A Buffer Solution and Its pH Calculation

Determine the pH for the original buffer solution

A buffer solution is prepared by combining 100 mL of concentrated ammonia (14.5 M) and 100 g of NH₄NO₃ with water to produce a total volume of 800 mL. Kb for ammonia is 1.8 x 10⁻⁵.

Final Answer:

The pH of the original buffer solution is approximately 9.64. This was calculated using the Henderson-Hasselbalch equation with the pKa of ammonia (NH₃) and the initial concentrations of NH₃ and NH₄⁺. The ammonia is a weak base, leading to a slightly basic pH.

Explanation:

To determine the pH of the buffer solution, we'll use the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

In this equation:

- pKa is the negative logarithm (base 10) of the dissociation constant (Kb) for ammonia, which is given as 1.8 x 10⁻⁵. So, pKa = -log(1.8 x 10⁻⁵) ≈ 4.74.

- [A-] is the concentration of the base (NH₃) in the buffer, which is initially 14.5 M * 0.1 L = 1.45 moles.

- [HA] is the concentration of the ammonium ion (NH₄⁺) in the buffer, which is initially 0.1 kg / 64.04274 g/mol = 1.56 moles.

Now, let's calculate the pH:

pH = 4.74 + log(1.45/1.56) ≈ 9.64

So, the pH of the original buffer solution is approximately 9.64.

Note: The mass of NH₄NO₃ was converted to moles by dividing by its molar mass (64.04274 g/mol), and the volume of concentrated ammonia was converted to moles by multiplying by its concentration (14.5 M). The Henderson-Hasselbalch equation is used to calculate the pH of a buffer solution.