Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Dissolving \(120 \mathrm{~g}\) of a compound of (mol. wt. 60) in \(1000 \mathrm{~g}\) of water gave a solution of density \(1.12 \mathrm{~g} / \mathrm{mL}\). The molarity of the solution is: (a) \(1.00 \mathrm{M}\) (b) \(2.00 \mathrm{M}\) (c) \(2.50 \mathrm{M}\) (d) \(4.00 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the solution is \(2.00 \text{ M}\).

Step 1: Calculate the Volume of the Solution

First, we need to find out the volume of the solution. Since the solution's density is given as \(1.12 \text{ g/mL}\), we can use the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). The total mass of the solution is the mass of the compound plus the mass of the water, which is \(120 \text{ g} + 1000 \text{ g} = 1120 \text{ g}\). Thus, the volume \(V\) of the solution can be calculated by rearranging the formula: \[ V = \frac{\text{Mass}}{\text{Density}} = \frac{1120 \text{ g}}{1.12 \text{ g/mL}} = 1000 \text{ mL} = 1 \text{ L} \]

Step 2: Calculate the Number of Moles of the Compound

Next, we calculate the number of moles of the compound dissolved. The molecular weight of the compound is \(60 \text{ g/mol}\). Therefore, the number of moles \(n\) is given by \[ n = \frac{\text{Mass}}{\text{Molecular Weight}} = \frac{120 \text{ g}}{60 \text{ g/mol}} = 2 \text{ moles} \]

Step 3: Calculate the Molarity of the Solution

Finally, we find the molarity of the solution, which is the number of moles of solute per liter of solution. Since the volume of the solution is \(1 \text{ L}\) and we calculated \(2\) moles of the compound in the solution, the molarity \(M\) is: \[ M = \frac{\text{Number of Moles}}{\text{Volume of Solution in Liters}} = \frac{2 \text{ moles}}{1 \text{ L}} = 2.00 \text{ M} \]

Key Concepts

Density

Density is a concept that helps us understand how heavy an object is for its size. It's essentially a measure of mass per unit volume. In calculations, the formula used is:\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}}\]

• Mass is typically measured in grams (g).
• Volume is often in milliliters (mL) or cubic centimeters (cm³).

In this exercise, density is given as 1.12 g/mL, which indicates that each milliliter of the solution weighs 1.12 grams.
Understanding density is crucial, as it helps us calculate the volume of a solution when its mass and density are known. By rearranging the density formula, the volume of the solution can be found using:\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}}\]For the given problem, the total mass of the solution was 1120 grams, allowing the calculation of the solution's volume.

Moles

The concept of moles is central in chemistry, serving as a bridge between the atomic scale and the macroscopic world we handle daily. A mole denotes a specific number—Avogadro's number, which is approximately \(6.022 \times 10^{23}\). Understanding moles allows chemists to count particles by weighing them.
In practice, we calculate the number of moles by dividing the mass of a substance by its molecular weight (or molar mass):\[ \text{Moles} = \frac{\text{Mass}}{\text{Molecular Weight}}\]

• This formula helps determine how many particles exist in a given mass of substance.
• For instance, dissolving 120 grams of a compound with a molecular weight of 60 g/mol results in 2 moles of that compound.

The mole concept connects mass to the number of atoms or molecules in a sample, making it easier to engage in chemical calculations and reactions.

Volume of Solution

Volume is a measure of space that a substance or object occupies. In chemical solutions, the volume is especially important as it determines concentrations. In this exercise, the volume was determined using the solution's density.
Because the density of the solution was 1.12 g/mL, and the total mass was 1120 grams, we calculated the volume by rearranging the formula for density:\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1120 \text{ g}}{1.12 \text{ g/mL}} \approx 1000 \text{ mL} = 1 \text{ L}\]

• Volume is crucial in determining the molarity of solutions.
• Makes sure that the number of moles of solutes is per liter of solution to find concentration.

This calculation showed that the solution occupies 1000 mL, equivalently 1 liter, which is essential for the subsequent calculation of molarity.

Molecular Weight

Molecular weight, also known as molar mass, is the mass of one mole of a substance. It tells us how much one mole of a molecule weighs in grams.

• Expressed in units of grams per mole (g/mol).
• Determined by adding up the atomic weights of all the atoms in a molecule.

In this particular problem, the molecular weight of the compound is given as 60 g/mol, which means one mole of this substance weighs 60 grams.
To find out how many moles are in a specific mass of a compound, we divide the mass by the molecular weight using the formula:\[ \text{Number of Moles} = \frac{\text{Mass}}{\text{Molecular Weight}}\]Understanding molecular weight allows chemists to make accurate calculations in reactions and ensures that substances combine in the right proportions.