Question

Balance each of the following chemical equations. a. \(\mathrm{ZnCl}_{2}(a q)+\mathrm{Na}_{2} \mathrm{CO}_{3}(a q) \rightarrow \mathrm{ZnCO}_{3}(s)+\mathrm{NaCl}(a q)\) b. \(\mathrm{Al}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+\mathrm{H}_{2}(g)\) c. \(\operatorname{Mn}(s)+S(s) \rightarrow \operatorname{MnS}_{2}(s)\) d. \(C_{5} H_{12}(l)+O_{2}(g) \rightarrow C O_{2}(g)+H_{2} O(g)\) e. \(\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Br}_{2}(l) \rightarrow \mathrm{HBr}(a q)+\mathrm{HOBr}(a q)\) f. \(\operatorname{MnS}_{2}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{SO}_{2}(g)\) g. \(\mathrm{PbCl}_{2}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \rightarrow \mathrm{PbCrO}_{4}(s)+\mathrm{KCl}(a q)\) h. \(\mathrm{AgNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{SO}_{4}(s)+\mathrm{HNO}_{3}(a q)\)

Short answer

a. ZnCl\(_2\) + Na\(_2\)CO\(_3\) → ZnCO\(_3\) + 2NaCl b. 2Al + 3H\(_2\)SO\(_4\) → Al\(_2\)(SO\(_4\))\(_3\) + 3H\(_2\) c. Mn + 2S → MnS\(_2\) d. C\(_5\)H\(_{12}\) + 8O\(_2\) → 5CO\(_2\) + 6H\(_2\)O e. 2H\(_2\)O + Br\(_2\) → 2HBr + 2HOBr f. 2MnS\(_2\) + 5O\(_2\) → 2MnO\(_2\) + 2SO\(_2\) g. PbCl\(_2\) + K\(_2\)CrO\(_4\) → PbCrO\(_4\) + 2KCl h. 2AgNO\(_3\) + H\(_2\)SO\(_4\) → Ag\(_2\)SO\(_4\) + 2HNO\(_3\)

Step-by-step solution

a. Balancing ZnCl2 + Na2CO3 → ZnCO3 + NaCl Equation

First, list out the elements involved in the reaction: Zn, Cl, Na, C, and O. Then, identify the number of each element in the reactants and products: Reactants: \(\) 1 Zn, 2 Cl, 2 Na, 1 C, 3 O Products: \(\) 1 Zn, 1 Cl, 1 Na, 1 C, 3 O The equation is not balanced because of the different numbers of chlorine and sodium atoms. To balance the equation, put a coefficient of 2 before the NaCl: ZnCl\(_2\) + Na\(_2\)CO\(_3\) → ZnCO\(_3\) + 2NaCl Now, the number of atoms for each element is equal on both sides.

b. Balancing Al + H2SO4 → Al2(SO4)3 + H2 Equation

List the elements present in the reaction: Al, H, S, and O. Count the number of each element in the reactants and products: Reactants: \(\) 1 Al, 2 H, 1 S, 4 O Products: \(\) 2 Al, 2 H, 3 S, 12 O To balance aluminum, place a coefficient of 2 in front of Al: 2Al + H\(_2\)SO\(_4\) → Al\(_2\)(SO\(_4\))\(_3\) + H\(_2\) This gives the same amount of aluminum on both sides of the equation. Now, the only unbalanced element is sulfur. To balance sulfur, place a coefficient of 3 in front of H\(_2\)SO\(_4\): 2Al + 3H\(_2\)SO\(_4\) → Al\(_2\)(SO\(_4\))\(_3\) + 3H\(_2\) Now, the equation is balanced for all elements.

c. Balancing Mn + S → MnS2 Equation

The elements involved in the reaction are Mn and S. The number of atoms for each element in the reactants and products is as follows: Reactants: \(\) 1 Mn, 1 S Products: \(\) 1 Mn, 2 S To balance the sulfur atoms, place a coefficient of 2 in front of S: Mn + 2S → MnS\(_2\) The equation is now balanced.

d. Balancing C5H12 + O2 → CO2 + H2O Equation

List the elements present in the reaction: C, H, and O. Count the number of atoms for each element in the reactants and products: Reactants: \(\) 5 C, 12 H, 2 O Products: \(\) 1 C, 2 H, 3 O To balance carbon, place a coefficient of 5 in front of CO\(_2\): C\(_5\)H\(_{12}\) + O\(_2\) → 5CO\(_2\) + H\(_2\)O Now balance hydrogen by placing a coefficient of 6 in front of H\(_2\)O: C\(_5\)H\(_{12}\) + O\(_2\) → 5CO\(_2\) + 6H\(_2\)O Lastly, balance oxygen by placing a coefficient of 8 in front of O\(_2\): C\(_5\)H\(_{12}\) + 8O\(_2\) → 5CO\(_2\) + 6H\(_2\)O The equation is now balanced. Repeat the same process for the remaining chemical equations e, f, g, and h.

Key concepts

Chemical Reactions

Chemical reactions describe the process where substances, known as reactants, transform into different substances, known as products. These reactions are fundamental to understanding chemistry because they explain how compounds form, breakdown, and reconfigure to create new products with different properties.

Chemical reactions can involve simple changes, such as when two elements combine to form a compound, or more complex processes where multiple reactants produce several products. Recognizing the type of reaction is crucial, as it guides us on how elements will interact.

A chemical equation is a symbolic representation of a chemical reaction, showing the reactants and the products along with their quantities. This representation is key for scientists to predict how chemicals will behave and react under different conditions.

Stoichiometry

Stoichiometry is a branch of chemistry that quantitatively analyzes the reactants and products in a chemical reaction. It involves calculating the proportions of elements in compounds and determining how much of each reactant is needed or how much product will be formed.

In practical terms, stoichiometry helps us make predictions about reactions, ensuring that we can design experiments where reactants are fully consumed without wastage, or understand how much product can be expected from given reactants.

Understanding stoichiometry requires grasping the mole concept, which translates abstract chemical equations into usable measurements in the lab. Balancing equations is a direct application of stoichiometry because it ensures that we understand how atoms are shared between reactants and products.

Chemical Equation Balancing

Balancing chemical equations is the process of ensuring that a chemical equation accurately reflects the law of conservation of mass. This law states that in a chemical reaction, atoms are neither created nor destroyed. Therefore, the number of atoms for each element must be the same in both the reactants and products.

To balance a chemical equation, you adjust the coefficients—the numbers before the compounds—without altering the chemical structures themselves. Each equation is unique and requires a visual inspection of how each element is represented on either side.

Start by identifying any compound or element that appears in a single molecule form on each side, then progressively balance more complex substances. Typically, balance metals first, followed by non-metals, and finally oxygen and hydrogen. This systematic approach facilitates the proper balancing of chemical reactions.

Reactants and Products

In any chemical reaction, reactants are the starting materials that undergo a reaction to form new substances known as products. Understanding reactants and products is essential because it provides insight into the transformation that occurs during a reaction.

Reactants are typically found on the left side of a chemical equation, while products are on the right. This layout standard keeps chemical equations organized and consistent.

The nature of reactants can heavily influence the rate and outcome of a reaction. For example, solids, liquids, gases, and aqueous solutions often react differently. Knowledge about reactants allows scientists to control and manipulate conditions to optimize product yields.

When balancing equations, an important aspect is understanding how the identity and number of particles change from reactants to products, helping ensure the equation satisfies both physical and chemical laws.