Question

20 mL of 0.1 M NH₄OH is mixed with 40 mL of 0.05 M HCl.The pH of the mixture is nearest to:(Given: K_b(NH₄OH) = 1 × 10^–5 ,log 2 = 0.30,log 3 = 0.48, log 5 = 0.69, log 7 = 0.84, log 11 =1.04)

• A. 3.2
• B. 4.2
• C. 5.2
• D. 6.2

Answer 1

The Correct Option is C

To find the pH of the mixture formed by mixing 20 mL of 0.1 M NH₄OH with 40 mL of 0.05 M HCl, we need to follow these steps:

1. Calculate the millimoles of NH₄OH and HCl:
   • Millimoles of NH₄OH = Volume (mL) × Molarity (M) = 20 × 0.1 = 2 mmol
   • Millimoles of HCl = Volume (mL) × Molarity (M) = 40 × 0.05 = 2 mmol
2. Determine the reaction between NH₄OH and HCl:
   • The reaction: NH₄OH + HCl → NH₄Cl + H₂O
   • This is a neutralization reaction, where 1 mole of NH₄OH completely reacts with 1 mole of HCl to form NH₄Cl.
   • Since initial millimoles of NH₄OH and HCl are equal, they completely neutralize each other, forming 2 mmol of NH₄Cl.
3. Since a weak base (NH₄OH) reacts with a strong acid (HCl), the resulting solution contains the salt NH₄Cl, which slightly hydrolyzes to affect pH.
4. To calculate the pH of the resultant weak acid (from NH₄Cl hydrolysis):
   • The hydrolysis of NH₄Cl in water is primarily influenced by the K_a of its conjugate acid NH₄⁺:
   • K_a(NH₄⁺) = \frac{K_w}{K_b} where K_w = 1 \times 10^{-14}
   • Using given K_b(NH₄OH) = 1 × 10^–5, K_a(NH₄⁺) = \frac{1 \times 10^{-14}}{1 \times 10^{-5}} = 1 \times 10^{-9}
5. Apply the formula to calculate pH:
   • Total Volume = 20 mL + 40 mL = 60 mL
   • [NH₄⁺] = \frac{2 \text{ mmol}}{60 \text{ mL}} = \frac{1}{30} \text{ M}
   • Using pH formula for weak acid salt: pH = 7 + 0.5 log \frac{K_w}{[NH_4^+] \cdot K_a}
   • Substitute the values: 7 + 0.5 \cdot \log \left(\frac{1 \times 10^{-14}}{\left(\frac{1}{30}\right) \cdot 1 \times 10^{-9}}\right)
   • This simplifies to: 7 + 0.5 \cdot \log(30 \times 10^{-5})
   • Calculate: \log 30 \approx \log(3 \times 10) = \log 3 + \log 10 = 0.48 + 1 = 1.48
   • pH = 7 + 0.5 × (1.48 - 5) = 7 + 0.5 × -3.52 = 7 - 1.76 = 5.24

Therefore, the pH of the mixture is nearest to 5.2.