Problem 95 - A Complete Resource Book in Chemistry for JEE Main

Question

\(75 \mathrm{ml}\) of \(0.2 \mathrm{M} \mathrm{HCl}\) is mixed with \(25 \mathrm{ml}\) of \(\mathrm{M} \mathrm{HCl}\). To this solution, \(300 \mathrm{ml}\) of distilled water is added. What is the \(\mathrm{pH}\) of the resultant solution? (a) 1 (b) 2 (c) 4 (d) \(0.2\)

Step-by-Step Solution

Answer

The pH of the resultant solution is 1.

Step 1: Find Moles of HCl in 75 ml of 0.2 M Solution

First, calculate the moles of HCl in the initial 75 ml of 0.2 M solution using the formula: \( ext{moles} = ext{volume (L)} \times ext{molarity} \). Convert 75 ml to liters (0.075 L) and multiply by 0.2 M: \[ ext{moles} = 0.075 \times 0.2 = 0.015 \text{ moles} \].

Step 2: Find Moles of HCl in 25 ml of 1 M Solution

Calculate the moles of HCl in the 25 ml (0.025 L) of 1 M solution using the formula: \( ext{moles} = ext{volume (L)} \times ext{molarity} \): \[ ext{moles} = 0.025 \times 1 = 0.025 \text{ moles} \].

Step 3: Find Total Moles of HCl in Mixed Solution

Add the moles from Step 1 and Step 2 to find the total moles of HCl: \[ ext{total moles} = 0.015 + 0.025 = 0.04 \text{ moles} \].

Step 4: Calculate the Total Volume of the Final Solution

Calculate the total volume of the solution after adding all components: initial 100 ml (75 ml + 25 ml) plus 300 ml of water, totaling 400 ml or 0.4 L.

Step 5: Find the Molarity of HCl in the Final Solution

The molarity of the resultant solution is calculated as \( ext{molarity} = \frac{ ext{total moles}}{ ext{total volume}} \). Plug in the values: \[ ext{molarity} = \frac{0.04}{0.4} = 0.1 \text{ M} \].

Step 6: Calculate the pH of the Final Solution

Since HCl is a strong acid and fully dissociates, its pH is determined from its molarity. The pH is the negative logarithm of the hydrogen ion concentration: \( ext{pH} = - ext{log}_{10}(0.1) = 1 \).

Key Concepts

strong acids

When dealing with pH calculations of acidic solutions, it is important to understand the nature of strong acids like Hydrochloric Acid (HCl). Strong acids are characterized by their complete dissociation in water. This means that, when dissolved, they release all their hydrogen ions into the solution.
In practice:

• Strong acids have very low pH values, making them very acidic.
• They dissociate completely, contributing directly to the hydrogen ion concentration in the solution.

The complete dissociation makes the calculation of pH straightforward, since the concentration of the strong acid is effectively equal to the concentration of hydrogen ions in solution. So, when you mix HCl with water, you can directly use its molarity to calculate pH, simplifying the computation.

molarity

Molarity is a measure of the concentration of a solute in a solution. Specifically, it is the number of moles of solute per liter of solution.
This is important for calculating pH because:

• The pH of a solution directly depends on the concentration of hydrogen ions present.
• In the case of strong acids like HCl, molarity equals the concentration of hydrogen ions due to complete dissociation.

When calculating molarity, remember to:

• Convert volumes to liters as the base unit.
• Multiply the volume by the molarity to find the total moles of solute.
• A higher molarity indicates a more concentrated solution, leading to a lower pH.

Understanding molarity helps you determine how much of the hydrogen ions are present and thus calculate the correct pH.

solution mixing

Mixing solutions involves combining different volumes and concentrations to form a final mixture. The challenge is to understand how these combine to influence the final concentration and ultimately the pH.

• Start by calculating the moles of solute in each solution using their respective volumes and molarities.
• Next, sum the moles to find the total amount of solute in the mixed solution.
• Calculate the total volume after mixing all liquids, including any additional water added.
• Finally, use the total moles and total volume to determine the molarity of the final solution.

This process is crucial for accurate pH calculations as combining different strengths and volumes of solutions can alter the overall acidity or basicity.

acid dissociation

Acid dissociation refers to the process where an acid releases its hydrogen ions when dissolved in water. For strong acids like HCl:

• They dissociate completely, and all molecules release hydrogen ions.
• This complete dissociation means that calculating hydrogen ion concentration directly from the acid’s molarity is straightforward.
• There are no intermediate steps like partial dissociation, simplifying the mathematics.

For weak acids, this would be much more complicated, involving equilibrium constants. However, with strong acids, the assumptions are cleaner, allowing for direct pH calculations by taking the negative logarithm of the hydrogen ion concentration.