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 \(0.1 \text{ mol/L}\), option (a).

Step 1: Calculate molar mass of NaOH

First, we need to determine the molar mass of sodium hydroxide (NaOH). The atomic mass of sodium (Na) is approximately 23 g/mol, oxygen (O) is 16 g/mol, and hydrogen (H) is 1 g/mol. Therefore, the molar mass of NaOH is calculated as follows: \(23 + 16 + 1 = 40 \text{ g/mol}\).

Step 2: Calculate moles of NaOH

Next, we calculate the number of moles of NaOH using the formula \(\text{Number of moles} = \frac{\text{Mass of substance (g)}}{\text{Molar mass (g/mol)}}\). Substituting the given values, we have \(\frac{20 \text{ g}}{40 \text{ g/mol}} = 0.5 \text{ mol}\).

Step 3: Calculate molar concentration

The molar concentration of a solution is given by \(\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}}\). Here, the volume of the solution is given as 5 L. Therefore, substituting the values we found: \(\frac{0.5 \text{ mol}}{5 \text{ L}} = 0.1 \text{ mol/L}\).

Key Concepts

Molar Mass

Molar mass is essentially the mass of one mole of a substance. It's a pivotal concept in chemistry because it provides the bridge between the atom and the gram scale. For sodium hydroxide (NaOH), the molar mass is calculated by summing the atomic masses of each constituent element.

• Sodium (Na) has an atomic mass of about 23 g/mol.
• Oxygen (O) has an atomic mass of 16 g/mol.
• Hydrogen (H) has an atomic mass of approximately 1 g/mol.

Thus, by adding these together: \[\text{Molar mass of NaOH} = 23 \text{ g/mol} + 16 \text{ g/mol} + 1 \text{ g/mol} = 40 \text{ g/mol}\] This calculation tells us that one mole of NaOH weighs 40 grams. Knowing the molar mass is essential for converting grams to moles, a common calculation in chemistry.

Number of Moles

The number of moles is a measure of the quantity of a substance. Essentially, it tells us how many units (atoms, molecules, etc.) are present in a sample of matter. To find the number of moles, you divide the mass of the sample by its molar mass, using the formula:\[\text{Number of moles} = \frac{\text{Mass of the substance (g)}}{\text{Molar mass (g/mol)}}\]In our example, we have 20 grams of NaOH, and the molar mass is 40 g/mol. Therefore:\[\text{Number of moles} = \frac{20 \text{ g}}{40 \text{ g/mol}} = 0.5 \text{ mol}\]This tells us that in 20 grams of NaOH, there are 0.5 moles. Understanding this concept is crucial, as moles are a foundational unit in chemistry that allows us to relate masses to quantities of molecules or atoms.

Volume of Solution

The volume of the solution is important in calculating molarity, which is the measure of concentration in a solution. Molarity is expressed in moles per liter (mol/L), and it's necessary to use the volume of the solution in liters to calculate it correctly.

• The formula for molarity is:\[\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}}\]

In our scenario, the solution volume is given as 5 liters. With the calculated 0.5 moles of NaOH, the molarity calculation is:\[\text{Molarity} = \frac{0.5 \text{ mol}}{5 \text{ L}} = 0.1 \text{ mol/L}\]This calculation shows us how concentrated the NaOH solution is. Understanding how to work with solution volumes and molarity is crucial when preparing solutions and analyzing chemical reactions.