A buffer is created by mixing equal concentrations of NH4+ and NH3. Calculate the volume of both solutions needed to create a buffer of pH=8.75 with a total volume of 100 mL.
Use the Henderson-Hasselbalch equation.
pH = pKa + log (base/acid)
I've gotten so far, but am still unsure of how to proceed. Please correct me if I am wrong:
I know that since the concentrations of the base/acid are the same, the log(1) is 0, so the pH = pKa.
I determined the Kb by finding the Ka and using the Kw relationship.
I have a Kb value, and can determine from Kb = (OH)(A)/(HA), that Kb = (OH) since the concentrations are equal.
Now I don't know where to go from here.
would we be able to assume that the moles are equal?
To calculate the volumes of NH4+ and NH3 needed to create a buffer of pH=8.75, we need to use the Henderson-Hasselbalch equation for buffers:
pH = pKa + log([A-] / [HA])
In this equation, [A-] represents the concentration of the conjugate base (in this case, NH3) and [HA] represents the concentration of the acid (in this case, NH4+). pKa is the negative logarithm of the acid dissociation constant of NH4+/NH3.
First, we need to find the pKa of NH4+/NH3. The pKa of NH4+/NH3 is approximately 9.25.
Now, let's rearrange the Henderson-Hasselbalch equation to solve for the ratio of [A-] / [HA]:
[A-] / [HA] = 10^(pH - pKa)
Substituting the given pH=8.75 and pKa=9.25 into the equation:
[A-] / [HA] = 10^(8.75 - 9.25) = 10^(-0.5)
[A-] / [HA] = 0.3162
This means that the concentration of NH3 should be approximately 0.3162 times the concentration of NH4+.
Now, let's consider the total volume of the buffer. The total volume of the buffer is given as 100 mL.
Let's assume the concentration of NH4+ in the buffer is x M. Then, the concentration of NH3 would be approximately 0.3162x M.
The volume of NH4+ solution needed can be calculated using the formula:
Volume(NH4+) = (concentration(NH4+) * Total Volume) / concentration(NH4+)
Substituting the known values:
Volume(NH4+) = (x M * 100 mL) / x M = 100 mL
Similarly, the volume of NH3 solution can be calculated using the formula:
Volume(NH3) = (concentration(NH3) * Total Volume)/(concentration(NH3))
Substituting the known values for NH3:
Volume(NH3) = (0.3162x M * 100 mL) / (0.3162x M) = 100 mL
Therefore, you would need to mix equal volumes (50 mL each) of NH4+ solution and NH3 solution to create a buffer of pH=8.75 with a total volume of 100 mL.