Question

How many chromium atoms and how many oxygen atoms are indicated on the right side of this balanced chemical equation: $$ 4 \mathrm{Cr}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{Cr}_{2} \mathrm{O}_{3}(\mathrm{~g}) $$

Short answer

4 chromium atoms and 6 oxygen atoms.

Step-by-step solution

Understand the Balanced Equation

The balanced chemical equation is given as \(4 \mathrm{Cr}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{Cr}_{2} \mathrm{O}_{3}(\mathrm{~g})\). This represents the reaction of chromium with oxygen to produce chromium(III) oxide.

Identify the Product

Focus on the right side of the equation, where \(2 \mathrm{Cr}_{2} \mathrm{O}_{3}(\mathrm{~g})\) is the product. Each molecule of chromium(III) oxide is \(\mathrm{Cr}_{2} \mathrm{O}_{3}\), indicating 2 chromium atoms and 3 oxygen atoms per molecule.

Calculate Total Chromium Atoms

Since there are 2 molecules of \(\mathrm{Cr}_{2} \mathrm{O}_{3}\), multiply the number of chromium atoms per molecule by 2: \(2 \times 2 = 4\) chromium atoms.

Calculate Total Oxygen Atoms

Similarly, multiply the number of oxygen atoms per molecule by the number of molecules: \(2 \times 3 = 6\) oxygen atoms.

Key concepts

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, change into new substances called products. Viewing the balanced chemical equation \( 4 \mathrm{Cr}(\mathrm{s}) + 3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Cr}_{2} \mathrm{O}_{3}(\mathrm{g}) \), we see a reaction between chromium and oxygen. Here:

• The reactants are chromium (solid) and oxygen (gas).
• The product is chromium(III) oxide (gas).

The equation gives us the proportions in which reactants combine and transform into products. It tells us, specifically, that 4 atoms of solid chromium combine with 3 molecules of gaseous oxygen to form 2 formula units of chromium(III) oxide. Being balanced is essential because it reflects the conservation of mass principle, where the number of each type of atom is the same both before and after the reaction.

Atom Counting

Atom counting is vital for understanding and balancing chemical reactions. It involves determining the number of each type of atom on both sides of the equation. This ensures that the equation adheres to the law of conservation of mass.In the given equation:

• The product side, contain \(2 \mathrm{Cr}_{2} \mathrm{O}_{3}\), each molecule composed of 2 chromium atoms and 3 oxygen atoms.
• Multiply by the coefficient 2 given in \(2 \mathrm{Cr}_{2} \mathrm{O}_{3}\) to find the total counts:
• For chromium: \(2 \times 2 = 4\) chromium atoms.
• For oxygen: \(2 \times 3 = 6\) oxygen atoms.

Counting atoms helps confirm that the equation is balanced. We need the same quantity and type of each atom before and after the reaction. Here, 4 chromium and 6 oxygen atoms are present on the product side, showing a balanced equation.

Chromium(III) Oxide

Chromium(III) oxide, represented by the formula \( \mathrm{Cr}_{2} \mathrm{O}_{3} \), is an important compound in chemistry. In the context of the given chemical reaction, \( \mathrm{Cr}_{2} \mathrm{O}_{3} \) is the product formed when chromium and oxygen react together.Key attributes of chromium(III) oxide include:

• It is a dark green, inorganic compound often utilized in pigments and coatings.
• Chemically, it is formed by 2 chromium atoms bonded with 3 oxygen atoms.
• This specific arrangement leads to its usage in various industrial applications, including leather tanning and metal finishing.

Understanding the composition of \( \mathrm{Cr}_{2} \mathrm{O}_{3} \) helps us grasp why the reaction behaves as it does and how the atoms combine to form stable products. By knowing the number of each atom in the compound, we appreciate how the balanced chemical equation represents a real-world chemical transformation.