Problem 158 - A Complete Resource Book in Chemistry for JEE Main

Question

Two solutions of a substance (non-electrolyte) are mixed in the following manner. \(480 \mathrm{~mL}\) of \(1.5 \mathrm{M}\) first solution \(+520 \mathrm{~mL}\) of \(1.2 \mathrm{M}\) second solution. What is the molarity of the final mixture? (a) \(1.344 \mathrm{M}\) (b) \(2.70 \mathrm{M}\) (c) \(1.50 \mathrm{M}\) (d) \(1.20 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the final mixture is \(1.344 \, \text{M}\). Option (a).

Step 1: Calculate Moles in 1st Solution

Determine the number of moles in the first solution using the formula for moles, which is \( \text{Moles} = \text{Molarity} \times \text{Volume (L)} \). Here, \( \text{Molarity} = 1.5 \, \text{M} \) and \( \text{Volume} = 480 \, \text{mL} = 0.480 \, \text{L} \).\[\text{Moles in 1st solution} = 1.5 \times 0.480 = 0.72 \text{ moles}\]

Step 2: Calculate Moles in 2nd Solution

Determine the number of moles in the second solution similarly, where the molarity is \( 1.2 \, \text{M} \) and the volume is \( 520 \, \text{mL} = 0.520 \, \text{L} \).\[\text{Moles in 2nd solution} = 1.2 \times 0.520 = 0.624 \text{ moles} \]

Step 3: Combine Total Moles

Add the moles from the first and second solutions to find the total moles in the mixture.\[\text{Total moles} = 0.72 + 0.624 = 1.344 \text{ moles} \]

Step 4: Calculate Total Volume

Add the volumes of the two solutions to find the total volume of the mixture.\[\text{Total volume} = 480 \, \text{mL} + 520 \, \text{mL} = 1000 \, \text{mL} = 1.000 \, \text{L} \]

Step 5: Calculate Molarity of Mixture

Use the formula for molarity \( \text{Molarity} = \frac{\text{Total moles}}{\text{Total volume} (\text{L})} \) to find the molarity of the mixture.\[\text{Molarity of mixture} = \frac{1.344}{1.000} = 1.344 \, \text{M} \]

Key Concepts

Understanding the Mole Concept

The mole concept is fundamental in chemistry, allowing measurement of substances in a manner similar to counting atoms or molecules in large quantities. One mole contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\) of any chemical unit, be it atoms, molecules, ions, etc.
This large numerical value helps in dealing with the quantities we encounter in chemical reactions everyday.
When discussing solutions, we often refer to the amount of solute in terms of moles.
This makes calculations more uniform and is essential for processes like determining the molarity of solutions. In terms of solutions, where the composition is homogeneously mixed throughout, using moles helps us easily compare and predict reactions and concentrations. To recap, the mole serves as a bridge between the microscopic scale of atoms, which we cannot count directly, and the macroscopic scale of substances that we can measure in the lab. With the mole concept in hand, solving complex chemical equations becomes more manageable.

Solution Mixing: Combining Solutions

Solution mixing is an important aspect of chemistry, involving blending two solutions to achieve a desired concentration or volume.
This can involve straightforward mixing, as well as sophisticated reactions, and it plays a key role across fields of science and industry.
When mixing solutions, the main aspects we pay attention to are:

• Volume of each solution
• Concentration (molarity) of each solution

In the context of our exercise, we had two solutions with known volumes and molarities.
First, we identified the moles present in each by multiplying the volume (converted to liters) by the molarity.
We then added the number of moles from each solution since the moles are the moving parts that react or contribute in a reaction.
Finally, we combined the volumes of the solutions to find the overall mixture volume, making it an ideal preparation for calculating the new concentration.
This exemplifies solution mixing to achieve a new desired molarity, highlighting its utility in chemical analysis and preparation.

Determining Concentration: Calculating Molarity

Concentration determination, specifically molarity, is an essential calculation in chemical solutions to express the amount of solute in a given volume.
Molarity is defined as the number of moles of solute per liter of solution, signifying the concentration of a solution.
The formula for calculating molarity is:

• \[\text{Molarity} = \frac{\text{Total moles of solute}}{\text{Total volume of solution in liters}} \]

After mixing the solutions, we calculated the total moles of solute from both initial solutions.
This was completed by adding the individual moles from each solution. Then, by dividing this total moles by the total volume (converted to liters), we arrived at the molarity of the final mixed solution.
Understanding this calculation is fundamental for tasks such as titration, chemical manufacturing, and even in pharmacology, where the precise concentration of a given component can significantly alter the effectiveness and outcomes of a product or medication.
This guides chemists in achieving desired reactions and properties, ensuring precise and predictable results.