Question

Balance each of the following chemical equations. a. \(\mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+\mathrm{CaCl}_{2}(a q) \rightarrow \mathrm{CaSO}_{4}(s)+\mathrm{NaCl}(a q)\) b. \(\mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{H}_{2}(g)\) c. \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{HCl}(a q) \rightarrow \mathrm{CaCl}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) d. \(\operatorname{Br}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{SO}_{2}(g) \rightarrow \mathrm{HBr}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q)\) e. \(\mathrm{NaOH}(s)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \rightarrow \mathrm{Na}_{3} \mathrm{PO}_{4}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) f. \(\operatorname{NaNO}_{3}(s) \rightarrow \operatorname{NaNO}_{2}(s)+\mathrm{O}_{2}(g)\) g. \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{NaOH}(a q)+\mathrm{O}_{2}(g)\) h \(\mathrm{i}(s)+\mathrm{S}_{8}(s) \rightarrow \mathrm{Si}_{2} \mathrm{~S}_{4}(s)\)

Short answer

a. \(1\mathrm{Na}_{2} \mathrm{SO}_{4} + 1\mathrm{CaCl}_{2} \rightarrow 1\mathrm{CaSO}_{4} + 2\mathrm{NaCl}\) b. \(3\mathrm{Fe} + 4\mathrm{H}_{2} \mathrm{O} \rightarrow 1\mathrm{Fe}_{3} \mathrm{O}_{4} + 4\mathrm{H}_{2}\) c. \(1\mathrm{Ca}(\mathrm{OH})_{2} + 2\mathrm{HCl} \rightarrow 1\mathrm{CaCl}_{2} + 2\mathrm{H}_{2} \mathrm{O}\) d. \(1\mathrm{Br}_{2} + 2\mathrm{H}_{2} \mathrm{O} + 1\mathrm{SO}_{2} \rightarrow 2\mathrm{HBr} + 1\mathrm{H}_{2} \mathrm{SO}_{4}\) e. \(3\mathrm{NaOH} + 1\mathrm{H}_{3} \mathrm{PO}_{4} \rightarrow 1\mathrm{Na}_{3} \mathrm{PO}_{4} + 3\mathrm{H}_{2} \mathrm{O}\) f. \(\mathrm{NaNO}_{3}(s) \rightarrow \mathrm{NaNO}_{2}(s)+\mathrm{O}_{2}(g)\) g. \(1\mathrm{Na}_{2} \mathrm{O}_{2} + 2\mathrm{H}_{2} \mathrm{O} \rightarrow 2\mathrm{NaOH} + 1\mathrm{O}_{2}\) h. \(2\mathrm{Si} + 1\mathrm{S}_{8} \rightarrow 1\mathrm{Si}_{2} \mathrm{~S}_{4}\)

Step-by-step solution

Identifying the reactants and products

The chemical equation is given as: \(\mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+\mathrm{CaCl}_{2}(a q) \rightarrow \mathrm{CaSO}_{4}(s)+\mathrm{NaCl}(a q)\) Reactants: \(\mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\) and \(\mathrm{CaCl}_{2}(a q)\) Products: \(\mathrm{CaSO}_{4}(s)\) and \(\mathrm{NaCl}(a q)\)

Balancing the equation

By adding coefficients to the reactants and products, we can balance the equation: \(1\mathrm{Na}_{2} \mathrm{SO}_{4} + 1\mathrm{CaCl}_{2} \rightarrow 1\mathrm{CaSO}_{4} + 2\mathrm{NaCl}\) b. Balancing the chemical equation for the reaction between iron and steam

Identifying the reactants and products

The chemical equation is given as: \(\mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{H}_{2}(g)\) Reactants: \(\mathrm{Fe}(s)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\) Products: \(\mathrm{Fe}_{3} \mathrm{O}_{4}(s)\) and \(\mathrm{H}_{2}(g)\)

Balancing the equation

By adding coefficients to the reactants and products, we can balance the equation: \(3\mathrm{Fe} + 4\mathrm{H}_{2} \mathrm{O} \rightarrow 1\mathrm{Fe}_{3} \mathrm{O}_{4} + 4\mathrm{H}_{2}\) c. Balancing the chemical equation for the reaction between calcium hydroxide and hydrochloric acid

Identifying the reactants and products

The chemical equation is given as: \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{HCl}(a q) \rightarrow \mathrm{CaCl}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) Reactants: \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)\) and \(\mathrm{HCl}(a q)\) Products: \(\mathrm{CaCl}_{2}(a q)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\)

Balancing the equation

By adding coefficients to the reactants and products, we can balance the equation: \(1\mathrm{Ca}(\mathrm{OH})_{2} + 2\mathrm{HCl} \rightarrow 1\mathrm{CaCl}_{2} + 2\mathrm{H}_{2} \mathrm{O}\) d. Balancing the chemical equation for the reaction among elemental bromine, water, and sulfur dioxide

Identifying the reactants and products

The chemical equation is given as: \(\mathrm{Br}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{SO}_{2}(g) \rightarrow \mathrm{HBr}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q)\) Reactants: \(\mathrm{Br}_{2}(g)\), \(\mathrm{H}_{2} \mathrm{O}(l)\), and \(mathrm{SO}_{2}(g)\) Products: \(\mathrm{HBr}(a q)\) and \(\mathrm{H}_{2} \mathrm{SO}_{4}(a q)\)

Balancing the equation

By adding coefficients to the reactants and products, we can balance the equation: \(1\mathrm{Br}_{2} + 2\mathrm{H}_{2} \mathrm{O} + 1\mathrm{SO}_{2} \rightarrow 2\mathrm{HBr} + 1\mathrm{H}_{2} \mathrm{SO}_{4}\) e. Balancing the chemical equation for the reaction between sodium hydroxide and phosphoric acid

Identifying the reactants and products

The chemical equation is given as: \(\mathrm{NaOH}(s)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \rightarrow \mathrm{Na}_{3} \mathrm{PO}_{4}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) Reactants: \(\mathrm{NaOH}(s)\) and \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q)\) Products: \(\mathrm{Na}_{3} \mathrm{PO}_{4}(a q)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\)

Balancing the equation

By adding coefficients to the reactants and products, we can balance the equation: \(3\mathrm{NaOH} + 1\mathrm{H}_{3} \mathrm{PO}_{4} \rightarrow 1\mathrm{Na}_{3} \mathrm{PO}_{4} + 3\mathrm{H}_{2} \mathrm{O}\) f. Balancing the chemical equation for the decomposition of sodium nitrate

Identifying the reactant and products

The chemical equation is given as: \(\mathrm{NaNO}_{3}(s) \rightarrow \mathrm{NaNO}_{2}(s)+\mathrm{O}_{2}(g)\) Reactant: \(\mathrm{NaNO}_{3}(s)\) Products: \(\mathrm{NaNO}_{2}(s)\) and \(\mathrm{O}_{2}(g)\)

Balancing the equation

The equation is already balanced. g. Balancing the chemical equation for the reaction between sodium peroxide and water

Identifying the reactants and products

The chemical equation is given as: \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{NaOH}(a q)+\mathrm{O}_{2}(g)\) Reactants: \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) Products: \(\mathrm{NaOH}(a q)\) and \(\mathrm{O}_{2}(g)\)

Balancing the equation

By adding coefficients to the reactants and products, we can balance the equation: \(1\mathrm{Na}_{2} \mathrm{O}_{2} + 2\mathrm{H}_{2} \mathrm{O} \rightarrow 2\mathrm{NaOH} + 1\mathrm{O}_{2}\) h. Balancing the chemical equation for the reaction between silicon and elemental sulfur

Identifying the reactants and products

The chemical equation is given as: \(\mathrm{Si}(s)+\mathrm{S}_{8}(s) \rightarrow \mathrm{Si}_{2} \mathrm{~S}_{4}(s)\) Reactants: \(\mathrm{Si}(s)\) and \(\mathrm{S}_{8}(s)\) Product: \(\mathrm{Si}_{2} \mathrm{~S}_{4}(s)\)

Balancing the equation

By adding coefficients to the reactants and products, we can balance the equation: \(2\mathrm{Si} + 1\mathrm{S}_{8} \rightarrow 1\mathrm{Si}_{2} \mathrm{~S}_{4}\)

Key concepts

Stoichiometry

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It's like a recipe: if you know the amounts of each ingredient you start with, you can predict how much of the final product you'll end up with. For example, the balanced chemical equation for the reaction of calcium hydroxide and hydrochloric acid, \(\mathrm{Ca}(\text{OH})_{2} + 2\text{HCl} \rightarrow \mathrm{CaCl}_{2} + 2\text{H}_2\text{O}\), shows that one mole of calcium hydroxide reacts with two moles of hydrochloric acid to produce one mole of calcium chloride and two moles of water.

Understanding stoichiometry is essential for balancing chemical equations because it helps us ensure that the same number of atoms of each element is present on both sides of the equation. This is a law known as the conservation of mass. When you're working through textbook exercises or homework, always start by identifying the reactants and products, just like in the solutions provided above. Then, use stoichiometry to determine the correct coefficients that balance the equation.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds, leading to new substances with different properties. These are the fascinating events where the ingredients (reactants) change into the cooked dish (products). It's essential to remember that chemical reactions follow the law of conservation of mass: the mass of the reactants equals the mass of the products.

In our daily lives, these reactions are everywhere, from the rusting of iron in the presence of water and oxygen to the digestion of food in our bodies. When studying reactions like the decomposition of sodium nitrate, \(\mathrm{NaNO}_{3} \rightarrow \mathrm{NaNO}_{2} + \text{O}_{2}\), it is not only important to balance the equation but also to grasp the type of reaction occurring, which is decomposition in this case. Observing such patterns can help you predict the products and balance future equations more quickly.

Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction where the reactants are shown on the left and the products on the right, often separated by an arrow indicating the direction of the reaction. Think of it as a snapshot that captures the essence of the chemical process. Each substance is represented by its chemical formula, and coefficients are added to the formulae to balance the equation.

Take, for instance, the reaction between silicon and sulfur, \(2\mathrm{Si} + \mathrm{S}_{8} \rightarrow \mathrm{Si}_{2} \mathrm{S}_{4}\). Here, the coefficients indicate that two atoms of silicon react with an eight-atom molecule of sulfur to produce a compound consisting of two silicon atoms and four sulfur atoms. It's essential to know how to read and write chemical equations because they are the language through which chemists communicate their science. While balancing, ensure that all atoms' tally is equal on both sides, thus validating the principle of conservation of mass and charge.