Buffer capacity is a measure of a buffer solution\'s resistance to changes in pH as strong acid or base is added. Suppose that you have 165 mL of a buffer that is 0.360 M in both benzoic acid (C6H5COOH) and its conjugate base (C6H5COO–). Calculate the maximum volume of 0.250 M HCl that can be added to the buffer before its buffering capacity is lost.
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To calculate the maximum volume of 0.250 M HCl that can be added to the buffer before its buffering capacity is lost, we need to first consider the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where:
pH = the desired pH of the buffer solution
pKa = the acid dissociation constant of benzoic acid (C6H5COOH), which is 4.20
[A-] = concentration of the conjugate base (C6H5COO–) in the buffer
[HA] = concentration of the acid (C6H5COOH) in the buffer
Given:
- Volume of the buffer solution = 165 mL = 0.165 L
- [A-] = [HA] = 0.360 M
- [HCl] = 0.250 M
The buffering region is typically considered to be within 1 pH unit of the pKa value. To determine the maximum volume of HCl that can be added, we will consider the point where the buffer pH reaches pKa + 1.
Let's calculate the initial pH of the buffer solution:
pH = pKa + log([A-]/[HA])
pH = 4.20 + log(0.360/0.360)
pH = 4.20
Next, calculate the moles of buffer components in the initial solution:
moles of C6H5COOH = volume (L) × concentration (M)
moles of C6H5COOH = 0.165 L × 0.360 M = 0.0594 moles
moles of C6H5COO– = moles of C6H5COOH = 0.0594 moles
Calculate the total moles of both species in the buffer solution:
total moles = moles of C6H5COOH + moles of C6H5COO–
total moles = 0.0594 moles + 0.0594 moles = 0.1188 moles
Now let's calculate the maximum moles of HCl that can react with the buffer:
maximum moles of HCl = total moles × (pH range / ΔpH)
ΔpH = (pHmax - pHmin) = (4.20 + 1 - 4.20) = 1
maximum moles of HCl = 0.1188 moles × (1 / 1)
maximum moles of HCl = 0.1188 moles
Finally, calculate the maximum volume of HCl that can be added:
maximum volume of HCl (L) = maximum moles of HCl / [HCl] (M)
maximum volume of HCl = 0.1188 moles / 0.250 M = 0.4752 L
Convert the volume to mL by multiplying by 1000:
maximum volume of HCl = 0.4752 L × 1000 mL/L = 475.2 mL
Therefore, the maximum volume of 0.250 M HCl that can be added to the buffer before its buffering capacity is lost is 475.2 mL.
To solve this problem, we need to calculate the buffer capacity of the given buffer solution and then use that information to determine the maximum volume of HCl that can be added before the buffering capacity is lost.
1. Calculate the buffer capacity of the buffer solution:
The buffer capacity (β) can be calculated using the Henderson-Hasselbalch equation: β = Δ[base]/ΔpH, where Δ[base] is the change in the concentration of the conjugate base and ΔpH is the change in pH.
In this case, the concentration of the conjugate base (C6H5COO–) is given as 0.360 M. Since the buffer contains equal concentrations of the acid (C6H5COOH) and its conjugate base, the concentration of the acid is also 0.360 M.
The pH of the buffer can be calculated using the Henderson-Hasselbalch equation: pH = pKa + log ([base]/[acid]), where pKa is the dissociation constant of the acid. In this case, benzoic acid has a pKa of 4.20.
Using the given information and the Henderson-Hasselbalch equation, we can calculate the pH of the buffer:
pH = 4.20 + log (0.360/0.360) = 4.20 + log(1) = 4.20.
Since the pH of the buffer is equal to the pKa, we can determine that the buffer capacity (β) is at its maximum value. The maximum buffer capacity occurs when the pH of the buffer is equal to the pKa of the acid.
2. Determine the maximum volume of 0.250 M HCl that can be added before the buffering capacity is lost:
The buffer capacity tells us how much strong acid or base can be added to the buffer before the pH starts to change significantly.
Since we determined that the buffer capacity (β) is at its maximum value when the buffer pH is equal to the pKa, we need to find the pH at which the buffer capacity is lost. This occurs when the concentration of the conjugate base is half the initial concentration.
The initial concentration of the conjugate base is 0.360 M, so the concentration at which buffering capacity is lost is 0.180 M.
Using the Henderson-Hasselbalch equation, we can calculate the pH at which buffering capacity is lost:
pH = pKa + log ([base]/[acid]) = 4.20 + log (0.180/0.360) = 4.20 - 0.3010 = 3.90.
Now that we have the pH at which buffering capacity is lost, we can calculate the volume of HCl that can be added before this point:
From the balanced chemical equation, we know that one mole of HCl neutralizes one mole of benzoic acid or its conjugate base. Therefore, the moles of HCl that can be neutralized by the given 165 mL of the buffer solution can be calculated as follows:
Moles of HCl = (0.360 M) x (0.165 L) = 0.0594 moles.
Now, we can calculate the maximum volume of 0.250 M HCl that can be added before the buffering capacity is lost:
Volume = (moles of HCl) / (concentration of HCl) = 0.0594 moles / 0.250 M = 0.238 L = 238 mL.
Therefore, the maximum volume of 0.250 M HCl that can be added to the buffer before its buffering capacity is lost is 238 mL.