Problem 64 - Chemistry Matter and Change

Question

When an oxide of potassium is decomposed, 19.55 g of \(\mathrm{K}\) and 4.00 \(\mathrm{g}\) of \(\mathrm{O}\) are obtained. What is the empirical formula for the compound?

Step-by-Step Solution

Answer

The empirical formula for the compound is \( \text{K}_2\text{O} \).

Step 1: Finding Moles of Potassium

First, find the moles of potassium. The molar mass of potassium (K) is approximately 39.1 g/mol. Use the formula for moles: \[ \text{moles of K} = \frac{\text{mass of K}}{\text{molar mass of K}} \]Substitute the given values:\[ \text{moles of K} = \frac{19.55}{39.1} \approx 0.500 \text{ moles} \]

Step 2: Finding Moles of Oxygen

Next, find the moles of oxygen. The molar mass of oxygen (O) is approximately 16.0 g/mol. Use the same formula for moles: \[ \text{moles of O} = \frac{\text{mass of O}}{\text{molar mass of O}} \]Substitute the given values:\[ \text{moles of O} = \frac{4.00}{16.0} = 0.250 \text{ moles} \]

Step 3: Determining the Empirical Formula

To find the empirical formula, compare the mole ratio of potassium to oxygen. Divide the moles of each element by the smallest number of moles found:For potassium: \[ \frac{0.500}{0.250} = 2 \]For oxygen:\[ \frac{0.250}{0.250} = 1 \]The ratio of potassium to oxygen is 2:1.

Step 4: Writing the Empirical Formula

Based on the mole ratio calculated, the empirical formula is composed of 2 potassium atoms for every 1 oxygen atom. Therefore, the empirical formula of the compound is \( \text{K}_2\text{O} \)

Key Concepts

Mole Calculation

Calculating moles is a fundamental concept in chemistry. Moles allow us to quantify the number of particles, such as atoms or molecules, in a given amount of substance. The mole is a basic unit in chemistry, often abbreviated as "mol." It's used to express amounts of a substance, defined as containing exactly 6.022 x 10²³ elementary entities (like atoms or molecules).

To determine moles from a given mass, the formula is simple:

• \[ \text{moles} = \frac{\text{mass of substance}}{\text{molar mass of substance}} \]

For instance, in this exercise, we determined the moles of potassium and oxygen using their respective molar masses. Every chemical element has a distinct molar mass, and these provide a bridge between the mass of a substance and the number of atoms or molecules it contains.

Potassium

Potassium is a soft, silvery-white alkali metal. It is one of the essential elements for life and plays a significant role in biological processes. In chemistry, potassium is represented by the symbol \( \text{K} \). It has an atomic number of 19.

Potassium is highly reactive, especially in water, where it forms \( \text{KOH} \) and hydrogen gas. Its reactivity makes it important in a variety of chemical reactions and compounds. The molar mass of potassium, used in mole calculations, is approximately 39.1 g/mol.

Oxygen

Oxygen, denoted by the symbol \( \text{O} \), is a vital element that supports life through its role in respiration and combustion processes. It is a non-metal and a member of the chalcogen group on the periodic table. Oxygen has an atomic number of 8.

In reactions, oxygen often forms oxides when combining with other elements. This includes potassium, forming potassium oxide (\( \text{K}_2\text{O} \)). To calculate moles of oxygen in any compound, its molar mass of around 16.0 g/mol serves as the basis.

Mole Ratio

Understanding mole ratios is crucial when determining empirical formulas, as they represent the simplest whole-number ratio of atoms in a compound. To find the mole ratio between two elements:

• First, calculate the moles of each individual element separately.
• Next, divide each amount by the smallest number of moles obtained. This process simplifies the ratio.

For the example given, the mole ratio of potassium to oxygen was found to be 2:1.

This means 2 atoms of potassium are found for every one atom of oxygen, resulting in the empirical formula \( \text{K}_2\text{O} \). Such ratios underline the importance of mole calculations in chemistry, reflecting the consistent relationship between reacting elements.