Write an equilibrium reaction for a buffer system made of the weak base, B, and its conjugate acid. If the buffer contains 1.05 M of B and 0.750M conjugate acid and has a pH of 9.50, what is the pH after 0.0050 mol HCl is added to 0.500 L of this solution?
B + H^+ ==> BH^+
In 500 mL of the buffer we have millimols of
B = 500 x 1.05 = 525
BH^+ = 500 x 0.750 = 375
add 0.005 = 5 millimols HCl.
...........B + H^+ ==> BH^+
initial...525.........375
add............5..............
change.....-5...-5....5
equil.....520.....0....380
Plug into the Henderson-Hasselbalch equation and solve for pH.
To write an equilibrium reaction for a buffer system made of a weak base, B, and its conjugate acid, we can use the generic expression:
B + H₂O ⇌ BH⁺ + OH⁻
In this case, B represents the weak base, BH⁺ represents its conjugate acid, and OH⁻ represents the hydroxide ion. The reaction can be reversible as both the weak base and its conjugate acid can react with water to create the hydroxide ion.
Now, let's calculate the initial concentrations of the weak base and conjugate acid before any HCl is added:
[B] = 1.05 M
[conjugate acid] = 0.750 M
Since the pH of the solution is given as 9.50, we can assume that the solution is basic due to the presence of the weak base. In a basic solution, the hydroxide ion (OH⁻) concentration is related to the pH through the expression:
[OH⁻] = 10^(-pOH)
where pOH is the negative logarithm of the hydroxide ion concentration.
To determine the pOH, we can use the pH provided:
pOH = 14 - pH
= 14 - 9.50
= 4.50
Now that we have the pOH, we can calculate the hydroxide ion concentration:
[OH⁻] = 10^(-pOH)
= 10^(-4.50)
≈ 3.16 × 10^(-5) M
Since a buffer system resists changes in pH, we can calculate the change in concentration of the weak base and conjugate acid when HCl is added.
Given that 0.0050 mol of HCl is added to 0.500 L of the solution, we can calculate the new volume and adjust the respective concentrations:
New volume = initial volume + volume of HCl
= 0.500 L + 0.0050 L
= 0.5050 L
To calculate the new concentration of the weak base, we can use the formula:
[B] = (initial concentration × initial volume) / new volume
= (1.05 M × 0.500 L) / 0.5050 L
To calculate the new concentration of the conjugate acid, we can use the formula:
[conjugate acid] = (initial concentration × initial volume) / new volume
= (0.750 M × 0.500 L) / 0.5050 L
Finally, let's calculate the new pH of the solution using the hydroxide ion concentration ([OH⁻]) after the addition of HCl. We know that [H⁺] × [OH⁻] = 1.0 × 10^(-14) from the ion product constant of water (Kw).
[H⁺] = Kw / [OH⁻]
= (1.0 × 10^(-14)) / (3.16 × 10^(-5) M)
≈ 3.16 × 10^(-10) M
pH = -log[H⁺]
= -log(3.16 × 10^(-10))
≈ 9.50
Therefore, after adding 0.0050 mol of HCl to 0.500 L of the given buffer solution, the new pH would still be approximately 9.50.