calculate the the pH of a buffer solution containing 0.246 M NH3 and 0.0954 M NH4Cl (for NH3 Kb = 1.74x 10-5)
Henderson-Hasselbalch equation:
pH=pKa+log((base)/(acid))
Kb*Ka=1.0*10^-14
1.74*10^-5*Ka=1.0*10^-14
Ka=1.0*10^-14/1.74*10^-5
Ka=5.75*10^-10
pKa=-log(5.75*10^-10)
pKa=9.24
pH=9.24+log((.246)/(.0954))
pH=9.65
To calculate the pH of a buffer solution, you need to consider the equilibrium between the weak acid and its conjugate base. In this case, NH3 (ammonia) is the weak base and NH4Cl is its conjugate acid.
First, you need to write the balanced equation for the reaction between NH3 and H2O:
NH3 + H2O ⇌ NH4+ + OH-
The Kb (base dissociation constant) for NH3 is given as 1.74 × 10^-5. This equation tells us that NH3 reacts with water to produce NH4+ and OH- ions.
Next, calculate the concentration of OH- ions produced:
[OH-] = sqrt(Kb × [NH3])
Where Kb is the base dissociation constant for NH3 and [NH3] is the concentration of NH3.
[OH-] = sqrt(1.74 × 10^-5 × 0.246)
[OH-] = 4.83 × 10^-3 M
Since NH4Cl is a strong electrolyte, it completely dissociates in water to produce NH4+ and Cl- ions. Therefore, the concentration of NH4+ ions is the same as the concentration of NH4Cl, which is 0.0954 M.
Now, you need to calculate the concentration of NH3 remaining in the solution:
[NH3] = initial [NH3] - [OH-]
[NH3] = 0.246 - 4.83 × 10^-3
[NH3] = 0.241 M
To calculate the pH of the buffer solution, you need to find the pOH first using the OH- concentration:
pOH = -log[OH-]
pOH = -log(4.83 × 10^-3)
pOH = 2.316
Finally, you can calculate the pH using the pOH:
pH = 14 - pOH
pH = 14 - 2.316
pH = 11.684
Therefore, the pH of the buffer solution containing 0.246 M NH3 and 0.0954 M NH4Cl is approximately 11.684.