What mass of NH4Cl must be added to 0.750 L of a 0.1M solution of NH3, to give a buffer solution with a pH of 9.26? (Hint: Assume a negligible change in volume as the solid is added.) Kb of NH3 = 1.8 x10-5 %3D Kw= 1 x 10-14
Kb for NH3 = 1.8E-5 from the problem. You need Ka. You know KaKb = Kw; therefore, Ka = Kw/Kb = 1E-14/1.8E-5 = 5.55E-10 and pKa = 9.26 . Now use the Henderson-Hasselbalch equation which is pH = pKa + log [(base)/(acid)].
9.26 = 9.26 + log B/A where B is base and A is acid.
0 = log (0.1/A)
1 = (0.1/A) or A = 0.1 M
So (NH4Cl) = 0.1 M
mols NH4Cl = M x L = 0.1 x 0.750 L = 0.075
Then grams NH4Cl = mols x molar mass = ?
What mass of NH4Cl must be added to 0.750 L of a 0.1M solution of NH3, to give a buffer solution with a pH of 9.26? (Hint: Assume a negligible change in volume as the solid is added.) Kb of NH3 = 1.8 x10-5 %3D Kw= 1 x 10-14
To calculate the mass of NH4Cl required, we need to use the Henderson-Hasselbalch equation for buffer solutions:
pH = pKa + log ([A-]/[HA])
In this case, NH3 acts as the weak base (A-) and NH4Cl acts as the weak acid (HA).
To find pKa, we can use the relationship: pKa + pKb = 14.
Given that Kb of NH3 is 1.8 x 10^(-5), we have:
pKa = 14 - pKb
pKa = 14 - (-log(Kb))
pKa = 14 - (-log(1.8 x 10^(-5)))
pKa = 14 - (-(-4.74))
pKa = 14 + 4.74
pKa = 18.74
Now, let's substitute the values into the Henderson-Hasselbalch equation:
9.26 = 18.74 + log ([A-]/[HA])
To simplify, let's assume that the concentration of NH3 and NH4Cl is x mol/L after the addition of NH4Cl. This will allow us to assume negligible volume changes.
9.26 = 18.74 + log (x/x)
0.26 = log(1)
Since log(1) = 0, we have:
0.26 = 18.74
This is not possible. Therefore, no NH4Cl should be added to the NH3 solution to achieve the desired pH of 9.26.
To solve this problem, we need to consider the principles of buffer solutions and the properties of weak bases.
Step 1: Determine the concentration of NH3 in the given solution.
We are given that the initial solution is 0.1M NH3. Since NH3 is a weak base, we can assume that it is partially ionized in water. The Kb value provided allows us to calculate the concentration of OH- ions that have been produced by NH3's reaction with water.
First, let's calculate the concentration of OH- ions using the Kb value:
Kb = [NH4+][OH-] / [NH3]
We are given the value of Kb as 1.8 x 10^-5, and the concentration of NH3 is 0.1M. Since we assume a negligible change in volume, the concentration of NH4+ and NH3 will be the same.
Let x represent the concentration of OH- ions.
Kb = x^2 / (0.1 - x)
Solving the above equation will give us the concentration of OH- ions.
Step 2: Calculate the concentration of H+ ions.
Since we are given the pH of the buffer solution as 9.26, we can calculate the concentration of H+ ions using the following equation:
pOH = -log[OH-]
pH + pOH = 14
Substituting the given pH and calculated pOH values into the equation will give us the concentration of H+ ions.
Step 3: Apply the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentrations of the weak acid and its conjugate base. In this case, NH3 acts as the weak base, and NH4+ acts as the conjugate acid.
pH = pKa + log([NH4+]/[NH3])
We know the pH of the buffer solution and can assume that the pKa value for NH4+ is 9.26 since NH4+ is a weak acid.
By rearranging the Henderson-Hasselbalch equation, we can calculate the ratio of [NH4+] to [NH3].
Step 4: Calculate the required mass of NH4Cl.
Adding NH4Cl to the solution will increase the concentration of NH4+ ions. Since the initial concentration of NH4+ and NH3 in the solution is the same, we can calculate the mass of NH4Cl needed to achieve the desired ratio after substituting the known values into the equation.
NH4Cl (s) → NH4+ (aq) + Cl- (aq)
Finally, calculate the molar mass of NH4Cl and convert it to grams to determine the mass required.
Remember to double-check your calculations and apply significant figures as needed.