Problem 38 - General Chemistry: Principles and Modern Applications

Question

Two solutions are mixed: \(100.0 \mathrm{mL}\) of \(\mathrm{HCl}(\mathrm{aq})\) with \(\mathrm{pH} 2.50\) and \(100.0 \mathrm{mL}\) of \(\mathrm{NaOH}(\text { aq) with } \mathrm{pH} 11.00\) What is the pH of the resulting solution?

Step-by-Step Solution

Answer

The pH of the resulting solution can be calculated by first determining the concentrations of the \(H^{+}\) ions and \(OH^{-}\) ions in the mixed solution, and then using this information to calculate the resulting pH. The specific values are subject to the calculated numerical values.

Step 1: Calculate the concentration of Hydronium ions

First, use the provided pH of 2.50 for Hydrochloric acid (HCl) to find the Hydronium ion concentration. This can be done using the formula \(H^{+} = 10^{-\text{pH}}\). Hence the \(H^{+}\) concentration will be \(10^{-2.5}\).

Step 2: Calculate the concentration of Hydroxide ions

Next, find the Hydroxide ion concentration using the pH of 11 for Sodium Hydroxide (NaOH). However firstly we need to convert this to pOH using formula \(\text{pOH} = 14 - \text{pH}\) which gives us the pOH as 3.00. Then, find the \(OH^{-}\) ion concentration, similar as before, with formula \(OH^{-} = 10^{-pOH}\), giving \(10^{-3}\).

Step 3: Find the concentrations after dilution

The solution has been diluted by mixing 100ml of HCl with 100ml of NaOH, to give a 200ml solution. The acid and base ion concentrations will thus be halved, resulting to \(H^{+} = 10^{-2.5}/2\) and \(OH^{-} = 10^{-3}/2\).

Step 4: Establish and solve the neutralization reaction

In solution, there will be a neutralization reaction, where \(H^{+}\) from HCl reacts with \(OH^{-}\) from NaOH to form water. As per the concentrations we have, it is evident that there is excess \(H^{+}\). Therefore, we have to compute the remaining \(H^{+}\) concentration after all the \(OH^{-}\) ions have reacted and formed water. This will be \((10^{-2.5}/2) - (10^{-3}/2)\).

Step 5: Calculate the pH of the resulting solution

The final task is finding the pH of the resulting solution, which can be achieved by using \(\text{pH} = -\log[\(H^{+}\)]\) on the remaining \(H^{+}\) concentration.

Key Concepts

Neutralization

When you mix an acid like hydrochloric acid (HCl) with a base such as sodium hydroxide (NaOH), a reaction called neutralization occurs. This involves the hydrogen ions ( H^{+} ) from the acid reacting with hydroxide ions ( OH^{-} ) from the base to form water ( H_2O ). This process effectively reduces the number of free H+ and OH- ions in the solution.
Neutralization reactions are significant in chemistry because they can lead to the formation of a neutral solution if the acid and base are mixed in stoichiometrically equivalent quantities.
In practical terms, these reactions are behind many everyday processes, like antacid tablets neutralizing stomach acid. When conducting a neutralization reaction, knowing the concentrations of the involved solutions is crucial to predict the reaction's outcome accurately.

pH Calculation

Calculating pH is fundamental in chemistry for understanding a solution's acidity or basicity. The pH scale typically ranges from 0 to 14: with values below 7 indicating acidity, 7 being neutral, and above 7 representing basicity.
The pH is calculated using the formula, ext{pH} = - ext{log}[H^{+}] , where [H^{+}] is the concentration of hydrogen ions in the solution.
In the exercise, we start by finding the H^{+} ion concentration from the pH. For hydrochloric acid with a pH of 2.50, the hydrogen ion concentration is found by H^{+} = 10^{-2.5} .
After mixing solutions with different pH levels, like in our exercise, the resulting pH is determined by whichever ion, H^{+} or OH^{-} , is in excess. Once you calculate the concentrate of the leftover ions, you can determine the final pH using the aforementioned formula.

Solution Concentration

Solution concentration is a crucial concept in understanding how mixing different volumes of solutions affects the outcomes of chemical reactions, such as neutralization. Concentration refers to the amount of solute (like H^{+} or OH^{-} ions) in a given volume of solution.
There's a direct relationship between concentration and the volume of liquid: when you dilute a solution by adding more solvent, the concentration of solutes decreases because the solute particles spread out over a larger volume.
In our exercise, when 100 mL of HCl is mixed with 100 mL of NaOH, each solution is effectively diluted because the total volume becomes 200 mL. As a result, the initial hydrogen ion and hydroxide ion concentrations halve, which directly influences the subsequent pH calculation.

Chemistry Education

Learning about acid-base reactions, such as neutralization, is a fundamental part of chemistry education. These reactions not only illustrate the balance and interconversion between acids and bases but also introduce significant concepts like pH and molarity.
Chemistry education here emphasizes understanding the underlying principles behind observable phenomena, like changes in pH when substances mix.
By mastering the steps in this exercise, involving solution dilution and pH calculations, students gain key skills applicable in real-world scenarios.

• Basis for understanding biological processes that involve acid-base balance.
• Relevance to industrial processes like waste treatment and product formulation.
• Applications in everyday life, like understanding how household cleaning products work.

A strong grasp of these concepts enriches students' critical thinking and problem-solving abilities, integral in advanced scientific studies and various professional fields.