Problem 17 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The density of \(3 \mathrm{M}\) solution of sodium chloride is \(1.252 \mathrm{~g} \mathrm{~mL}^{-1}\). The molality of the solution will be : (molar mass, \(\mathrm{NaCl}=58.5 \mathrm{~g} \mathrm{~mol}^{-1}\) ) (a) \(260 \mathrm{~m}\) (b) \(2.18 \mathrm{~m}\) (c) \(2.79 \mathrm{~m}\) (d) \(3.00 \mathrm{~m}\)

Step-by-Step Solution

Answer

The molality of the solution is approximately \(2.79 \text{ m}\).

Step 1: Understand Molarity and Molality

Molarity (M) is defined as moles of solute per liter of solution, while molality (m) is defined as moles of solute per kilogram of solvent. To convert molarity to molality, we need to account for the mass of the solvent.

Step 2: Calculate Mass of NaCl

Determine the mass of NaCl in 1 L of solution. Since the solution is 3 M, it contains \(3 \text{ moles} \times 58.5 \text{ g/mol} = 175.5 \text{ g of NaCl.}\)

Step 3: Calculate Mass of Solution

Find the mass of 1 L of the solution using its density: \(1.252 \text{ g/mL} \times 1000 \text{ mL} = 1252 \text{ g.}\)

Step 4: Calculate Mass of Solvent

Subtract the mass of NaCl from the total mass of the solution to find the mass of the solvent: \(1252 \text{ g (total)} - 175.5 \text{ g (NaCl)} = 1076.5 \text{ g of water.}\)

Step 5: Convert Solvent Mass to Kilograms

Convert the mass of the solvent from grams to kilograms: \(1076.5 \text{ g} = 1.0765 \text{ kg.}\)

Step 6: Calculate Molality

Finally, calculate molality using the formula \(\text{molality} (m) = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}\). This yields \(\frac{3 \text{ moles}}{1.0765 \text{ kg}} \approx 2.79 \text{ m.}\)

Key Concepts

Molarity

Molarity is a central concept in chemistry that helps us understand concentrations of solutions. It is defined as the number of moles of a solute present in one liter of solution, denoted by the symbol \( M \). This unit is crucial when performing chemical reactions because it allows us to calculate the necessary amounts of reactants or products.

For instance, when we say a solution is 3 M, we are referring to a solution where 3 moles of a solute, such as sodium chloride (NaCl), are dissolved in every liter of the solution. This helps in determining the exact proportions needed during reactions, ensuring that the reaction proceeds as expected with minimal wastage.

When computing molarity, always remember:

• Use moles of solute as the numerator.
• Use liters of solution as the denominator.

This precise concentration measurement is what differentiates molarity from other concentration metrics, making it indispensable in laboratory settings.

Density

Density is another fundamental element in chemistry and physics, describing how much mass is in a given volume of a substance. Typically expressed in units such as grams per milliliter \( ext{g/mL} \) or kilograms per cubic meter \( ext{kg/m}^3 \), density helps us understand how substances relate to one another in terms of mass and volume.

In our sodium chloride solution example, the density is specified as \(1.252 ext{ g/mL} \). This means that every milliliter of this solution weighs 1.252 grams. Knowing the density is essential in calculations to determine how much material is present within a specific volume, allowing easy conversion from volume measurements to mass, and vice versa.

To reiterate:

• Density = Mass/Volume
• Expresses how "heavy" a material is for a given space it occupies

Density can influence physical properties and activities such as buoyancy and pressure.

Sodium Chloride

Sodium chloride, widely known as table salt, is a neutral compound formed when sodium (Na) and chlorine (Cl) combine. Its chemical formula is NaCl. Understanding sodium chloride is important in both everyday life and scientific applications, as it is one of the most common salts found and used worldwide.

Sodium chloride is not only essential for flavor and food preservation but plays key roles in various chemical processes and biological reactions. Its molar mass is 58.5 g/mol, which informs us about the weight of one mole of salt. This information is crucial when preparing solutions with specific concentrations, like in laboratory experiments, to achieve the desired chemical conditions.

Considerations with NaCl include:

• It is soluble in water, making it easy to form solutions.
• Important in regulating water balance in cells through osmosis.
• Acts as a preservative due to its ability to inhibit microbial growth.

Such properties make sodium chloride a versatile and essential chemical in both culinary and scientific domains.