Calculate the ph of a buffer made from 0.25 m NH4Cl and 0.42 M NH3. Kb= 1.8 x 10^-5
Use the Henderson-Hasselbalch equation. Be careful with the caps key; m stands for molality; M stands to molarity.
To calculate the pH of a buffer solution, you need to consider the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa (acid dissociation constant) of the weak acid and the ratio of the concentrations of the conjugate acid and base of the buffer.
In this case, we are given the concentration of NH4Cl (a source of NH4+) and NH3, which are a conjugate acid-base pair. NH3 acts as the weak base and NH4+ is its conjugate acid.
The pKa can be calculated using the Kb value (base dissociation constant) of NH3, since pKa + pKb = 14 at 25 degrees Celsius. So, we can calculate the pKa as follows:
pKa = 14 - pKb
= 14 - (-log10(1.8 x 10^-5))
= 14 + 4.74
= 18.74
Now, using the Henderson-Hasselbalch equation:
pH = pKa + log10([conjugate acid]/[weak base])
Substituting the values:
pH = 18.74 + log10(0.25/0.42)
Now, let's calculate the concentration ratio:
Concentration ratio = [conjugate acid]/[weak base]
= 0.25/0.42
= 0.595
Therefore, substituting the concentration ratio into the equation:
pH = 18.74 + log10(0.595)
Using a calculator, we can find the log10(0.595) = -0.225
Finally, substituting the value of log10(0.595) into the equation:
pH = 18.74 - 0.225
= 18.515
Thus, the pH of the buffer solution made from 0.25 M NH4Cl and 0.42 M NH3 is approximately 18.515.