Question

Balance each of the following chemical equations. a. \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \rightarrow\) \(\mathrm{PbCrO}_{4}(s)+\mathrm{KNO}_{3}(a q)\) b. \(\mathrm{BaCl}_{2}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{BaSO}_{4}(s)+\mathrm{NaCl}(a q)\) c. \(\mathrm{CH}_{3} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) d. \(\mathrm{Na}_{2} \mathrm{CO}_{3}(a q)+\mathrm{S}(s)+\mathrm{SO}_{2}(g) \rightarrow\) \(\mathrm{CO}_{2}(g)+\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)\) e. \(\mathrm{Cu}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow\) \(\operatorname{CuSO}_{4}(a q)+\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) f. \(\operatorname{MnO}_{2}(s)+\operatorname{HCl}(a q) \rightarrow \operatorname{MnCl}_{2}(a q)+\mathrm{Cl}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) g. \(\mathrm{As}_{2} \mathrm{O}_{3}(s)+\mathrm{KI}(a q)+\mathrm{HCl}(a q) \rightarrow\) \(\mathrm{AsI}_{3}(s)+\mathrm{KCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) h. \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)+\mathrm{I}_{2}(a q) \rightarrow \mathrm{Na}_{2} \mathrm{S}_{4} \mathrm{O}_{6}(a q)+\mathrm{NaI}(a q)\)

Short answer

a. \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{K}_{2}\mathrm{CrO}_{4}(a q) \rightarrow\mathrm{PbCrO}_{4}(s)+2\mathrm{KNO}_{3}(a q)\) b. \(\mathrm{BaCl}_{2}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q) \rightarrow\mathrm{BaSO}_{4}(s)+2\mathrm{NaCl}(a q)\) c. \(\mathrm{CH}_{3} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \rightarrow\mathrm{CO}_{2}(g)+2\mathrm{H}_{2} \mathrm{O}(g)\) d. \(\mathrm{Na}_{2} \mathrm{CO}_{3}(a q)+2\mathrm{S}(s)+\mathrm{SO}_{2}(g)\rightarrow\mathrm{CO}_{2}(g)+2\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)\) e. \(\mathrm{Cu}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow\operatorname{CuSO}_{4}(a q)+\mathrm{SO}_{2}(g)+\frac{1}{2}\mathrm{H}_{2} \mathrm{O}(l)\) f. \(\mathrm{MnO}_{2}(s)+4\mathrm{HCl}(a q) \rightarrow\mathrm{MnCl}_{2}(a q)+\frac{1}{2}\mathrm{Cl}_{2}(g)+\frac{1}{2}\mathrm{H}_{2} \mathrm{O}(l)\) g. \(\operatorname{As}_{2} \mathrm{O}_{3}(s)+6\mathrm{KI}(a q)+6\mathrm{HCl}(a q)\rightarrow\mathrm{AsI}_{3}(s)+\mathrm{KCl}(a q)+3\mathrm{H}_{2} \mathrm{O}(l)\) h. \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)+2\mathrm{I}_{2}(a q)\rightarrow \mathrm{Na}_{2} \mathrm{S}_{4} \mathrm{O}_{6}(a q)+2\mathrm{NaI}(a q)\)

Step-by-step solution

Identify Elements

Identify all the unique elements in the equation: Pb, N, O, K, and Cr.

Balance Elements Individually

Balance each element one by one: Pb, N, O, K, and Cr.\[2\mathrm{KNO}_{3}(a q)\] So the balanced equation is: \[\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{K}_{2}\mathrm{CrO}_{4}(a q) \rightarrow\mathrm{PbCrO}_{4}(s)+2\mathrm{KNO}_{3}(a q)\] b. Balance \(\mathrm{BaCl}_{2}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q) \rightarrow\mathrm{BaSO}_{4}(s)+\mathrm{NaCl}(a q)\)

Identify Elements

Identify all the unique elements in the equation: Ba, Cl, Na, S, and O.

Balance Elements Individually

Balance each element one by one: Ba, Cl, Na, S, and O. \[2\mathrm{NaCl}(a q)\] So the balanced equation is: \[\mathrm{BaCl}_{2}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q) \rightarrow\mathrm{BaSO}_{4}(s)+2\mathrm{NaCl}(a q)\] c. Balance \(\mathrm{CH}_{3} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \rightarrow\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)

Identify Elements

Identify all the unique elements in the equation: C, H, and O.

Balance Elements Individually

Balance each element one by one: C, H, and O. \[2\mathrm{H}_{2} \mathrm{O}(g)\quad \mathrm{O}_{2}(g)\] So the balanced equation is: \[\mathrm{CH}_{3} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \rightarrow\mathrm{CO}_{2}(g)+2\mathrm{H}_{2} \mathrm{O}(g)\] d. Balance \(\mathrm{Na}_{2} \mathrm{CO}_{3}(a q)+\mathrm{S}(s)+\mathrm{SO}_{2}(g)\rightarrow\mathrm{CO}_{2}(g)+\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)\)

Identify Elements

Identify all the unique elements in the equation: Na, C, O, S.

Balance Elements Individually

Balance each element one by one: Na, C, O, and S. \[2\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)\] So the balanced equation is: \[\mathrm{Na}_{2} \mathrm{CO}_{3}(a q)+2\mathrm{S}(s)+\mathrm{SO}_{2}(g)\rightarrow\mathrm{CO}_{2}(g)+2\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)\] e. Balance \(\mathrm{Cu}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow\operatorname{CuSO}_{4}(a q)+\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\)

Identify Elements

Identify all the unique elements in the equation: Cu, H, S, and O.

Balance Elements Individually

Balance each element one by one: Cu, H, S, and O. \[\frac{1}{2}\mathrm{H}_{2} \mathrm{O}(l)\] So the balanced equation is: \[\mathrm{Cu}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow\operatorname{CuSO}_{4}(a q)+\mathrm{SO}_{2}(g)+\frac{1}{2}\mathrm{H}_{2} \mathrm{O}(l)\] f. Balance \(\mathrm{MnO}_{2}(s)+\mathrm{HCl}(a q) \rightarrow\mathrm{MnCl}_{2}(a q)+\mathrm{Cl}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\)

Identify Elements

Identify all the unique elements in the equation: Mn, O, H, and Cl.

Balance Elements Individually

Balance each element one by one: Mn, O, H, and Cl. \[4\mathrm{HCl}(a q)\quad \frac{1}{2}\mathrm{Cl}_{2}(g)\quad \frac{1}{2}\mathrm{H}_{2} \mathrm{O}(l)\] So the balanced equation is: \[\mathrm{MnO}_{2}(s)+4\mathrm{HCl}(a q) \rightarrow\mathrm{MnCl}_{2}(a q)+\frac{1}{2}\mathrm{Cl}_{2}(g)+\frac{1}{2}\mathrm{H}_{2} \mathrm{O}(l)\] g. Balance \(\operatorname{As}_{2} \mathrm{O}_{3}(s)+\mathrm{KI}(a q)+\mathrm{HCl}(a q)\rightarrow\mathrm{AsI}_{3}(s)+\mathrm{KCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

Identify Elements

Identify all the unique elements in the equation: As, O, K, I, H, and Cl.

Balance Elements Individually

Balance each element one by one: As, O, K, I, H, and Cl. \[6\mathrm{KI}(a q)\quad 6\mathrm{HCl}(a q)\] So the balanced equation is: \[\operatorname{As}_{2} \mathrm{O}_{3}(s)+6\mathrm{KI}(a q)+6\mathrm{HCl}(a q)\rightarrow\mathrm{AsI}_{3}(s)+\mathrm{KCl}(a q)+3\mathrm{H}_{2} \mathrm{O}(l)\] h. Balance \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)+\mathrm{I}_{2}(a q)\rightarrow \mathrm{Na}_{2} \mathrm{S}_{4} \mathrm{O}_{6}(a q)+\mathrm{NaI}(a q)\)

Identify Elements

Identify all the unique elements in the equation: Na, S, O, and I.

Balance Elements Individually

Balance each element one by one: Na, S, O, and I. \[2\mathrm{I}_{2}(a q)\quad 2\mathrm{NaI}(a q)\] So the balanced equation is: \[\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}(a q)+2\mathrm{I}_{2}(a q)\rightarrow \mathrm{Na}_{2} \mathrm{S}_{4} \mathrm{O}_{6}(a q)+2\mathrm{NaI}(a q)\]

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. It allows us to predict how much of each substance is needed or produced in a given reaction. Stoichiometry is based on the balanced chemical equation, which shows the stoichiometric coefficients of each reactant and product. These coefficients tell us the proportions in which chemicals react. For example, in the balanced reaction equation

• \(2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}\)

the coefficients indicate that two molecules of hydrogen react with one molecule of oxygen to form two molecules of water.
Using stoichiometry, you can determine the amount of reactants required or the amount of product formed. It is essential for chemical analysis in both theoretical calculations and real-world applications. Understanding this concept is crucial for tasks such as scaling reactions for industrial production or laboratory syntheses.

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, are transformed into different substances, called products. During a chemical reaction, the chemical bonds in the reactants are broken and new bonds are formed to create the products.
Chemical reactions can be classified into different types, such as

• synthesis (combination) reactions,
• decomposition reactions,
• single-replacement reactions, and
• double-replacement reactions.

Each type involves specific interactions between molecules or ions.
Reactions must follow certain rules, the most important being the conservation of mass, which means no atoms are lost or gained in the process. Additionally, chemical equations must be balanced to reflect this conservation, ensuring that the number of atoms for each element is the same on both sides of the equation. This concept pairs with stoichiometry to allow chemists to accurately describe and predict the behavior of reactions.

Reaction Balancing

Balancing chemical equations is an essential step in the study of stoichiometry. It ensures that the equation adheres to the law of conservation of mass, meaning that the quantity of each element remains constant throughout the reaction. To balance a chemical equation, one must ensure that the number of atoms for each element is equal on both the reactant and product sides.
The process usually involves:

• Listing all elements involved in the reaction.
• Counting the number of atoms for each element on both sides.
• Adding coefficients in front of chemical formulas to equalize the number of atoms.

Sometimes, trial and error is needed, adjusting coefficients until the correct balance is achieved. For instance, if the initial equation has unbalanced oxygen atoms, one must adjust the coefficients of the compounds containing oxygen accordingly.
This methodical approach helps chemists predict the outcomes of reactions and is crucial for practical applications such as creating new compounds or in energy release through combustion.

Conservation of Mass

The principle of conservation of mass states that mass cannot be created or destroyed in a chemical reaction. This principle was established by Antoine Lavoisier in the late 18th century and remains a core tenet of chemistry. It implies that the mass of the reactants in a chemical reaction must equal the mass of the products.
This principle underpins the need to balance chemical equations. If an equation is unbalanced, it would suggest that atomic matter could spontaneously appear or disappear in a reaction, which does not occur.
In practical terms, conservation of mass is essential in laboratory settings and in industrial chemistry, as it helps ensure that reactions are safe, efficient, and predictable. Engineers and chemists use this principle to calculate the quantities of materials needed and the likely yields of products, aiding in cost analysis and environmental safety assessments. Understanding conservation of mass, alongside complementary concepts like stoichiometry, provides a complete picture of chemical processes and their predictable nature.