Problem 169 - A Complete Resource Book in Chemistry for JEE Main

Question

\(.6 .02 \times 10^{20}\) molecules of urea are present in \(100 \mathrm{~mL}\) of its solution. The concentration of urea solution is [2004] (a) \(0.02 \mathrm{M}\) (b) \(0.001 \mathrm{M}\) (c) \(0.01 \mathrm{M}\) (d) \(0.1 \mathrm{M}\)

Step-by-Step Solution

Answer

The concentration of the urea solution is 0.1 M (option d).

Step 1: Determine the Number of Molecules Present

We start with the number of molecules given: \( .6 \times 10^{20} \). Simplifying this, it becomes \( 6 \times 10^{19} \) molecules.

Step 2: Convert Molecules to Moles of Urea

To find the number of moles, we use Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules per mole. Thus, the number of moles of urea is \[ \text{Moles of urea} = \frac{6 \times 10^{19}}{6.022 \times 10^{23}} = \frac{1}{100} = 0.01 \text{ moles}. \]

Step 3: Convert 100 mL to Liters

The concentration is calculated in terms of moles per liter, so we need to convert 100 mL to liters. \[ 100 \text{ mL} = 0.1 \text{ Liters}. \]

Step 4: Calculate Molarity of the Solution

Using the formula for molarity (\( M = \frac{\text{moles of solute}}{\text{liters of solution}} \)), we find: \[ M = \frac{0.01 \text{ moles}}{0.1 \text{ liters}} = 0.1 \text{ M}. \]

Step 5: Choose the Correct Answer

Based on the calculated molarity, the concentration of the urea solution is \( 0.1 \text{ M} \), which matches with option \( (d) \).

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental concept in chemistry that enables us to connect microscale and macroscale measurements. It is named after the Italian scientist Amedeo Avogadro and is defined as the number of constituent particles, usually atoms or molecules, that are contained in one mole of a given substance. This number is approximately \( 6.022 \times 10^{23} \).

Understanding this concept is crucial because:

• It allows chemists to calculate the number of atoms, ions, or molecules in a sample.
• By using Avogadro's number, one can easily convert between the number of molecules and moles, making chemical calculations more manageable.
• It helps in establishing a clear relationship between mass, moles, and molecular quantity, which is critical for stoichiometry in chemical reactions.

When dealing with a large number of molecules, such as the \( 6 \times 10^{19} \) molecules in this exercise, Avogadro's number provides a convenient way to convert these into moles.

Moles

Moles serve as a bridge between the atomic world and the tangible world of masses we deal with daily. A mole is a unit in chemistry used to quantify the amount of substance. Similar to how dozen is used for counting eggs or items, a mole amounts to \( 6.022 \times 10^{23} \) units of any substance (Avogadro's constant).

Key aspects of moles include:

• It's a way to express amounts of a chemical substance.
• Using moles simplifies the measurement of chemicals involved in reactions because it relates directly to the scale at which chemical reactions occur.
• By expressing amounts in moles, chemists can more easily visualize and calculate the reactants required and products produced in stoichiometric calculations.

In the original exercise, converting \( 6 \times 10^{19} \) molecules to moles was done by dividing by Avogadro's number, resulting in \( 0.01 \) moles of urea. This demonstrates the practical application of moles in real-world scenarios.

Molecules to Moles Conversion

Converting molecules to moles is a common practice in chemistry that relies on Avogadro's number. This conversion helps simplify calculations involved in determining concentrations and reacting amounts in chemical solutions.

Here's how molecules to moles conversion is typically performed:

• Determine the total number of molecules you have. For instance, the example provides \( 6 \times 10^{19} \) molecules of urea.
• Use the formula: \( \text{Moles} = \frac{\text{number of molecules}}{\text{Avogadro's number}} \).
• Substitute the known values into the formula to get the result.

In our example, applying this conversion told us that \( 6 \times 10^{19} \) molecules are equivalent to \( 0.01 \) moles. This process is essential because it translates the microscopic count of particles into a usable quantity for calculating solute concentration in solutions, ensuring accurate and efficient chemical analysis.