Solution: Calculating pH of a Solution with NH4+Cl and NaOH

[kasse]

[SOLVED] pH of buffer solution

Homework Statement

Calculate the pH of a solution made by mixing 750 mL 1.00 M NH₄⁺Cl and 250 mL 1.00 M NaOH

The Attempt at a Solution

NH₄⁺ will react with H₂O to form NH₃ and H₂O⁺. If my calculations are correct, [H⁺] after the reaction will be 2.07E-5.

Then H⁺ will react with OH^-. But since there's almost no H⁺ compared to NO^-, this reaction is irrelevant. The pOH is therefore

pOH = -log [0.25], and the pH is 13.4

which is wrong. What's my mistake(s)?

 

[Borek]

You should use Henderson-Hasselbalch equation. Your approach neglects shifting of the NH₄⁺ dissociation equilibrium to the right with H⁺ neutralization.

 

[Blueshift5]

In this case, the mistake is in assuming that the reaction between NH4+ and H2O is the only relevant reaction occurring in the solution. In reality, there are multiple reactions happening simultaneously, including the reaction between NH3 and H2O to form NH4+ and OH-. This reaction will consume some of the OH- ions and therefore affect the overall pH of the solution.

To accurately calculate the pH, you would need to consider all relevant reactions occurring in the solution and use the appropriate equilibrium equations to determine the concentrations of each species. It is also important to note that the pH of a buffer solution is affected by the ratio of the conjugate acid and base, and the total concentrations of each component.

In this case, the solution is a buffer solution made up of NH4+ and NH3, so the Henderson-Hasselbalch equation can be used to calculate the pH. The pH of a buffer solution is given by:

pH = pKa + log([conjugate base]/[weak acid])

In this case, the pKa of NH4+ is 9.25, so the pH of the solution can be calculated as:

pH = 9.25 + log([0.25]/[0.75]) = 9.25 + log(0.33) = 9.25 - 0.48 = 8.77

Therefore, the pH of the solution is 8.77, which is significantly different from the previously calculated value of 13.4. This highlights the importance of considering all relevant reactions and using appropriate equations to accurately calculate the pH of a solution.