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 \(0.01 \mathrm{M}\), which matches option (c).

Step 1: Identify Given Values

We are given that there are \(6.02 \times 10^{20}\) molecules of urea present in \(100\text{ mL}\) of the solution. We need to determine the concentration of this solution in moles per liter (Molarity, \(M\)).

Step 2: Use Avogadro's Number to Find Moles

First, recall Avogadro's number, \(6.02 \times 10^{23}\), which is the number of molecules per mole. To find the number of moles of urea, we divide the number of molecules by Avogadro's number:\[\text{Moles of urea} = \frac{6.02 \times 10^{20}}{6.02 \times 10^{23}} = 10^{-3} \text{ moles.}\]

Step 3: Convert Volume to Liters

Since we need molarity in terms of moles per liter, we convert the given volume from milliliters to liters. The given volume is \(100 \text{ mL}\), which is equivalent to:\[100 \text{ mL} = 0.1 \text{ L}.\]

Step 4: Calculate the Molarity of the Solution

Molarity (\(M\)) is defined as moles of solute per liter of solution. Substitute the moles and volume into the molarity formula:\[\text{Molarity} = \frac{\text{Moles of urea}}{\text{Volume in Liters}} = \frac{10^{-3}}{0.1} = 0.01 \, \text{M}.\]

Step 5: Compare with Given Options

The calculated concentration of the urea solution is \(0.01 \, \text{M}\). Among the provided options, this matches option (c).

Key Concepts

Avogadro's Number

Understanding Avogadro's Number is crucial for grasping the concept of moles. Avogadro's Number is a constant that represents the number of molecules or atoms in one mole of a substance. This number is approximately \(6.02 \times 10^{23}\). It allows scientists to count and work with molecules in a systematic way.

When you have a specific number of molecules, like the \(6.02 \times 10^{20}\) molecules of urea mentioned in the exercise, you can use Avogadro's Number to convert this count into moles. This conversion lets you understand how many moles you have based on the actual count of molecules.

• Divide the count of molecules by Avogadro’s Number: \(\frac{6.02 \times 10^{20}}{6.02 \times 10^{23}} = 10^{-3} \text{ moles }\).
• This step simplifies working with chemical calculations, as working with moles rather than individual molecules makes equations more manageable.

This approach is fundamental in chemistry for determining how reactants will behave and interact with each other on a molecular level.

Concentration Calculation

Concentration calculation is an integral part of understanding solution chemistry. Concentration provides insight into the amount of solute present in a given volume of solution. One common way to express concentration is through molarity (\(M\)), which indicates moles of solute per liter of solution.

In our example, once you've calculated the moles of urea as \(10^{-3}\) moles, the next task is to calculate its molarity by considering the volume of the solution. The formula for molarity is:

• \(\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}\)

This formula underscores the importance of both moles and liters, where the amount of solute depends on both the given number of moles and the volume they are dissolved in. For our example:

• Substitute the values: \(\frac{10^{-3}}{0.1} = 0.01 \text{ M }\).

Understanding the concept of molarity enables students to predict how changing the amount of solute or the volume of the solution will affect the concentration, a frequent requirement in experimental chemistry.

Moles and Volume Conversion

Converting units accurately is a backbone skill in chemistry. The ability to switch between different units of measure is essential, especially when dealing with moles and volumes.

To convert volume from milliliters to liters, remember that 1 liter is equal to 1000 milliliters. Thus, converting 100 milliliters to liters is a simple process:

• Divide by 1000: \(100 \text{ mL} = 0.1 \text{ L}\).

This conversion is necessary because molarity, as seen in concentration calculations, requires the volume to be in liters. Only then will the equation \(\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume in liters}}\) make sense.

Ignoring proper conversions can lead to huge miscalculations, causing errors in experiments or misunderstandings when comparing concentrations. Thus, being comfortable with unit conversions is key to success in chemistry problem-solving.