and water:
H+ + OH- -> H2O
CH3COOH + OH- -> CH3COO- + H2O
Since acetic acid is a weak acid, it does not completely dissociate in water, so some of it remains in the solution as undissociated molecules:
CH3COOH <--> H+ + CH3COO-
The acetate ion is the conjugate base of acetic acid, and since the reaction above consumes hydroxide ions, the acetate ion will act as a buffer to resist any changes to the hydrogen ion concentration of the solution.
To calculate the amount of acetate ion in the solution, we can use the equation for the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where pH is the desired pH of the buffer solution, pKa is the dissociation constant for acetic acid (4.76), and [A-] and [HA] are the concentrations of the conjugate base and the weak acid, respectively.
Assuming that the pH of the buffer solution is close to the pKa of acetic acid, we can rearrange this equation to solve for [A-]/[HA]:
[A-]/[HA] = 10^(pH - pKa)
If we assume a pH of 4.76, then [A-]/[HA] = 1, since log(1) = 0. This means that the concentration of acetate ion and acetic acid are equal in the buffer solution.
Therefore, the amount of acetate ion in the solution is also 0.20 mol.
To calculate the hydrogen ion concentration of the buffer solution, we can use the equation for the dissociation constant of acetic acid:
Ka = [H+][A-]/[HA]
Solving for [H+], we get:
[H+] = Ka * [HA]/[A-]
Plugging in the values we calculated above, we get:
[H+] = 1.8 x 10^-5 M
Therefore, the hydrogen ion concentration of the buffer solution is 1.8 x 10^-5 M.