Final answer:
To obtain a buffer solution with a pH of 9.60, you would need to add approximately 638.88 g of ammonium chloride (NH₄Cl) to a 2.60 L solution of 0.160 M NH₃. The calculation involves using the Henderson-Hasselbalch equation and the formula M1V1 = M2V2.
Step-by-step explanation:
To calculate the mass of ammonium chloride (NH₄Cl) needed to make a buffer solution, we need to use the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch 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.
In this case, the weak acid is NH₄Cl, and the conjugate base is NH₃. The pKa of NH₄Cl is the negative logarithm of its acid dissociation constant (Ka). The Ka of NH₄Cl is the concentration of [NH₃]/[NH₄+].
We can rearrange the Henderson-Hasselbalch equation to solve for [A-]: [A-] = 10^(pH - pKa).
Given that the pH of the buffer solution is 9.60, the pKa of NH₄Cl is the negative logarithm of 10^(-9.60), which is 9.60. We can substitute this value into the equation and solve for [A-]: [A-] = 10^(9.60 - 9.60) = 1.
Therefore, the concentration of [A-] should be 1 M. Since the volume of the solution is 2.60 L and the concentration is 0.160 M, we can use the formula M1V1 = M2V2 to find the mass of NH₄Cl needed:
M1V1 = M2V2, (0.160 M)(2.60 L) = (1 M)(V2).
Solving for V2, we get V2 = (0.160 M)(2.60 L)/(1 M) = 0.416 L.
Finally, to find the mass of NH₄Cl, we use the formula mass = density × volume, where density is the density of NH₄Cl. The density of NH₄Cl is approximately 1.53 g/cm³. Converting the volume to cm³, we get 0.416 L × 1000 cm³/L = 416 cm³.
Therefore, the mass of NH₄Cl needed is (1.53 g/cm³)(416 cm³) = 638.88 g.