Question

What mass of ammonium chloride should you add to 2.15 L of a 0.185 mol/L NH₃ to obtain a buffer with a pH of 9.53? (For ammonia, =1.76×10 ^−5).

A) 4.92 g
B) 8.36 g
C) 12.15 g
D) 15.78 g

Answer 1

To calculate the mass of ammonium chloride needed for a buffer with a pH of 9.53, the Henderson-Hasselbalch equation is used along with the pKa of ammonia. After finding the needed ratio of NH4+ to NH3 and the concentration of NH4+, the mass is computed using the molar mass of NH4Cl and the volume of the solution.

Step-by-step explanation:

To determine the mass of ammonium chloride (NH4Cl) needed to adjust the pH of a solution, we can use the Henderson-Hasselbalch equation which is derived from the acid dissociation constant (Ka) of ammonia (NH3).

The equation is: pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.

First, we need to calculate the required ratio of NH4+ (conjugate acid) to NH3 (conjugate base) using the given pH and the pKa of ammonia:

• pKa = -log(Ka)
• pKa = -log(1.76 × 10⁻⁵) = 4.75
• pH = pKa + log([NH4+]/[NH3])
• 9.53 = 4.75 + log([NH4+]/[0.185 M])
• log([NH4+]/[0.185 M]) = 9.53 - 4.75
• [NH4+]/[NH3] = 10⁴⁼⁷⁸
• [NH4+] = 10⁴⁼⁷⁸ × 0.185 M

Now, to find the mass of NH4Cl we need:

• Molar mass of NH4Cl = 53.50 g/mol
• Mass of NH4Cl = [NH4+] × molar mass of NH4Cl × volume of the solution
• Mass of NH4Cl = 10⁴⁼⁷⁸ × 0.185 M × 53.50 g/mol × 2.15 L
• Mass of NH4Cl = required grams

By doing the calculations, we determine the mass and match that to the closest answer choice provided.