A buffer solution is prepared by adding 0.10 liter of 2.0 molar acetic acid solution to 0.1 liter
of a 1.0 molar sodium hydroxide solution. Compute the hydrogen ion concentration of the buffer solution
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.
Suppose that 0.10 liter of 0.50 molar hydrochloric acid is added to 0.040 liter of the buffer
prepared in (b). Compute the hydrogen ion concentration of the resulting solution.
The buffer solution we prepared in (b) is made up of acetic acid and acetate ions, which means it can resist changes in pH by absorbing or releasing hydrogen ions.
When we add the hydrochloric acid to the buffer solution, the hydrogen ions from the hydrochloric acid will react with the acetate ions in the buffer to form acetic acid:
H+ + CH3COO- -> CH3COOH
This reaction will consume some of the acetate ions in the buffer and shift the equilibrium towards the weak acid. However, since the buffer solution has roughly equal concentrations of acetic acid and acetate ions, we can assume that the system will still act as a buffer and resist large changes in pH.
To calculate the hydrogen ion concentration of the resulting solution, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Assuming that the acetate/acetic acid equilibrium is still roughly balanced, we can simplify this equation to:
pH = pKa + log(1)
Since the pKa of acetic acid is 4.76, we can estimate that the pH of the buffer solution is around 4.76.
Next, we can calculate the amount of hydrogen ions added to the solution by the hydrochloric acid:
0.10 L * 0.50 mol/L = 0.05 mol HCl
This will increase the hydrogen ion concentration by 0.05 moles. To calculate the new hydrogen ion concentration, we can use the equation:
[H+] = (moles of HCl added) / (total volume of solution)
The total volume of the solution after adding the HCl is:
0.10 L + 0.040 L = 0.14 L
Therefore, the new hydrogen ion concentration is:
[H+] = 0.05 mol / 0.14 L = 0.357 M
So the hydrogen ion concentration of the resulting solution is 0.357 M.
To compute the hydrogen ion concentration of the buffer solution, we need to calculate the moles of acetic acid and sodium hydroxide, and determine the resulting concentration of hydrogen ions.
Step 1: Calculate the moles of acetic acid.
Moles = Molarity * Volume (in liters)
Moles of acetic acid = 2.0 M * 0.10 L = 0.20 moles
Step 2: Calculate the moles of sodium hydroxide.
Moles of sodium hydroxide = 1.0 M * 0.10 L = 0.10 moles
Step 3: Determine the limiting reactant.
Since the moles of sodium hydroxide are less than the moles of acetic acid, sodium hydroxide is the limiting reactant.
Step 4: Determine the excess reactant.
Moles of excess acetic acid = Moles of acetic acid - Moles of sodium hydroxide
= 0.20 moles - 0.10 moles
= 0.10 moles
Step 5: Calculate the total volume of the buffer solution.
Total volume = Volume of acetic acid + Volume of sodium hydroxide
= 0.10 L + 0.10 L
= 0.20 L
Step 6: Calculate the concentration of hydrogen ions.
Concentration of hydrogen ions = Moles of excess acetic acid / Total volume
= 0.10 moles / 0.20 L
= 0.50 M
Therefore, the hydrogen ion concentration of the buffer solution is 0.50 M.
To compute the hydrogen ion concentration of the buffer solution, we need to determine the number of moles of acetic acid and sodium hydroxide present in the solution, as well as the total volume of the buffer solution.
Step 1: Calculate the moles of acetic acid:
Moles of acetic acid = concentration × volume
Moles of acetic acid = 2.0 M × 0.10 L
Moles of acetic acid = 0.20 mol
Step 2: Calculate the moles of sodium hydroxide:
Moles of sodium hydroxide = concentration × volume
Moles of sodium hydroxide = 1.0 M × 0.10 L
Moles of sodium hydroxide = 0.10 mol
Step 3: Determine the limiting reactant:
The limiting reactant is the one with fewer moles, which is sodium hydroxide in this case.
Step 4: Calculate the moles of water produced when sodium hydroxide reacts with acetic acid:
The balanced equation for the reaction between acetic acid and sodium hydroxide is:
CH3COOH + OH- → CH3COO- + H2O
From the equation, we can see that 1 mole of sodium hydroxide produces 1 mole of water. Therefore, the moles of water produced = moles of sodium hydroxide
Moles of water = 0.10 mol
Step 5: Calculate the volume of the buffer solution:
The volume of the buffer solution is the sum of the initial volumes of acetic acid and sodium hydroxide:
Volume of buffer solution = 0.10 L + 0.10 L
Volume of buffer solution = 0.20 L
Step 6: Calculate the hydrogen ion concentration:
Hydrogen ion concentration (H+ concentration) is calculated using the formula:
[H+] = moles of H+ / volume of solution
Since the moles of water produced when sodium hydroxide reacts with acetic acid is equal to the moles of H+ ions, we can use the moles of water to calculate the hydrogen ion concentration.
Hydrogen ion concentration = Moles of water / Volume of solution
Hydrogen ion concentration = 0.10 mol / 0.20 L
Hydrogen ion concentration = 0.50 M
Therefore, the hydrogen ion concentration of the buffer solution is 0.50 M.