Calculate the pH of 100.0 mL of 0.30 M NH3 before and after the addition of 4.0 g of NH4NO3, and account for the change. Assume that the volume remains constant.

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Identify the initial concentration of NH3, which is 0.30 M, and recognize that NH3 is a weak base.

Use the Kb expression for NH3 to calculate the initial pH. The Kb for NH3 is typically around 1.8 \(\times\) 10^{-5}. Set up the equation: Kb = \(\frac{[OH^-][NH4^+]}{[NH3]}\) and solve for [OH^-].

Convert [OH^-] to pOH using the formula pOH = -\(\log\)[OH^-], and then find the initial pH using pH = 14 - pOH.

Calculate the moles of NH4NO3 added: 4.0 g / (molar mass of NH4NO3). NH4NO3 dissociates completely in water to give NH4^+ and NO3^-.

Use the Henderson-Hasselbalch equation to find the new pH after adding NH4NO3: pH = pKa + \(\log\[\left\)(\(\frac{[base]}{[acid]}\]\right\)), where [base] is the concentration of NH3 and [acid] is the concentration of NH4^+.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pH and pOH

pH is a measure of the hydrogen ion concentration in a solution, indicating its acidity or basicity. It is calculated using the formula pH = -log[H+]. The pOH, which measures hydroxide ion concentration, is related to pH by the equation pH + pOH = 14. Understanding these concepts is essential for calculating the pH of solutions, especially when dealing with weak bases like NH3.

Weak Base and Conjugate Acid

Ammonia (NH3) is a weak base that partially ionizes in water to form ammonium ions (NH4+) and hydroxide ions (OH-). The addition of NH4NO3 introduces NH4+, the conjugate acid of NH3, which affects the equilibrium of the ammonia solution. This relationship is crucial for understanding how the pH changes upon the addition of NH4NO3.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acid and base components. For a weak base and its conjugate acid, the equation is pH = pKa + log([base]/[acid]). This equation is particularly useful in calculating the pH after the addition of NH4NO3, as it allows for the quantification of the ratio of NH3 to NH4+ in the solution.

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