a solution is prepared by adding 5g of ammonia,Nh3, and 20g of ammonium chloride, NH4Cl , to enough water to form 2.5 L of solution. What is the ph of the buffer? Kb= 1.8*10^-5
Use the Henderson-Hasselbalch equation.
Post your work if you run into trouble.
To find the pH of the buffer solution, we need to determine the concentration of NH3 and NH4Cl in the solution. Since both compounds dissociate into their respective ions, we can use the total mass of each compound to find their individual concentrations.
1. Calculate the moles of NH3 (ammonia):
Moles of NH3 = mass / molar mass = 5g / 17.03 g/mol = 0.293 mol
2. Calculate the moles of NH4Cl (ammonium chloride):
Moles of NH4Cl = mass / molar mass = 20g / 53.49 g/mol = 0.374 mol
3. Calculate the concentration of NH3 (ammonia):
Concentration of NH3 = moles / volume = 0.293 mol / 2.5 L = 0.117 M
4. Calculate the concentration of NH4Cl (ammonium chloride):
Concentration of NH4Cl = moles / volume = 0.374 mol / 2.5 L = 0.150 M
Now, we can use the relationship between the concentrations of NH3 and NH4Cl and the Kb value to find the pOH of the solution and convert it to pH.
5. Calculate the pOH of the solution:
pOH = -log10(Kb) = -log10(1.8 * 10^-5) ≈ 4.744
6. Calculate the concentration of OH- ions:
[OH-] = √(Kw / Kb) = √(1.0 * 10^-14 / 1.8 * 10^-5) ≈ 0.00185 M
7. Calculate the concentration of H+ ions:
[H+] = Kw / [OH-] = (1.0 * 10^-14) / (0.00185) ≈ 5.405 * 10^-12 M
8. Calculate the pH:
pH = -log10([H+]) = -log10(5.405 * 10^-12) ≈ 11.267
So, the pH of the buffer solution is approximately 11.267.
To find the pH of the buffer solution, we'll need to determine the concentrations of the conjugate acid (NH4+) and the conjugate base (NH3) in the solution. The equation for the reaction between ammonia (NH3) and ammonium chloride (NH4Cl) in water is as follows:
NH3 + NH4Cl ⇌ NH4+ + Cl-
First, let's calculate the number of moles of ammonia (NH3) and ammonium chloride (NH4Cl) in the solution:
Moles of NH3 = mass / molar mass
= 5 g / 17 g/mol (molar mass of NH3)
= 0.294 moles
Moles of NH4Cl = mass / molar mass
= 20 g / (14 + 1 + 35.5) g/mol (molar mass of NH4Cl)
= 0.513 moles
Next, let's determine the volume of the solution in liters:
Volume of solution = 2.5 L
Now, we can calculate the concentrations of NH3 and NH4+ in the solution:
Concentration of NH3 = moles of NH3 / volume of solution
= 0.294 moles / 2.5 L
= 0.118 M
Concentration of NH4+ = moles of NH4Cl / volume of solution
= 0.513 moles / 2.5 L
= 0.205 M
Since we have the value of Kb (1.8 * 10^-5), we can use the Henderson-Hasselbalch equation to find the pH of the buffer:
pH = pKa + log([concentration of conjugate base] / [concentration of conjugate acid])
First, let's find pKa, which is the negative logarithm of the Kb value:
pKa = -log(Kb)
= -log(1.8 * 10^-5)
≈ 4.74
Now, we can substitute the given values into the Henderson-Hasselbalch equation:
pH = 4.74 + log(0.205 / 0.118)
After evaluating the logarithm and performing the addition:
pH ≈ 4.74 + log(1.74)
pH ≈ 4.74 + 0.24
pH ≈ 4.98
Therefore, the pH of the buffer solution is approximately 4.98.