Problem 27 - General Chemistry: Principles and Modern Applications

Question

Without doing detailed calculations, arrange the following in order of increasing \(\% \mathrm{Cr},\) by mass, and explain your reasoning: \(\mathrm{CrO}, \mathrm{Cr}_{2} \mathrm{O}_{3}, \mathrm{CrO}_{2}, \mathrm{CrO}_{3}\)

Step-by-Step Solution

Answer

The compounds in increasing order by Chromium mass percentage are: CrO, Cr2O3, CrO2, CrO3.

Step 1: Understand the Chemistry

First, we need to understand that the higher the number of Oxygen atoms in the compound, the lesser will be the percentage of Chromium. This is due to the addition of the mass of the Oxygen atoms which will cause the percentage by mass of Chromium to decrease.

Step 2: Get the Cr and O Atomic Mass

Using the periodic table, Chromium (Cr) has an atomic weight of approximately 52 while Oxygen (O) has an approximate atomic weight of 16. This information will help to understand how the presence of oxygen impacts the mass percentage of Chromium.

Step 3: Arrange Compounds

Since we're not required to do the detailed calculations, we can now arrange the compounds in increasing order of Chromium by mass percentage: CrO3, CrO2, Cr2O3, CrO. In this order, the oxygen atoms increase from one to three causing the Chromium percentage to decrease.

Key Concepts

Atomic Mass

Understanding atomic mass is crucial in chemistry calculations. Atomic mass, sometimes known as atomic weight, is the mass of an atom expressed in atomic mass units (amu).

• The atomic mass for each element is found on the periodic table and is a weighted average that considers the different isotopes of the element.
• For example, Chromium (Cr) has an atomic mass of approximately 52 amu, while Oxygen (O) has about 16 amu.

This knowledge allows us to compare the mass of different atoms, such as how many times heavier a chromium atom is compared to an oxygen atom. It is also the foundation for calculating the molecular weight of compounds.

Chemistry Concepts

The basic principles of chemistry are essential for explaining the behavior of compounds. In the context of the compound analysis, we focus on the composition of molecules.

• Molecules are formed by atoms of different elements bonding together, and each element contributes its own mass based on its atomic mass.
• Understanding the molecular formula, like in chromium compounds such as CrO, Cr₂O₃, CrO₂, and CrO₃, helps typify how many atoms of each element are part of the compound.

In the problem analyzed, the focus is on how adding more oxygen atoms impacts the total molecular mass. Increasing oxygen results in less mass percentage being attributed to chromium due to oxygen's contribution being more significant.

Mass Percentage Calculation

Mass percentage is a concept that allows us to determine what portion of a compound's mass is made up by each element.To calculate it, the formula is as follows: \[ \% \text{Mass of Element} = \left( \frac{\text{Mass of element in 1 mole of compound}}{\text{Mass of 1 mole of compound}} \right) \times 100 \% \] Let's break down the process:

• First, identify the atomic masses of every element in the compound (e.g., Cr and O).
• Use the molecular formula to find the mass contributed by each element in the compound.
• Sum the individual contributions to get the total molar mass.
• Finally, the mass percentage of an element like chromium in a compound gives insight into how much of the compound’s total mass is composed of that specific element.

For instance, with compounds like Chromium(III) oxide, Cr₂O₃, as the number of oxygen atoms increases, the total molecular weight increases, but the chromium content, by percentage, decreases.