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If a buffer contains 1.05M B and 0.750M BH+ has the pH of 9.5. What would be the pH after 0.005mol of HCL is added to 0.5L of solution

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jacob193

Answer:

Final pH: 9.49.

Round to two decimal places as in the question: 9.5.

Explanation:

The conjugate of B is a cation that contains one more proton than B. The conjugate of B is an acid. As a result, B is a weak base.

What's the pKb of base B?

Consider the Henderson-Hasselbalch equation for buffers of a weak base and its conjugate acid ion.

[tex]\displaystyle \text{pOH} = \text{pK}_b + \log{\frac{[\text{Salt}]}{[\text{Base}]}}[/tex].

[tex]\text{pOH} = \text{pK}_w - \text{pH}[/tex].

[tex]\text{pK}_w = 14[/tex].

[tex]\text{pOH} = 14 - 9.5 = 4.5[/tex]

[tex]\displaystyle \text{pK}_b = \text{pOH} -\log{\frac{[\text{Salt}]}{[\text{Base}]}}\\\phantom{\text{pK}_b} = 4.5 - \log{\frac{0.750}{1.05}} \\\phantom{\text{pK}_b} =4.64613[/tex].

What's the new salt-to-base ratio?

The 0.005 mol of HCl will convert 0.005 mol of base B to its conjugate acid ion BH⁺.

Initial:

  • [tex]n(\text{B}) = c\cdot V = 1.05 \times 0.5 = 0.525\;\text{mol}[/tex];
  • [tex]n(\text{BH}^{+}) = c\cdot V = 0.750 \times 0.5 = 0.375\;\text{mol}[/tex].

After adding the HCl:

  • [tex]n(\text{B}) = 0.525 - 0.005 = 0.520\;\text{mol}[/tex];
  • [tex]n(\text{BH}^{+}) = 0.375+ 0.005 = 0.380\;\text{mol}[/tex].

Assume that the volume is still 0.5 L:

  • [tex]\displaystyle [\text{B}] = \frac{n}{V} = \frac{0.520}{0.5} = 1.04\;\text{mol}\cdot\text{dm}^{-3}[/tex].
  • [tex]\displaystyle [\text{BH}^{+}] = \frac{n}{V} = \frac{0.380}{0.5} = 0.760\;\text{mol}\cdot\text{dm}^{-3}[/tex].

What's will be the pH of the solution?

Apply the Henderson-Hasselbalch equation again:

[tex]\displaystyle \text{pOH} = \text{pK}_b + \log{\frac{[\text{Salt}]}{[\text{Base}]}} = 4.64613 + \log{\frac{0.760}{1.04}} = 4.50991[/tex]

[tex]\text{pH} = \text{pK}_w - \text{pOH}= 14 - 4.50991 = 9.49[/tex].

The final pH is slightly smaller than the initial pH. That's expected due to the hydrochloric acid. However, the change is small due to the nature of buffer solutions: adding a small amount of acid or base won't significantly impact the pH of the solution.

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