Problem 176 - A Complete Resource Book in Chemistry for JEE Main

Question

The density of a solution prepared by dissolving \(120 \mathrm{~g}\) of urea (mol. Mass \(=60 \mathrm{u}\) ) in \(1000 \mathrm{~g}\) of water is \(1.15 \mathrm{~g} / \mathrm{mL}\). The molarity of this solutions is: [2012] (a) \(1.02 \mathrm{M}\) (b) \(0.50 \mathrm{M}\) (c) \(2.05 \mathrm{M}\) (d) \(1.78 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the solution is approximately 2.05 M.

Step 1: Calculate Moles of Solute (Urea)

To find the molarity, first calculate the number of moles of solute. Use the formula for calculating moles: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). Given the mass of urea is \(120 \text{ g}\) and its molar mass is \(60 \text{ g/mol}\), the moles of urea are: \( \frac{120}{60} = 2 \text{ moles} \).

Step 2: Calculate Total Mass of Solution

Add the mass of urea and the mass of water to find the total mass of the solution. Given the mass of water is \(1000 \text{ g}\), the total mass of the solution is: \(120 \text{ g} + 1000 \text{ g} = 1120 \text{ g}\).

Step 3: Convert Mass of Solution to Volume

To convert mass to volume, use the density formula: \( \text{Density} = \frac{\text{mass}}{\text{volume}} \). Rearrange to find the volume: \( \text{volume} = \frac{\text{mass}}{\text{density}} \). The density is given as \(1.15 \text{ g/mL}\), so the volume of the solution is: \( \frac{1120 \text{ g}}{1.15 \text{ g/mL}} \approx 973.91 \text{ mL} \).

Step 4: Calculate Molarity

Molarity is defined as moles of solute per liter of solution. Convert the volume from milliliters to liters by dividing by 1000. So, \(973.91 \text{ mL} = 0.97391 \text{ L}\). The molarity is then: \( \text{Molarity} = \frac{2 \text{ moles}}{0.97391 \text{ L}} \approx 2.05 \text{ M} \).

Key Concepts

Density

Density is a fundamental concept often used to relate mass and volume, particularly in solutions. In chemistry, density (901) is expressed in grams per milliliter (900g/mL1f8b7) and is defined as the mass of a solution divided by its volume. This relationship is crucial.

• Formula: \( \text{Density} = \frac{\text{mass}}{\text{volume}} \)
• Used to convert between mass and volume, helping determine solution properties.

Knowing the density allows us to find out how much space a given mass of solution occupies. If the density of a solution is known and you have the total mass, you can calculate its volume. This is essential for determining other properties like molarity.

Moles of Solute

Understanding moles is key when working with solutions. The number of moles of a solute helps in calculating the concentration of a solution, expressed in terms of molarity. The concept of moles bridges the gap between the micro-world of atoms and molecules and the macroscopic quantities we measure in the lab.

• Formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \)
• Essential for determining how much of a substance is present.

In our exercise, we calculated the moles of urea (the solute) as 2 moles. This value is crucial for finding the molarity and fully understanding how concentrated a solution is.

Molecular Mass

Molecular mass, or molar mass, represents the mass of one mole of a substance – typically expressed in grams per mole. This quantity is calculated from the sum of the atomic masses of all the atoms in a molecule. It's essential for converting mass to moles and vice versa.

• Connects the mass of individual molecules to measurable quantities.
• Crucial for calculating moles, serving as a conversion factor.

For urea in our problem, the molecular mass is 60 grams per mole. Knowing this value allowed us to convert the measured mass of urea into moles, thus making it possible to calculate the solution's molarity.

Solution Volume

Solution volume is vital because it helps in determining the molarity of a solution, describing how many moles of solute are present in a given volume of solution. This measure often depends on the method of how the solution's mass and density were utilized.

• Calculated by the formula \( \text{volume} = \frac{\text{mass}}{\text{density}} \).
• Specifies how much space the entire solution occupies.

In our case, we derived the volume of the solution as approximately 973.91 mL. Converting this volume to liters (0.97391 L) enabled us to find the molarity, crucial for understanding the solution's composition.