Question

Which of the following cquations is balanced? (1) \(5 \mathrm{BiO}_{3}+2 \mathrm{H}^{+}+\mathrm{Mn}^{2+} \longrightarrow 5 \mathrm{Bi}^{3+}+12 \mathrm{H}_{2} \mathrm{O}+\) \(\mathrm{MnO}_{4}^{-}\) (2) \(5 \mathrm{BiO}_{3}+14 \mathrm{H}^{+}+2 \mathrm{Mn}^{2+} \longrightarrow 5 \mathrm{Bi}^{3+}+7 \mathrm{H}_{2} \mathrm{O}+\) \(2 \mathrm{MnO}_{4}^{-}\) (3) \(2 \mathrm{BiO}_{3}+4 \mathrm{H}^{\prime}+\mathrm{Mn}^{21} \longrightarrow 2 \mathrm{Bi}^{31}+2 \mathrm{H}_{2} \mathrm{O}\) \(+\mathrm{MnO}_{4}\) (4) \(6 \mathrm{BiO}_{3}+12 \mathrm{II}+3 \mathrm{Mn}^{21} \longrightarrow 6 \mathrm{Bi}^{3}+6 \mathrm{II}_{2} \mathrm{O}\) \(+3 \mathrm{MnO}_{4}^{-}\)

Short answer

Equation 4 is balanced.

Step-by-step solution

Identify the Elements

List all the elements involved in the reaction to keep track of their counts.

Analyze Equation 1

Count the atoms for each element on both sides of the equation. Ensure the number of atoms for each element are the same on both sides.Reactants: 5 Bi, 15 O, 2 H, 1 MnProducts: 5 Bi, 12 O, 12 H, 1 Mn, 4 O (from MnO4)The equation is not balanced as the number of oxygen and hydrogen atoms are different on both sides.

Analyze Equation 2

Count the atoms for each element on both sides of the equation. Ensure the number of atoms for each element are the same on both sides.Reactants: 5 Bi, 15 O, 14 H, 2 MnProducts: 5 Bi, 7 O (from H2O), 14 H, 2 Mn, 8 O (from 2 MnO4)The equation is not balanced because the oxygen atoms differ on both sides.

Analyze Equation 3

Count the atoms for each element on both sides of the equation. Ensure the number of atoms for each element are the same on both sides.Reactants: 2 Bi, 6 O, 4 H, 1 MnProducts: 2 Bi, 2 O, 4 H, 1 Mn, 4 O (from MnO4)This equation is not balanced due to the difference in the number of oxygen atoms.

Analyze Equation 4

Count the atoms for each element on both sides of the equation. Ensure the number of atoms for each element are the same on both sides.Reactants: 6 Bi, 18 O, 12 H, 3 MnProducts: 6 Bi, 6 O (from H2O), 12 H, 3 Mn, 12 O (from 3 MnO4)This equation is balanced because the number of each type of atom is the same on both sides.

Key concepts

Stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to predict the amounts of substances consumed and produced. To be good at stoichiometry, you'll need to understand formulas, balance chemical equations, and know about mole ratios.
When balancing a chemical equation, you align the number of atoms for each element on both sides of the equation. This ensures the law of conservation of mass is upheld. Visualizing and imagining the reactants turning into products can also make it easier.
In the context of this exercise, to determine if a reaction is balanced, we follow the stoichiometric principles by counting and comparing the atoms of each element in the reactants and the products.
Why is it important?

• Helps in calculating reactants required and products formed.
• Ensures reactions conserve mass by following the law of conservation of mass.
• Essential in industrial processes and laboratory practices.

Counting Atoms

In a chemical equation, it's crucial to count the number of atoms for each element to ensure both sides are balanced. This may seem simple, but it often requires careful attention to detail.
Each chemical formula's subscript indicates the number of atoms of an element in a molecule. For example, in \(\text{H2O}\), the subscript '2' means there are two hydrogen atoms.
During the exercise, you followed these steps for counting atoms:

• Identify the elements: List all elements involved in the reaction.
• Count atoms in reactants and products: Ensure the count is the same on both sides.
• Adjust coefficients: Use coefficients on molecules to balance the equation.

A balanced equation will have the same number of each type of atom on both sides, which is fundamentally required for the stoichiometric calculations.
Key Point: Never alter subscripts to balance an equation! Instead, adjust the coefficients in front of the compounds or elements.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. These reactions occur when atomic bonds are broken and new bonds form. There are several types of chemical reactions, such as synthesis, decomposition, single replacement, and double replacement.
In any chemical reaction, the equation represents the process. For instance, in the exercise:
\(6 \text{BiO3} + 12 \text{H} + 3 \text{Mn}^{2+} \rightarrow 6 \text{Bi}^{3+} + 6 \text{H2O} + 3 \text{MnO4}^-\)
This reaction involves bismuth (Bi), hydrogen (H), and manganese (Mn), showing a transfer and sharing of electrons to create the products.
Steps in Analyzing a Reaction:

• Identify Types of Reactants and Products: Match them to known kinds of reactions.
• Write and Balance the Equation: Ensure mass and charge balance are achieved.
• Understand the Process: Conceptualize what reactant bonds break and what product bonds form.

Understanding these steps ensures a solid grip on chemical reactivity, crucial for predicting and manipulating chemical behaviors in practical applications.