Question

Determine whether each of the following equations is balanced or not balanced: a. \(\mathrm{PCl}_{3}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(s)\) b. \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)\) c. \(2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+\mathrm{O}_{2}(g)\) d. \(\mathrm{Mg}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Mg}_{3} \mathrm{~N}_{2}(s)\)

Short answer

a. Balanced b. Balanced c. Not balanced; correct by changing \(\text{O}_{2}\) to \(\text{3O}_{2}\) d. Not balanced; correct by changing \(\text{Mg}\) to \(\text{3Mg}\).

Step-by-step solution

Write down each equation

Begin by writing down each given chemical equation clearly. a. \(\text{PCl}_{3}(s)+\text{Cl}_{2}(g) \rightarrow \text{PCl}_{5}(s)\) b. \(\text{CO}(g) + 2\text{H}_{2}(g) \rightarrow \text{CH}_{3}\text{OH}(g)\) c. \(\text{2KClO}_{3}(s) \rightarrow \text{2KCl}(s) + \text{O}_{2}(g)\) d. \(\text{Mg}(s) + \text{N}_{2}(g) \rightarrow \text{Mg}_{3}\text{N}_{2}(s)\)

Balance the first equation (a)

For \(\text{PCl}_{3}(s) + \text{Cl}_{2}(g) \rightarrow \text{PCl}_{5}(s)\), count the atoms of each element on both sides:- Reactants: 1 P, 5 Cl- Products: 1 P, 5 ClSince the number of each type of atom is the same on both sides, this equation is balanced.

Balance the second equation (b)

For \(\text{CO}(g) + 2\text{H}_{2}(g) \rightarrow \text{CH}_{3}\text{OH}(g)\), count the atoms:- Reactants: 1 C, 1 O, 4 H- Products: 1 C, 1 O, 4 HThe number of each type of atom is the same on both sides, so this equation is balanced.

Balance the third equation (c)

For \(\text{2KClO}_{3}(s) \rightarrow \text{2KCl}(s) + \text{O}_{2}(g)\), count the atoms:- Reactants: 2 K, 2 Cl, 6 O- Products: 2 K, 2 Cl, 2 OThe number of oxygen atoms is not the same on both sides. Adjust it by changing the product to \(\text{3O}_{2}\). Updated equation: \(\text{2KClO}_{3}(s) \rightarrow \text{2KCl}(s) + \text{3O}_{2}(g)\), now it's balanced.

Balance the fourth equation (d)

For \(\text{Mg}(s) + \text{N}_{2}(g) \rightarrow \text{Mg}_{3}\text{N}_{2}(s)\), count the atoms:- Reactants: 1 Mg, 2 N- Products: 3 Mg, 2 NThe number of Mg atoms is not the same on both sides. Adjust it to match by placing a coefficient of 3 before Mg in the reactants. Updated equation: \(\text{3Mg}(s) + \text{N}_{2}(g) \rightarrow \text{Mg}_{3}\text{N}_{2}(s)\), now it's balanced.

Key concepts

chemical reactions

Chemical reactions are processes where substances, known as reactants, undergo transformation to form new substances, called products. This transformation involves breaking existing chemical bonds and forming new ones. In a chemical reaction, the substances involved can change in composition, state, and properties. For instance:
1. **Combination Reactions**: Two or more reactants combine to form a single product, like in the reaction between hydrogen and oxygen to form water.
2. **Decomposition Reactions**: A complex molecule breaks down into simpler substances, like the breakdown of water into hydrogen and oxygen.
By understanding chemical reactions, we can predict how different substances will interact and the types of products that will form.

stoichiometry

Stoichiometry is the study of the quantitative relationships between the reactants and products in a chemical reaction. It allows us to predict the amounts of substances consumed and produced. Here's how you can understand it better:
1. **Coefficients**: These numbers in front of chemical formulas indicate the proportion of molecules or moles involved.
2. **Mole Concept**: A mole is a unit that measures the amount of substance. One mole contains Avogadro's number of entities (atoms, molecules, etc.).
3. **Balanced Equations**: These equations adhere to the Law of Conservation of Mass, showing the same number of each type of atom on both sides.
Stoichiometry is crucial for tasks like calculating yield in chemical manufacturing or ensuring the right mix of ingredients in a state-of-the-art chemical lab.

atom conservation

The principle of atom conservation means that the number of atoms of each element must be the same before and after a reaction. This is due to the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction. Here's a deeper look:
1. **Reactants and Products**: Always count the atoms of each element on both sides of the equation.
2. **Balancing Process**: Adjust coefficients of the reactants and products to ensure the same number of atoms for each element. For example, \( \text{2H}_2 + \text{O}_2 \rightarrow \text{2H}_2\text{O} \)
3. **Importance**: Ensures accurate representation and calculation of the substances involved.
By applying atom conservation, scientists can reliably predict the outcomes of chemical reactions.

reactants and products

In a chemical reaction, reactants are the starting substances that react to form products, the new substances formed. Understanding this relationship is key to analyzing chemical reactions:
1. **Reactants**: These are listed on the left side of the chemical equation. For instance, in the reaction \( \text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O} \), hydrogen and oxygen are reactants.
2. **Products**: These appear on the right side of the equation. Using the previous example, water is the product.
3. **Reaction Direction**: The arrow (\( \rightarrow \)) shows the direction from reactants to products.
4. **Identifying Changes**: Products will have different properties from reactants due to the reorganization of atoms.
This fundamental concept allows us to understand how substances interact and transform during chemical reactions, forming the basis for further chemical study and application.