Calculate the concentrations of NH4+ and NH3 and the pH in a solution prepared by mixing 20.0 g of NaOH and 0.500 L of 1.5 M NH4Cl. Assume that the volume remains constant.

Verified step by step guidance

1. Step 1: Calculate the moles of NaOH. Use the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). The molar mass of NaOH is approximately 40.00 g/mol.
2. Step 2: Calculate the moles of NH4Cl. Use the formula: \( \text{moles} = \text{concentration (M)} \times \text{volume (L)} \).
3. Step 3: Determine the reaction between NaOH and NH4Cl. NaOH will react with NH4Cl to form NH3 and water. The balanced chemical equation is: \( \text{NaOH} + \text{NH4Cl} \rightarrow \text{NH3} + \text{H2O} + \text{NaCl} \).
4. Step 4: Calculate the limiting reactant. Compare the moles of NaOH and NH4Cl to determine which one is the limiting reactant, as it will determine the amount of NH3 produced.
5. Step 5: Calculate the concentrations of NH4+ and NH3. Use the stoichiometry of the reaction to find the moles of NH3 formed and the remaining moles of NH4+. Then, divide by the total volume (0.500 L) to find their concentrations.

Key Concepts

Acid-Base Chemistry

Acid-base chemistry involves the study of proton donors (acids) and proton acceptors (bases). In this context, NH4Cl acts as a source of NH4+, a weak acid, while NaOH is a strong base. The interaction between these species will influence the pH of the solution and the concentrations of NH4+ and NH3, which are crucial for understanding buffer systems.

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. In this scenario, the mixture of NH4+ and NH3 creates a buffer system, where NH4+ can donate protons and NH3 can accept protons. The Henderson-Hasselbalch equation can be used to calculate the pH of this buffer solution, which is essential for determining the concentrations of the species involved.

Stoichiometry and Concentration Calculations

Stoichiometry involves the calculation of reactants and products in chemical reactions. To find the concentrations of NH4+ and NH3, one must first determine the moles of each component based on the given mass of NaOH and the volume and molarity of NH4Cl. This requires converting grams to moles and using the final volume of the solution to calculate the concentrations, which is fundamental for solving the problem.