Problem 99 - Chemistry Matter and Change

Question

Snowflakes A snowflake contains \(1.9 \times 10^{18}\) molecules of water. How many moles of water does it contain?

Step-by-Step Solution

Answer

The snowflake contains approximately \(3.15 \times 10^{-6}\) moles of water.

Step 1: Understanding the Question

The problem asks us to find out how many moles are in a snowflake with a given number of molecules of water. We know the number of molecules in the snowflake is \(1.9 \times 10^{18}\). We need to find the equivalent number of moles.

Step 2: Know Avogadro's Number

Avogadro's number tells us that one mole of any substance contains approximately \(6.022 \times 10^{23}\) molecules. This is a constant in chemistry for converting between moles and molecules.

Step 3: Convert Molecules to Moles

Use the formula: \\[ \text{Number of Moles} = \frac{\text{Number of Molecules}}{\text{Avogadro's Number}} \] \Substitute the given values: \\[ \text{Number of Moles} = \frac{1.9 \times 10^{18}}{6.022 \times 10^{23}} \] \Calculate the result to find the moles of water.

Step 4: Calculate the Result

Divide the value \(1.9 \times 10^{18}\) by \(6.022 \times 10^{23}\): \\[\text{Number of Moles} \approx 3.15 \times 10^{-6} \] \Thus, the number of moles of water in the snowflake is approximately \(3.15 \times 10^{-6}\) moles.

Key Concepts

Avogadro's Number

Avogadro's number is a key concept in chemistry that is essential for understanding how atoms and molecules relate to moles, a standard unit of measure in chemistry.
Avogadro's number is defined as \(6.022 \times 10^{23}\). This number represents the quantity of atoms or molecules in one mole of a substance.
It simplifies chemical calculations by allowing chemists to count atoms and molecules in large quantities. Without Avogadro's number, dealing with atoms directly would be impractical due to their incredibly small size.

• It acts as a bridge connecting the macroscopic world that we can observe and measure, with the microscopic world of atoms and molecules.
• Scientists use Avogadro's Number, not only for calculations involving moles and molecules, but also to determine the amounts of substances needed in chemical reactions.

Understanding this constant enables students to grasp further concepts in chemistry and is vital for converting molecules into moles accurately.

Conversion of Molecules to Moles

When given a specific number of molecules, converting them into moles allows us to quantify that substance in a manageable way.
This conversion is crucial because it translates an otherwise incomprehensible number of molecules into the mole unit, which is more practical for calculations.

To convert the number of molecules to moles, use Avogadro's number as the conversion factor. The formula for this conversion is:

• \[\text{Number of Moles} = \frac{\text{Number of Molecules}}{\text{Avogadro's Number}}\]

This equation lets you input the total molecules you have and divide it by Avogadro’s number.
For example, if there are \(1.9 \times 10^{18}\) molecules of water in a snowflake, dividing by \(6.022 \times 10^{23}\) results in approximately \(3.15 \times 10^{-6}\) moles.

• This translates the exorbitant molecular quantity into a small, easily manageable figure in terms of moles.
• Comprehending this process is foundational for further chemical calculations and understanding material quantities.

Chemical Calculations

Chemical calculations often involve converting units and quantities to understand the composition, reactions, and processes.
These calculations are simplified by using moles, a universally recognized unit, which applies universally for substances.
Basic chemical calculations begin with translating quantities into moles, leveraging Avogadro's number as a key conversion tool.

• This translation from molecules to moles facilitates straightforward calculations, especially when dealing with reaction stoichiometry.
• In stoichiometry, the mole concept helps in determining the exact amount of reactants and products involved in a chemical reaction.

Using the example from the snowflake exercise, knowing the number of moles allows prediction and manipulation of chemical reactions potentially involving water.
Understanding these calculations is essential for virtually any laboratory or academic work in chemistry, providing a reliable framework for understanding material interactions.