Problem 2 - Chemistry Matter and Change

Question

Calculate the number of molecules in 11.5 mol of water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\)

Step-by-Step Solution

Answer

There are approximately \(6.9253 \times 10^{24}\) molecules in 11.5 mol of water.

Step 1: Understand the Concept

To find the number of molecules in a given sample, we need to use Avogadro's number, which tells us how many entities (atoms, molecules, etc.) are in one mole of substance. Avogadro's number is approximately \(6.022 \times 10^{23}\).

Step 2: Set Up the Calculation

Since we know the number of moles of water, we can multiply the moles by Avogadro's number to determine the number of molecules. The formula for this calculation is: Number of molecules = Number of moles \(\times\) Avogadro's number.

Step 3: Perform the Calculation

Plug in the known values into the formula. For 11.5 mol of water, it is calculated as follows:\[11.5 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = 6.9253 \times 10^{24} \text{ molecules}\]

Step 4: Interpret the Result

Thus, in 11.5 mol of water, there are approximately \(6.9253 \times 10^{24}\) molecules. The result is a large number, which is expected when dealing with moles due to Avogadro's large constant.

Key Concepts

Avogadro's number: The Mole's Key Player

In chemistry, Avogadro's number is a fundamental constant used to understand the scale of chemical entities in a mole. It represents the number of atoms, molecules, or particles found in one mole of a substance. Avogadro's number is approximately \(6.022 \times 10^{23}\). This massive number helps bridge the microscopic world of atoms and molecules with the macroscopic world we observe. To visualize, imagine a mole of sand grains, and you'd have enough to cover all of Earth at the surface's depth. Though it's almost impossible to comprehend such large quantities without using concepts like Avogadro's number, this constant provides a manageable way to calculate, interpret, and understand the quantities involved in chemical reactions.

Molecule Calculations: Translating Moles to Molecules

Finding the number of molecules in a sample requires some simple calculations with Avogadro's number. It involves multiplying the number of moles by Avogadro's number to convert moles into actual number of molecules.Let's break it down:

• Identify the number of moles in your sample, which could be from laboratory measurements or a given value.
• Use the formula: Number of molecules = Number of moles \(\times\) Avogadro's number.
• Substitute the values in the formula to perform the calculation.

For example, to find out how many molecules are in 11.5 moles of water, multiply 11.5 moles by \(6.022 \times 10^{23}\) molecules/mol. This equals \(6.9253 \times 10^{24}\) molecules, providing a concrete figure to work with in scientific studies.

Chemical Quantities: Understanding Moles and Mass

Chemical quantities are essential to chemistry for converting between mass, moles, and number of particles. The mole is a core unit in chemistry that enables the quantification of substances in a straightforward manner. Consider these relationships:

• Mass to Moles: You can calculate how many moles are in a given mass by using a substance's molar mass, which is found on the periodic table.
• Moles to Particles: Use Avogadro's number to convert moles to particles, just like in the equation used in molecule calculations.

These conversions are foundational for experiments, allowing chemists to seamlessly shift between theoretical calculations and practical measurements. Understanding how to manipulate these quantities is crucial for mastering chemical reactions and stoichiometry.

Molecular Formula: The Blueprint of Chemical Compounds

The molecular formula provides the number and type of atoms present in a molecule of a compound. It serves as the blueprint, revealing the composition of elements in a specific molecule. Key aspects include:

• Exact Count: The molecular formula gives the exact number of each type of atom in the molecule, such as \(\text{H}_2\text{O}\), which specifies two hydrogen atoms and one oxygen atom per molecule.
• Comparison to Empirical Formula: While the empirical formula is simplified, showing the smallest ratio of atoms, the molecular formula contains actual counts.

Molecular formulas are used in calculations and chemical equations, providing clear communication among scientists and precise understanding of a compound's structure and behavior. Knowing the molecular formula is vital for grasping the innate properties and potential reactions involving the substance.