Problem 177 - A Complete Resource Book in Chemistry for JEE Main

Question

The molarity of a solution obtained by mixing 750 \(\mathrm{mL}\) of \(0.5(\mathrm{M}) \mathrm{HCl}\) with \(250 \mathrm{~mL}\) of \(2(\mathrm{M}) \mathrm{HCl}\) will be (a) \(1.75 \mathrm{M}\) (b) \(0.975 \mathrm{M}\) (c) \(0.875 \mathrm{M}\) (d) \(1.78 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the solution is \(0.875 \, \text{M}\), which corresponds to option (c).

Step 1: Find the Total Moles of HCl in the First Solution

First, we calculate the total moles of HCl in the first solution. We use the formula \( ext{moles} = ext{molarity} \times ext{volume (L)} \). For the first solution, \( ext{moles} = 0.5 \, (M) \times 0.75 \, (L) = 0.375 \, ext{moles} \).

Step 2: Find the Total Moles of HCl in the Second Solution

Next, we calculate the total moles of HCl in the second solution using the same formula. For the second solution, \( ext{moles} = 2 \, (M) \times 0.25 \, (L) = 0.5 \, ext{moles} \).

Step 3: Calculate the Total Moles of HCl in the Mixture

Add the moles from both solutions to get the total moles in the mixture: \( ext{Total Moles} = 0.375 \, ext{moles} + 0.5 \, ext{moles} = 0.875 \, ext{moles} \).

Step 4: Calculate the Total Volume of the Mixture

Add the volumes of both solutions to get the total volume: \( ext{Total Volume} = 750 \, ext{mL} + 250 \, ext{mL} = 1000 \, ext{mL} = 1 \, ext{L} \).

Step 5: Find the Molarity of the Mixture

Finally, calculate the molarity of the resulting mixture using the formula: \( ext{Molarity} = \frac{\text{Total Moles}}{\text{Total Volume (L)}} \). Thus, \( ext{Molarity} = \frac{0.875 \, ext{moles}}{1 \, ext{L}} = 0.875 \, ext{M} \).

Key Concepts

Solution Mixing

Mixing solutions involves combining two or more substances to create a new mixture, often in the context of chemistry. It's an essential process when dealing with molarity calculations or solution dilutions. When you mix two solutions, the moles of solute from each solution combine, which is crucial for finding the final molarity. Here's what happens during solution mixing:

• Identify the volume and concentration (molarity) of each solution you're mixing.
• Calculate the number of moles of solute in each solution using the formula: \[ \text{Moles} = \text{Molarity} \times \text{Volume (in Liters)} \]
• Combine the moles from all solutions to find the total moles present in the final mixture.
• Ensure that volumes are correctly added to establish the total new volume of the combined solution.
  

By focusing on the moles and volume changes when mixing solutions, we can accurately determine the properties of the new mixture such as molarity.

Mole Concept

The mole concept is fundamental in chemistry and serves as the basis for counting and measuring atoms, ions, and molecules. It enables chemists to work with the submicroscopic worlds of atoms by using manageable amounts. Here’s how it operates in solution mixing:

• A mole is defined as \(6.022 \times 10^{23} \) individual particles (Avogadro's number).
• In solutions, we often use moles to express concentrations, making it easier to work with chemical reactions.
• For example, in the exercise above, knowing the moles of HCl present in each initial solution is vital for calculating the final concentration after mixing.
• Utilizing the moles allows for precise calculations when determining how reactants and products will interact.
  

Understanding the mole concept simplifies the complex task of gauging substance amounts, essential for solution mixing.

Volume Conversion

Volume conversion is crucial in chemistry as it ensures that all measurements are consistent, especially when performing calculations like molarity. Often, chemists have to convert between units such as milliliters (mL) and liters (L), and here's how that is generally done:

• You should know that \(1 \text{ L} = 1000 \text{ mL} \)
• To convert from mL to L, divide the number of mL by 1000.
• In our exercise, converting the volumes of the HCl solutions from mL to L was essential for calculating molarity accurately.
• Ensuring all components of your calculation are in the same units helps prevent errors and makes results comparable.
  

Knowing how to convert volumes is a simple yet powerful tool, helping keep computations straightforward and error-free.