Question

What is the \(\mathrm{pH}\) of the solution that results from adding \(25.0 \mathrm{mL}\) of \(0.12 \mathrm{M}\) HCl to \(25.0 \mathrm{mL}\) of \(0.43 \mathrm{M} \mathrm{NH}_{3} ?\)

Short answer

The resulting pH of the solution is approximately 4.34.

Step-by-step solution

Determine Moles of HCl and NH3

First, calculate the number of moles of hydrochloric acid (HCl) and ammonia (NH3) using the formula: \( ext{moles} = ext{concentration} imes ext{volume(L)} \). For HCl: \( 0.12 ext{ M} \times 0.025 ext{ L} = 0.003 ext{ moles} \). For NH3: \( 0.43 ext{ M} \times 0.025 ext{ L} = 0.01075 ext{ moles} \).

Determine Reaction and Limiting Reactant

Write the reaction equation: \( ext{HCl} + ext{NH}_3 ightarrow ext{NH}_4^+ + ext{Cl}^- \). Since the reaction ratio is 1:1, the limiting reactant is HCl because it has fewer moles (0.003 moles) compared to NH3 (0.01075 moles). Thus, all 0.003 moles of HCl will react with 0.003 moles of NH3.

Calculate Remaining Moles of NH3

Since all of the HCl reacts, you are left with \( 0.01075 - 0.003 = 0.00775 \) moles of NH3 unreacted. No HCl remains since it is the limiting reactant, and you have 0.003 moles of NH4+ produced.

Calculate Total Volume of Solution

The total volume of the solution after mixing is the sum of the volumes: \( 25.0 ext{ mL} + 25.0 ext{ mL} = 50.0 ext{ mL} = 0.050 ext{ L} \).

Determine New Concentrations

The concentration of remaining NH3 is \( \frac{0.00775 ext{ moles of NH}_3}{0.050 ext{ L}} = 0.155 ext{ M} \). The concentration of NH4+ is \( \frac{0.003 ext{ moles of NH}_4^+}{0.050 ext{ L}} = 0.060 ext{ M} \).

Use Henderson-Hasselbalch Equation

Determine the pH using the Henderson–Hasselbalch equation for a buffer solution: \( \text{pH} = \text{p}K_b + \log{\left( \frac{[ ext{NH}_4^+]}{[ ext{NH}_3]} \right)} \). The \( \text{p}K_b \) of NH3 is approximately 4.75. Substitute the values: \( \text{pH} = 4.75 + \log{\left(\frac{0.060}{0.155}\right)} \approx 4.75 - 0.415 = 4.34 \).

Key concepts

pH calculation

Calculating the \(\text{pH}\) of a solution can sometimes seem tricky, but understanding the basics can clarify the process. \(\text{pH}\) stands for 'power of hydrogen.' It measures how acidic or basic a solution is on a scale of 0 to 14. To find the \(\text{pH}\) of a solution, particularly when dealing with acids and bases, it's essential first to determine the concentrations of the reacting substances after any reaction has occurred.
In the case of mixing hydrochloric acid (HCl) with ammonia (NH3), a chemical reaction takes place. The acknowledgment of a neutralization process where acids and bases combine makes all the difference. After the reaction, you'll typically deal with leftover reactants or newly formed products in the solution, each contributing to the \(\text{pH}\).
Once you have the concentrations of these components, these values directly contribute to evaluating the \(\text{pH}\) using specific equations, ensuring precise and accurate results.

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a vital tool when dealing with buffer solutions, which are slightly acidic or basic solutions capable of resisting drastic changes in \(\text{pH}\). It simplifies the process of \(\text{pH}\) calculation when you have a mixture of a weak acid or base and its conjugate partner.
This equation is written as:
\( \text{pH} = \text{p}K_b + \log \left( \frac{\text{[Base]}}{\text{[Acid]}} \right) \)
For our solution, ammonia (NH3) is the base, and ammonium ion \(\text{NH}_4^+\) is the conjugate acid. This relationship allows consideration of small changes in concentrations of components when substances are added or removed, providing a steady \(\text{pH}\) amidst reactions.

• Identify the weak base (ammonia, NH3) and its conjugate acid (ammonium ion, NH4+).
• Know the \(\text{p}K_b\) value of NH3, usually around 4.75.
• Plug these values into the Henderson-Hasselbalch equation to find the result.

Understanding this equation aids in preparing solutions with desired \(\text{pH}\), crucial in laboratory and industrial settings.

limiting reactant

In chemical reactions, the limiting reactant is fundamental in determining how far the reaction will go and thus influences the product quantities. It is the substance that is entirely consumed during the reaction, limiting the amount of product formed.
To find the limiting reactant, compare the mole ratio from the balanced equation to the moles available from the reactants.
Here's a quick guide:

• Look at the initial moles of each reactant using their given concentrations and volumes.
• Refer to the balanced chemical equation to understand the stoichiometric relationships (e.g., HCl + NH3).
• The reactant that produces the lesser amount of product is your limiting reactant; it determines the maximum product formation—as seen with HCl in our problem.

Remaining reactants like NH3 after HCl is used up, can continue affecting the \(\text{pH}\), highlighting the importance of knowing the limiting reactant for any \(\text{pH}\) calculation in buffer solutions.