What mass of NH4Cl must be added to 0.750 L of a 0.100 M solution of NH3 to give a buffer solution with a pH of 9.26? Kb(NH3) = 1.8 x 10^-5. (Hint: Assume a negligible change in volume as the solid is added.)
pH = pKa + log [(base)/(acid)]
Calculate pKa = pKw/pKb
(base) = NH3
(acid) = NH4Cl
Post your work if you get stuck.
25.5
To calculate the mass of NH4Cl needed to create a buffer solution with a pH of 9.26, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
In this case, NH3 acts as the base (A-) and NH4Cl acts as the acid (HA). The pKa for NH4Cl can be calculated using the equation:
pKa = -log(Ka)
First, let's calculate pKa:
pKa = -log(Ka) = -log([H+][A-]/[HA])
Given that Kb(NH3) = 1.8 x 10^-5, we can calculate Ka(NH4Cl):
Kw = Ka(NH4Cl) * Kb(NH3)
Where Kw is the ionization constant of water, which is 1.0 x 10^-14.
Ka(NH4Cl) = Kw / Kb(NH3)
= (1.0 x 10^-14) / (1.8 x 10^-5)
= 5.556 x 10^-10
Now, let's calculate pKa:
pKa = -log(Ka)
= -log(5.556 x 10^-10)
= 9.26
Since we want a pH of 9.26, the concentration of [A-] and [HA] should be equal. Therefore, the ratio of [A-] to [HA] is 1:1.
Now, let's solve for the concentration of NH3:
pH = pKa + log([A-]/[HA])
9.26 = 9.26 + log([A-]/[HA])
log([A-]/[HA]) = 0
[A-]/[HA] = 1
Given that [A-] and [HA] are equal concentrations, we can assume that they cancel each other out. Therefore, the concentration of NH3 is 0.100 M.
Now, let's calculate the number of moles of NH3 in 0.750 L of the solution:
moles = concentration x volume
= 0.100 M x 0.750 L
= 0.075 moles
Since the ratio of NH3 to NH4Cl is 1:1, the number of moles of NH4Cl needed is also 0.075 moles.
Finally, let's calculate the mass of NH4Cl:
mass = moles x molar mass
= 0.075 moles x (14.01 g/mol + 1.01 g/mol)
= 1.5025 g
Therefore, you need to add 1.5025 grams of NH4Cl to 0.750 L of the 0.100 M solution of NH3 to create a buffer solution with a pH of 9.26.
To solve this problem, we need to use the Henderson-Hasselbalch equation for buffer solutions. The Henderson-Hasselbalch equation is given as:
pH = pKa + log([A-]/[HA])
Where, pH is the desired pH of the buffer solution, pKa is the negative logarithm of the acid dissociation constant of the weak acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.
For this problem, we are given the pH of the buffer solution (pH = 9.26) and the Kb value for NH3 (Kb = 1.8 x 10^-5).
To find the pKa value, we can use the equation:
pKa + pKb = 14
Therefore, pKa = 14 - pKb = 14 - (-log10(Kb)).
Substituting the given Kb value, we can calculate the pKa value.
Now, we need to calculate the concentrations of [A-] and [HA] in the buffer solution. [A-] will be the concentration of NH3 and [HA] will be the concentration of NH4Cl.
Given:
Volume of solution (V) = 0.750 L
Concentration of NH3 (initial) = 0.100 M
Assuming the change in volume after adding NH4Cl is negligible, the final volume of the solution will remain the same (V = 0.750 L).
To calculate the final concentration of NH3 ([A-]), we can use the formula:
[A-] = (initial concentration of NH3) - (concentration of NH4Cl added)
To calculate the concentration of NH4Cl ([HA]), we assume that all the NH4Cl dissociates into NH4+ and Cl-. Therefore, the concentration of NH4Cl ([HA]) will be equal to the concentration of NH4+.
Now, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Substitute the given values and solve for [A-]/[HA].
Now, we have the ratio of [A-]/[HA]. Since we want the pH to be 9.26, we have:
pH = 9.26 = pKa + log([A-]/[HA])
Using the known ratio of [A-]/[HA], solve for pKa. Now, you have the pKa value.
Next, use the pKa value to find the ratio of [A-]/[HA].
Finally, we need to calculate the mass of NH4Cl required to give the desired concentration of NH4+ ([HA]).
To calculate the mass of NH4Cl, we can use the formula:
mass = (molar mass of NH4Cl) x (moles of NH4Cl)
The molar mass of NH4Cl is the sum of the atomic masses of nitrogen (N), hydrogen (H), and chlorine (Cl).
By substituting the known values and calculating the masses, you will determine the mass of NH4Cl required to prepare the buffer solution with a pH of 9.26.