What is the pH of a buffer system prepared by dissolving 10.70 grams of NH4Cl and 25.00 mL of 12 M NH3 in enough water to make 1.000 L of solution? Kb = 1.80 x 10-5 for NH3.
Use the Henderson-Hasselbalch equation.
pH = pKa + log[(base)/(acid)]
To determine the pH of the buffer system, we need to consider the reaction between NH4Cl (ammonium chloride) and NH3 (ammonia). The NH4Cl will dissociate into NH4+ and Cl- ions, while NH3 will act as a base and accept a proton (H+) to form NH4+.
Here's the step-by-step process to determine the pH of the buffer system:
Step 1: Calculate the concentration of NH4Cl:
- Convert the given mass of NH4Cl (10.70 grams) to moles by dividing it by the molar mass of NH4Cl.
- Molar mass of NH4Cl = 14.01 g/mol (N) + 1.01 g/mol (H) * 4 + 35.45 g/mol (Cl)
- Calculate moles = mass / molar mass
Step 2: Calculate the concentration of NH4+:
- Since NH4Cl dissociates into one NH4+ ion, the moles of NH4+ will be equal to the moles of NH4Cl.
- Convert the volume of the solution (1.000 L) into liters.
Step 3: Calculate the concentration of NH3:
- Convert the volume of NH3 (25.00 mL) to liters.
- Calculate moles of NH3 by multiplying the molarity (12 M) by the volume (in liters).
Step 4: Calculate the concentration of NH3 after its reaction with H+:
- Since NH3 accepts a proton (H+) to form NH4+, the moles of NH3 will decrease by the moles of NH4+ formed in the reaction.
Step 5: Calculate the pOH:
- Use the concentration of NH3 after reaction to determine the pOH using the Kb value (1.80 x 10^-5) for NH3.
- pOH = -log10([NH3 after reaction])
Step 6: Calculate the pH:
- Use the pOH value to determine the pH.
- pH = 14 - pOH
By following these steps and performing the necessary calculations, you will determine the pH of the buffer system prepared using NH4Cl and NH3.
To calculate the pH of a buffer solution, we need to consider the equilibrium reaction between the weak acid (NH4+) and its conjugate base (NH3):
NH4+ + H2O ⇌ NH3 + H3O+
First, let's determine the concentration of NH4+ and NH3 in the solution.
1. Calculate the number of moles of NH4Cl:
Molar mass of NH4Cl = 14.01 + 1.008 × 4 + 35.45 = 53.49 g/mol
Number of moles of NH4Cl = mass / molar mass = 10.70 g / 53.49 g/mol = 0.20 mol
2. Calculate the concentration of NH4+ in the solution:
Concentration of NH4+ = moles / volume = 0.20 mol / 1.000 L = 0.20 M
3. Calculate the number of moles of NH3:
Molarity of 12 M NH3 = 12 mol/L
Number of moles of NH3 = molarity × volume = 12 mol/L × 0.025 L = 0.30 mol
4. Calculate the concentration of NH3 in the solution:
Concentration of NH3 = moles / volume = 0.30 mol / 1.000 L = 0.30 M
Next, we'll use the equation for the dissociation of NH4+ to find the concentration of H3O+:
Kb = [NH3][H3O+] / [NH4+]
1.80 × 10^(-5) = (0.30 M)([H3O+]) / (0.20 M)
Solving for [H3O+]:
[H3O+] = (1.80 × 10^(-5))(0.20 M) / (0.30 M) = 1.20 × 10^(-5) M
Finally, we can calculate the pH using the equation:
pH = -log[H3O+]
pH = -log(1.20 × 10^(-5))
pH ≈ 4.92
Therefore, the pH of the buffer solution prepared from 10.70 grams of NH4Cl and 25.00 mL of 12 M NH3 is approximately 4.92.