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) \(0.1 \mathrm{M}\)

Short answer

The concentration of the urea solution is (c) 0.01 M.

Step-by-step solution

Convert Molecules to Moles

Using Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules per mole, convert the given number of molecules to moles. \[ \text{Moles of urea} = \frac{6.02 \times 10^{20}}{6.022 \times 10^{23}} \] Calculate this to find the number of moles.

Calculation of Moles

Perform the calculation: \[ \text{Moles of urea} = \frac{6.02 \times 10^{20}}{6.022 \times 10^{23}} \approx 1 \times 10^{-3} \text{ moles} \]

Convert Volume to Liters

Convert the volume of the solution from milliliters to liters: \[ 100 \text{ mL} = 0.1 \text{ L} \]

Calculate Molarity

Molarity is defined as moles of solute per liter of solution. Use the moles from Step 2 and the volume from Step 3 to calculate the molarity: \[ \text{Molarity (M)} = \frac{1 \times 10^{-3} \text{ moles}}{0.1 \text{ L}} = 0.01 \text{ M} \]

Choose the Correct Option

Compare the calculated molarity with the given options. The correct answer is (c) \(0.01 \mathrm{M}\).

Key concepts

Molarity

Molarity is an important concept in chemistry that helps us describe the concentration of solutes in a solution.
It specifically tells us how many moles of a solute are present per liter of solution. Having this information allows us to understand the strength or concentration of a solution.
To calculate molarity, we use the formula:

• \( \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \)

For example, if you have 1 mole of salt in 1 liter of water, the molarity is 1 M. In our given problem, we calculated 0.01 M which tells us that there are 0.01 moles of urea per liter of the solution. This measurement provides a clear picture of how concentrated the solution is.
Understanding molarity helps with practical applications, like understanding mixing solutions in labs and industries.
It’s vital for performing titrations and predicting reactions in both education and work settings.

Moles Conversion

Converting between molecules and moles is a key step in solving problems that involve chemicals on a microscopic scale.
In order to work with real-world quantities, we must convert these incredibly large numbers into manageable moles, which is more convenient for calculations. To convert molecules to moles, we use the formula:

• \( \text{Moles} = \frac{\text{Number of molecules}}{6.022 \times 10^{23}} \)

This formula uses Avogadro's number, which we’ll get to in the next section. For example, if you have \(6.02 \times 10^{20}\) molecules of urea, you can calculate the number of moles as approximately \(1 \times 10^{-3}\) moles. This conversion is critical in chemistry because it bridges the gap between molecular-level interactions and the macroscopic amounts we measure in labs.
Converting molecules to moles allows chemists to analyze reactions, purchase the correct amounts of substances, and perform calculations with higher precision.
It's a foundational tool in chemistry, making large-scale chemical equations and solutions manageable.

Avogadro's Number

Avogadro's Number is the magic number in chemistry that connects the microscopic world of atoms and molecules with the macroscopic world we can measure.
It is defined as \( 6.022 \times 10^{23} \), representing the number of particles (whether atoms, molecules, ions, etc.) in one mole of a substance.Avogadro's Number ensures accuracy when converting between molecules and moles. It’s pivotal in chemistry calculations, particularly when determining the number of moles needed or measuring substances at a molecular level.
This number is named after Amedeo Avogadro, an Italian scientist, who hypothesized that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This principle laid the foundation for what we now call Avogadro's Law.

• Helps balance equations by understanding molecular scales.
• Facilitates conversions between quantity units in chemistry.
• Essential for stoichiometric calculations.

Avogadro's Number is not just a constant but a bridge connecting the theoretical aspects of chemistry with real-world quantities.
It allows chemists to work seamlessly from nanoscopic dimensions to measurable scales.