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 (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 (c) 0.01 M.

Step 1: Convert molecules to moles

First, we need to convert the number of molecules of urea to moles. Use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules per mole.Number of moles \(= \frac{6.02 \times 10^{20}}{6.022 \times 10^{23}}\).Calculate this value:\[ \frac{6.02 \times 10^{20}}{6.022 \times 10^{23}} \approx 1 \times 10^{-3} \] moles.

Step 2: Convert solution volume to liters

The volume of the solution is given in milliliters, so we need to convert this to liters since molarity is moles per liter. \(100 \text{ mL} = 0.1 \text{ L}\).

Step 3: Calculate molarity

Molarity is calculated using the formula:\[ \text{Molarity (M)} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]Insert the values from the previous steps:\[ \text{Molarity} = \frac{1 \times 10^{-3} \text{ moles}}{0.1 \text{ L}} = 0.01 \text{ M} \].

Step 4: Identify the correct option

Compare the calculated molarity, \(0.01 \text{ M}\), with the given options. The correct option is (c) \(0.01 \text{ M}\).

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental constant used in chemistry to bridge the gap between the atomic scale and the macroscopic world. It defines the number of particles, usually atoms or molecules, in one mole of a substance. Avogadro's number is approximately \(6.022 \times 10^{23}\) particles per mole.This constant is crucial for converting quantities from the number of molecules to moles, which is necessary for stoichiometric calculations in chemistry. For instance, if you are given \(6.02 \times 10^{20}\) molecules of a substance, you can determine the moles by using the formula:

• Number of moles \( = \frac{\text{Number of molecules}}{\text{Avogadro's number}}\)

So, in our exercise, we apply this formula to convert molecules of urea to moles, which is an essential step in finding the solution's molarity. Understanding Avogadro's number helps in visualizing amounts we cannot count directly, allowing chemists to quantify chemical reactions accurately.

Moles Conversion

In chemistry, moles are used to express amounts of a chemical substance. A mole is a unit that measures a specific number of particles, typically atoms or molecules.To convert molecules to moles, you need to apply Avogadro's number. For example, knowing that Avogadro's number is \(6.022 \times 10^{23}\), you can convert molecules to moles by dividing the given number of molecules by Avogadro's number. This step is necessary for calculating molarity.In our case, we had \(6.02 \times 10^{20}\) molecules of urea. Using the conversion formula:

• Number of moles \( = \frac{6.02 \times 10^{20}}{6.022 \times 10^{23}} \approx 1 \times 10^{-3}\) moles

Understanding how to convert quantities from molecules to moles is vital in chemistry, allowing for accurate calculations in reactions, compositions, and concentrations.

Solution Volume Conversion

In chemical solutions, volume conversions are important because they allow you to use standard units in your calculations. Specifically, molarity is defined as moles of solute per liter of solution, which means that volume must be in liters.In the exercise, the given volume of the urea solution was \(100\) mL. To convert milliliters to liters, use the conversion factor where \(1\) L equals \(1000\) mL:

• Volume in liters \( = \frac{100 \text{ mL}}{1000} = 0.1 \text{ L}\)

By converting \(100\) mL to \(0.1\) L, we adhere to the definition of molarity. This allows us to accurately compute the concentration of the solution, ensuring that our data aligns with the unit requirements inherent in the molarity formula. Proper volume conversion is vital for achieving precise results in chemical calculations, as it sets the foundation for accurately determining concentrations.