Problem 50 - Chemistry Matter and Change

Question

Apply How many moles of \(\mathrm{K}, \mathrm{C},\) and 0 atoms are there in 1 \(\mathrm{mol}\) of \(\mathrm{K}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) ?

Step-by-Step Solution

Answer

2 moles of K, 2 moles of C, and 4 moles of O.

Step 1: Understand the Compound Structure

The compound \( \text{K}_2\text{C}_2\text{O}_4 \) represents the chemical potassium oxalate. The subscript numbers indicate the number of atoms of each type in one formula unit of the compound. Specifically, there are 2 potassium (\(\text{K}\)) atoms, 2 carbon (\(\text{C}\)) atoms, and 4 oxygen (\(\text{O}\)) atoms in each \( \text{K}_2\text{C}_2\text{O}_4 \) unit.

Step 2: Determine Moles of Atoms in 1 Mole of Compound

In 1 mole of \( \text{K}_2\text{C}_2\text{O}_4 \), there are: - 2 moles of \( \text{K} \) atoms (since each formula unit contains 2 \( \text{K} \) atoms),- 2 moles of \( \text{C} \) atoms (since each formula unit contains 2 \( \text{C} \) atoms),- 4 moles of \( \text{O} \) atoms (since each formula unit contains 4 \( \text{O} \) atoms).

Key Concepts

Understanding Chemical Formulas

Chemical formulas are like the recipes for molecules. They provide essential information about the number and type of each atom present in a molecule. For example, in the compound potassium oxalate, which is represented as \( \text{K}_2\text{C}_2\text{O}_4 \), the subscript numbers indicate how many atoms of each element are included in the formula unit.
These subscripts are crucial because they help you determine the composition of the molecule:

• The subscript after potassium (\( \text{K} \)) indicates there are 2 potassium atoms.
• After carbon (\( \text{C} \)), the subscript shows there are 2 carbon atoms.
• For oxygen (\( \text{O} \)), the subscript means there are 4 oxygen atoms.

This molecular formula serves as a shorthand notation that aids in both understanding the composition and performing chemical calculations. Recognizing the values associated with each subscript is the first step in moving forward with mole and atom calculations.

The Art of Mole Calculation

The mole is a fundamental unit in chemistry, serving as a bridge between the atomic and macroscopic scales. One mole contains Avogadro's number of entities, equivalent to \( 6.022 \times 10^{23} \). When it comes to chemical compounds like potassium oxalate \( (\text{K}_2\text{C}_2\text{O}_4) \), knowing the molecular formula allows you to calculate how many moles of each atom are present per mole of compound.
For instance:

• Since there are 2 \( \text{K} \) atoms per molecule, 1 mole of \( \text{K}_2\text{C}_2\text{O}_4 \) contains 2 moles of potassium atoms.
• Similarly, with 2 \( \text{C} \) atoms in each molecule, it equals 2 moles of carbon atoms per mole of compound.
• Finally, the 4 \( \text{O} \) atoms per unit means 4 moles of oxygen atoms in 1 mole of compound.

This approach allows chemists to predict the quantity of each element in a given amount of substance, making mole calculations an indispensable tool in chemical analysis and reactions.

The Process of Atom Counting

Atom counting involves determining the actual number of atoms in a sample, given the mole values. Using the mole concept, you can convert moles into atoms, facilitating a deeper understanding of a compound's structure.
Here's how to break it down:

• To find out how many potassium atoms are in 1 mole of \( \text{K}_2\text{C}_2\text{O}_4 \), multiply Avogadro's number \( (6.022 \times 10^{23}) \) by the 2 moles of \( \text{K} \) atoms present per mole of compound.
• Repeat the same for carbon: 2 moles of \( \text{C} \) times \( 6.022 \times 10^{23} \). This gives the exact number of carbon atoms.
• For oxygen, multiply 4 moles by Avogadro's number to determine the total number of oxygen atoms.

Each multiplication provides the total number of atoms in one mole of the compound. This practical skill is essential for calculating the number of atoms involved in reactions, ensuring precise chemical synthesis and analysis.