Calculate the pH of a buffer solution containing 1.0 M ammonia (NH3 ; Kb = 1.8 x 10-5) and 1.0 M ammonium chloride (NH4Cl).
Use the Henderson – Hasselbalch equation.
4.77
To calculate the pH of a buffer solution, we can use the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log ([A-]/[HA])
where:
pH is the pH of the buffer solution,
pKa is the negative logarithm of the acid dissociation constant of the weak acid in the buffer solution,
[A-] is the concentration of the conjugate base,
[HA] is the concentration of the weak acid.
In this case, ammonia (NH3) acts as the weak base, and ammonium chloride (NH4Cl) provides the conjugate acid (NH4+).
The pKa can be calculated using the equation:
pKw = pKa + pKb
where pKw is the negative logarithm of the water dissociation constant (pKw = 14), and pKb is the negative logarithm of the base dissociation constant.
Given that the base dissociation constant (Kb) for ammonia (NH3) is 1.8 x 10^-5, we can calculate pKb as follows:
pKb = -log(Kb) = -log(1.8 x 10^-5) = 4.74
Substituting the pKw value and pKb value into the pKa equation, we can solve for pKa:
14 = pKa + 4.74
pKa = 14 - 4.74 = 9.26
Now, we can use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution:
pH = pKa + log ([A-]/[HA])
Since the concentration of ammonia (NH3) and ammonium chloride (NH4Cl) in the buffer solution is both 1.0 M, we have:
pH = 9.26 + log (1.0/1.0) = 9.26 + log(1) = 9.26
Therefore, the pH of the buffer solution is 9.26.
To calculate the pH of a buffer solution, you need to consider the equilibrium reactions that happen between the weak acid (NH4+) and its conjugate base (NH3) in the buffer system.
In this case, ammonia acts as a weak base (NH3) and ammonium chloride (NH4Cl) acts as its conjugate acid (NH4+).
The equilibrium reactions involved are as follows:
NH3 + H2O ⇌ NH4+ + OH-
NH4+ + H2O ⇌ NH3 + H3O+
The dissociation constant of ammonia, Kb, is given as 1.8 x 10^-5, which represents the equilibrium constant for the reaction NH3 + H2O ⇌ NH4+ + OH-.
The first step is to determine the concentration of the hydroxide ion (OH-) in the solution. Since we are given that the concentration of ammonia (NH3) is 1.0 M, the concentration of hydroxide ions can be calculated from Kb using the following equation:
Kb = [NH4+][OH-] / [NH3]
Using the given value of Kb and the concentration of ammonia (NH3) as 1.0 M, we can rearrange the equation to solve for [OH-], which is the concentration we need:
[OH-] = Kb * [NH3] / [NH4+]
Now, let's calculate the concentration of NH4+ in the solution. Since the concentration of ammonium chloride (NH4Cl) is also given as 1.0 M, the concentration of NH4+ is also 1.0 M.
Substituting the values into the equation, we have:
[OH-] = (1.8 x 10^-5) * (1.0) / (1.0) = 1.8 x 10^-5 M
Since the buffer solution contains equal concentrations of NH3 and NH4+, we know that [NH3] = [NH4+] = 1.0 M.
To determine the pH of the buffer solution, we can use the fact that pH is the negative logarithm of the concentration of hydronium ions (H3O+). In this case, we need to calculate the concentration of H3O+.
Since the reaction NH4+ + H2O ⇌ NH3 + H3O+ is in equilibrium, the concentration of H3O+ is the same as the concentration of NH4+, which is 1.0 M.
Therefore, the pH of the buffer solution can be calculated as follows:
pH = -log[H3O+] = -log(1.0) = 0
So, the pH of the buffer solution containing 1.0 M ammonia (NH3) and 1.0 M ammonium chloride (NH4Cl) is 0.