How do you calculate the number of moles of NaOH to add to a liter of 1M NH4CL (pka of NH4+ = 9.25 ) to produce a solution buffering the pH at 8.75 ? thanks
NiOOH
The Henderson-Hasselbalch equation is
pH = pKa + log[(base)/(acid)]
8.75 = 9.25 + log (B)/(1-B)
Solve for (base). I get approximately .25 but you need to go through it more accurately. THEN, I always like to check it to make sure I get a pH of 8.75.
Using the approximate numbers,
NH4^+ + OH^- ==> NH3 + H2O
1mole....0.........0
add......B.........
1-B......0..........B
If b = 0.25, then 1-B = 0.75 and
pH = 9.25 + log(0.25/0.75)
pH = 8.77. This will be 8.75 when you do it more accurately.
To calculate the number of moles of NaOH needed to create a buffer solution with a pH of 8.75, you'll need to use the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is:
pH = pKa + log([A-]/[HA]),
where pH is the desired pH, pKa is the logarithmic value of the acid dissociation constant (pKa = -log Ka), [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
In this case, NH4Cl acts as the acid (NH4+) and NaOH will provide the conjugate base (OH-).
Step 1: Calculate the concentration of NH4+:
Since you have a 1M NH4Cl solution, the concentration of NH4+ is also 1M.
Step 2: Calculate the concentration of OH- needed:
To buffer the pH at 8.75, you should aim for a near-equal concentration of NH4+ and OH-. Therefore, the concentration of OH- will also be 1M.
Step 3: Use the Henderson-Hasselbalch equation to calculate the amount of NaOH needed:
pH = pKa + log([A-]/[HA]) ---> 8.75 = 9.25 + log(1/[NH4+])
Rearranging the equation:
log(1/[NH4+]) = 8.75 - 9.25
log(1/[NH4+]) = -0.5
Taking the antilog of both sides:
1/[NH4+] = 10^(-0.5)
[NH4+] = 1 / 10^(-0.5)
[NH4+] = 1 / 0.316
[NH4+] = 3.16 M
Now that you know the desired concentration of NH4+, you can determine the concentration of NaOH needed to achieve the same concentration of OH-.
Step 4: Calculate the number of moles of NaOH needed:
Since NaOH dissociates to produce one OH- ion per molecule, the concentration of NaOH needed will be the same as OH- concentration.
Therefore, the number of moles of NaOH needed = concentration × volume
Given that the volume is 1 liter, the number of moles of NaOH needed = 1M × 1L = 1 mole.
So, you would need to add 1 mole of NaOH to a liter of 1M NH4Cl to create a solution buffering the pH at 8.75.