Problem 256 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the \(\mathrm{pH}\) of a mixture obtained by mixing \(75 \mathrm{ml}\) \(\mathrm{M} / 5 \mathrm{HCl}\) and \(25 \mathrm{ml} \mathrm{M} / 5 \mathrm{NaOH}\) aqueous solution?

Step-by-Step Solution

Answer

The pH of the mixture is 1.

Step 1: Calculate Moles of HCl

First, find the number of moles of hydrochloric acid (HCl). The concentration of HCl is given as \( \frac{1}{5} \text{ M} \), and the volume is \( 75 \text{ mL} \) or \( 0.075 \text{ L} \). Use the formula \( \, \text{moles} = Molarity \times Volume \, \): \[ \text{Moles of HCl} = \frac{1}{5} \times 0.075 = 0.015 \text{ moles} \].

Step 2: Calculate Moles of NaOH

Next, calculate the number of moles of sodium hydroxide (NaOH). The concentration of NaOH is also \( \frac{1}{5} \text{ M} \), and the volume is \( 25 \text{ mL} \) or \( 0.025 \text{ L} \). Use the formula as in the previous step: \[ \text{Moles of NaOH} = \frac{1}{5} \times 0.025 = 0.005 \text{ moles} \].

Step 3: Determine Net Moles of HCl

Since HCl and NaOH react in a 1:1 ratio, subtract the moles of NaOH from the moles of HCl to find the excess HCl: \[ \text{Net Moles of HCl} = 0.015 - 0.005 = 0.010 \text{ moles} \].

Step 4: Calculate Total Volume of Mixture

Add the volumes of the two solutions to find the total volume of the mixture: \[ \text{Total Volume} = 75 \text{ mL} + 25 \text{ mL} = 100 \text{ mL} = 0.100 \text{ L} \].

Step 5: Calculate Concentration of HCl in Mixture

Find the concentration of the remaining HCl in the total mixture. Use the formula \( \, \text{Molarity} = \frac{\text{Moles}}{\text{Volume}} \, \):\[ \text{Molarity of HCl} = \frac{0.010}{0.100} = 0.1 \text{ M} \].

Step 6: Calculate pH

Since HCl is a strong acid, it fully dissociates, making the concentration of H\(^+\) ions the same as the concentration of HCl. Calculate the \( \text{pH} \) using the formula \( \, \text{pH} = -\log[H^+] \, \):\[ \text{pH} = -\log(0.1) = 1 \].

Key Concepts

Acid-Base Reaction

An acid-base reaction involves the transfer of a proton ( ⁺ ) from an acid to a base. These reactions are fundamental in chemistry and occur frequently. In this type of reaction, initially, an acid releases hydrogen ions ( ⁺ ), which are then captured by a base.
A classic example of an acid-base reaction is the mixing of hydrochloric acid ( HCl ) with sodium hydroxide ( NaOH ). In this case, HCl acts as the acid and NaOH as the base.

• **HCl**: Strong acid, donates ⁺ ions.
• **NaOH**: Strong base, accepts ⁺ ions.

The result is the formation of water and salt, making these reactions essential for many chemical processes. The neutrality achieved when equal amounts of acid and base react is a key feature of acid-base reactions.

Molarity

Molarity is a measure of the concentration of a solute in a solution. It is defined as the number of moles of a substance (solute) present in one liter of solution.
The formula to calculate molarity (M) is:
\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]
In the exercise at hand, both HCl and NaOH have a molarity of \frac{1}{5} . Knowing the molarity helps determine how these substances interact in a reaction. By multiplying molarity with volume in liters, you can understand the total moles involved.

• It allows for accurate measurements in chemistry experiments.
• Essential for balancing chemical reactions and calculating pH.

Molarity plays a crucial role in determining how much acid or base is required for a particular reaction.

Strong Acids

Strong acids completely dissociate into their ions in water, meaning they release all their available hydrogen ions into a solution.
Hydrochloric acid (HCl) is a strong acid and is known for its complete dissociation:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
With strong acids like HCl, the concentration of hydrogen ions (⁺) will equal the concentration of the acid. Understanding strong acids is vital because:

• They have significant effects on pH levels.
• Their full dissociation simplifies calculations of ⁺ concentration.

Knowing a substance is a strong acid influences how we approach pH calculations and manage chemical safety and handling.

Neutralization

Neutralization is a chemical reaction in which an acid and a base combine to form a salt and water. It often results in a solution with a pH closer to 7, indicating a neutral solution.

• In our exercise, HCl and NaOH undergo neutralization.
• They react in a one-to-one molar ratio, making calculations straightforward.

The process can be represented as:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H2O} \]
One of the key takeaways from neutralization is that the pH of the resulting solution depends on the quantities of the acid and base mixed. After the reaction, any excess HCl in the problem dictates the pH. Understanding neutralization helps predict not just pH but also the composition of final solutions after mixing.