Problem 105 - Chemistry and Chemical Reactivity

Question

A solution of hydrochloric acid has a volume of \(250 .\) mL and a pH of \(1.92 .\) Exactly \(250 .\) mL of \(0.0105 \mathrm{M} \mathrm{NaOH}\) is added. What is the pH of the resulting solution?

Step-by-Step Solution

Answer

The pH of the resulting solution is approximately 3.12.

Step 1: Calculate Initial Moles of HCl

First, find the concentration of HCl using the pH value. Since \( \text{pH} = -\log[\text{H}^+] \), we have \( [\text{H}^+] = 10^{-1.92} \approx 0.012 \text{ M} \). Then, calculate the moles of HCl:\[ \text{Moles of HCl} = [\text{H}^+] \times \text{Volume (L)} = 0.012 \times 0.250 = 0.003 \text{ moles} \]

Step 2: Calculate Moles of NaOH Added

Next, compute the moles of NaOH in the solution. With \( 0.0105 \text{ M} \) NaOH and a volume of \( 250 \text{ mL} \) (or \( 0.250 \text{ L} \)), the moles of NaOH are:\[ \text{Moles of NaOH} = 0.0105 \times 0.250 = 0.002625 \text{ moles} \]

Step 3: Determine Excess HCl or NaOH

Subtract the moles of NaOH from the moles of HCl to find the excess moles:\[ \text{Excess moles of HCl} = 0.003 - 0.002625 = 0.000375 \text{ moles} \]

Step 4: Calculate Concentration of Excess HCl

The resulting solution volume is \( 250 \text{ mL} + 250 \text{ mL} = 500 \text{ mL} = 0.500 \text{ L} \). The concentration of excess HCl is:\[ \text{Concentration of HCl} = \frac{0.000375}{0.500} = 0.00075 \text{ M} \]

Step 5: Determine New pH

Use the concentration from Step 4 to find the pH:\[ \text{pH} = -\log[0.00075] \approx 3.12 \]

Key Concepts

Hydrochloric Acid

Hydrochloric acid, often abbreviated as HCl, is a strong acid commonly used in various laboratory and industrial processes. It dissociates completely in water to produce hydrogen ions (H⁺) and chloride ions (Cl⁻). This complete dissociation is what classifies it as a strong acid, as opposed to a weak acid that does not fully dissociate in solution.
Understanding the properties of hydrochloric acid is crucial, especially when dealing with pH calculations. The pH value is a measure of how acidic or basic a solution is, where a lower pH indicates a more acidic solution. For HCl, calculating the pH is straightforward based on its concentration since it is a strong acid.
It is worth noting that when you know the pH of a solution like HCl, you can determine the concentration of \([ ext{H}^+]\) ions in the solution by using the formula \( ext{pH} = -\log[ ext{H}^+]\). This allows us to calculate how many moles of HCl are present if the volume of the solution is known.

Acid-Base Titration

Acid-base titration is a technique used to determine the concentration of an acid or a base in a solution. During a titration, an acid is gradually added to a base, or vice versa, until the reaction reaches its endpoint. The point at which the amount of acid is equal to the amount of base is known as the equivalence point.
In our exercise, hydrochloric acid (HCl) is neutralized by sodium hydroxide (NaOH). An acid-base titration provides the necessary data to calculate the pH of mixtures because each step in the addition of a base to an acid helps us understand the extent of the neutralization reaction.
This technique is fundamental in chemistry labs because it offers a visual and precise way to calculate unknown concentrations. By carefully measuring the volume of titrant used, we can use mole calculations to determine changes in concentrations and, ultimately, changes in pH during the experiment.

Mole Calculation

Mole calculation is a central concept in chemistry, essential for understanding chemical reactions, such as acid-base neutralizations. The mole is a unit that measures the amount of substance; it represents a fixed number of particles, usually atoms or molecules.
In titrations like the one described in the exercise, mole calculations allow you to determine how much reactant is needed to neutralize another reactant. This involves multiplying the concentration of the solution by its volume to get the number of moles.
For example, the number of moles of HCl in our solution was calculated by multiplying the initial concentration derived from the pH and the solution's volume. Similarly, the moles of NaOH are found using its concentration and volume. These calculations ensure that we know exactly how much of each substance is present, which is crucial for determining any excess reactants and calculating the resulting pH.

Neutralization Reaction

A neutralization reaction occurs when an acid and a base react to form water and a salt. In the context of our exercise, hydrochloric acid reacts with sodium hydroxide. The equation for this reaction is:
\[ ext{HCl} + ext{NaOH} ightarrow ext{NaCl} + ext{H}_2 ext{O} \]
This type of reaction is exothermic, meaning it releases energy, usually in the form of heat. The reaction proceeds until one of the reactants is completely consumed. In the example problem, there was an excess of HCl after reacting with the NaOH, allowing us to determine the new pH of the solution.
Understanding neutralization is key not just because it helps calculate pH, but also because it forms the basis for many industrial processes and laboratory techniques. By knowing how much of each reactant is present, chemists can ensure complete neutralization or control how much product (water and salt) is formed in different chemical applications.