Problem 86 - A Complete Resource Book in Chemistry for JEE Main

Question

The molar concentration of \(20 \mathrm{~g}\) of \(\mathrm{NaOH}\) present in 5 litre of solution is (a) \(0.1 \mathrm{~mol} / \mathrm{L}\) (b) \(0.2 \mathrm{~mol} / \mathrm{L}\) (c) \(\mathrm{v} 1.0 \mathrm{~mol} / \mathrm{L}\) (d) \(2.0 \mathrm{~mol} / \mathrm{L}\)

Step-by-Step Solution

Answer

The molar concentration is 0.1 mol/L, corresponding to option (a).

Step 1: Understand the Problem

To find the molar concentration, we need to calculate the number of moles of \( \mathrm{NaOH} \) and then divide it by the volume of the solution in liters.

Step 2: Calculate Molar Mass of NaOH

The molar mass of \( \mathrm{NaOH} \) is the sum of the atomic masses of \( \mathrm{Na} \), \( \mathrm{O} \), and \( \mathrm{H} \). 1. \( \mathrm{Na} \) = 23 \( \mathrm{g/mol} \) 2. \( \mathrm{O} \) = 16 \( \mathrm{g/mol} \)3. \( \mathrm{H} \) = 1 \( \mathrm{g/mol} \) Thus, the molar mass of \( \mathrm{NaOH} \) = 23 + 16 + 1 = 40 \( \mathrm{g/mol} \).

Step 3: Calculate Moles of NaOH

The formula for moles is given by: \[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \]Given: Mass of \( \mathrm{NaOH} = 20 \mathrm{~g} \)So, moles of \( \mathrm{NaOH} = \frac{20 \mathrm{~g}}{40 \mathrm{~g/mol}} = 0.5 \text{ mol} \).

Step 4: Calculate Molar Concentration

To find the molar concentration, use the formula: \[ \text{Concentration (molarity)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]Given: Volume of solution = 5 liters.Thus, molarity \( = \frac{0.5 \text{ mol}}{5 \text{ L}} = 0.1 \text{ mol/L} \).

Step 5: Choose the Correct Answer

The calculated molarity is \( 0.1 \text{ mol/L} \), which corresponds to option (a).

Key Concepts

Moles of Solute

Moles of solute represent the amount of a substance present in a solution. This concept is fundamental when dealing with questions about molar concentration or molarity. To calculate the moles of a solute, you need to know both the mass of the solute in grams and its molar mass. The formula to use is:
\[ \text{Moles} = \frac{\text{Mass of Solute}}{\text{Molar Mass}} \] For example, in our problem, we have 20 grams of NaOH. Having calculated the molar mass of NaOH as 40 g/mol (which we will explore in further detail), we use the formula to find the moles:
\[ \text{Moles of } \mathrm{NaOH} = \frac{20 \text{ g}}{40 \text{ g/mol}} = 0.5 \text{ mol} \] Understanding moles helps in comprehending the amount of substance in a given mass, crucial for calculating other properties like molarity or participating in chemical reactions.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, sum the atomic masses of each element in the compound provided in the periodic table.For sodium hydroxide \(\mathrm{NaOH}\):- Sodium \(\mathrm{Na}\) has an atomic mass of 23 g/mol.- Oxygen \(\mathrm{O}\) has an atomic mass of 16 g/mol.- Hydrogen \(\mathrm{H}\) has an atomic mass of 1 g/mol.
Adding these, the molar mass of \(\mathrm{NaOH}\) is:
\[ 23 \text{ g/mol} + 16 \text{ g/mol} + 1 \text{ g/mol} = 40 \text{ g/mol} \] This calculation is essential because it allows us to convert grams into moles, using the formula for moles from the previous section. Each step in molar mass calculation must be carefully performed to ensure accurate results.

Molarity Formula

Molarity, also known as molar concentration, refers to the concentration of a solute in a solution. It is expressed in moles of solute per liter of solution (mol/L). The formula to calculate molarity is:
\[ \text{Molarity} = \frac{\text{Moles of Solute}}{\text{Volume of Solution in Liters}} \] In the context of our problem, we have already calculated 0.5 moles of NaOH, and the volume of the solution is given as 5 liters. To find the molarity:
\[ \text{Molarity} = \frac{0.5 \text{ mol}}{5 \text{ L}} = 0.1 \text{ mol/L} \] Molarity is a critical concept in chemistry, used for solution preparation and expressing reaction concentrations. It provides a standardized way of describing how much solute is present in a specific volume of solution. Understanding molarity is key to solving a wide range of problems in both academic and practical chemistry.