Calculate the pH of solution containing 0.06 M NH4Cl (Ka = 5.7 x 10-10) and 0.11 M NH3.
The correct answer and explanation is:
To calculate the pH of a solution containing NH₄Cl (ammonium chloride) and NH₃ (ammonia), we can use the Henderson-Hasselbalch equation for buffer systems: pH=pKa+log([Base][Acid])\text{pH} = \text{pKa} + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right)
Step-by-step solution:
- Identify the Acid and Base:
- NH₄Cl is the acid, as it dissociates into NH₄⁺ (ammonium ion) in water. NH₄⁺ acts as a weak acid.
- NH₃ is the base, as it accepts a proton (H⁺) to form NH₄⁺.
- Calculate pKa:
- The given Ka for NH₄⁺ is 5.7×10−105.7 \times 10^{-10}. The pKa can be found using the formula: pKa=−log(Ka)\text{pKa} = -\log(\text{Ka}) pKa=−log(5.7×10−10)≈9.24\text{pKa} = -\log(5.7 \times 10^{-10}) \approx 9.24
- Apply the Henderson-Hasselbalch equation:
- The concentration of the base (NH₃) is 0.11 M, and the concentration of the acid (NH₄⁺ from NH₄Cl) is 0.06 M.
- Calculate the ratio: 0.110.06=1.833\frac{0.11}{0.06} = 1.833
- Now find the logarithm: log(1.833)≈0.263\log(1.833) \approx 0.263
- So, the pH is: pH=9.24+0.263=9.50\text{pH} = 9.24 + 0.263 = 9.50
Final Answer:
The pH of the solution is approximately 9.50.
Explanation:
This solution acts as a buffer system, where the weak acid (NH₄⁺) and its conjugate base (NH₃) resist large changes in pH. The Henderson-Hasselbalch equation is used to find the pH based on the concentrations of the acid and the base. Since NH₄Cl is a weak acid and NH₃ is a weak base, their concentrations determine the solution’s ability to maintain a stable pH. The pKa value reflects the strength of NH₄⁺ as an acid, and the ratio of the base (NH₃) to the acid (NH₄⁺) gives the pH.