Question

Which of the following equations are balanced? Balance those that need it. (a) \(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) (b) \(3 \mathrm{Ca}(\mathrm{OH})_{2}(a q)+2 \mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow\) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(a q)+6 \mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\) (d) \(\mathrm{K}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{KOH}(a q)+\mathrm{H}_{2}(g)\)

Short answer

(a) and (b) are balanced; balance (c) using \(2\text{Mg}\) and (d) using \(2\text{K}\) and \(2\text{H}_2\text{O}\).

Step-by-step solution

Verify Equation (a)

The given equation is: \[2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\] Count the atoms on both sides. Reactants have 4 carbon atoms and 12 hydrogen atoms (from \(2 \mathrm{C}_{2} \mathrm{H}_{6}\)) and 10 oxygen atoms (from \(5 \mathrm{O}_{2}\)). Products have 4 carbon atoms, 12 hydrogen atoms, and 10 oxygen atoms (from \(2 \mathrm{CO}_{2}\) and \(6 \mathrm{H}_{2} \mathrm{O}\)). Atoms are equal on both sides; hence the equation is balanced.

Verify Equation (b)

The given equation is: \[3 \mathrm{Ca}(\mathrm{OH})_{2}(aq)+2 \mathrm{H}_{3} \mathrm{PO}_{4}(aq) \rightarrow \mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}(aq)+6 \mathrm{H}_{2} \mathrm{O}(l)\] Count the atoms: Reactants have 3 calcium, 6 oxygen, 6 hydrogen (from \(3 \mathrm{Ca}(\mathrm{OH})_{2}\)), and 6 hydrogen, 8 oxygen, and 2 phosphorus (from \(2 \mathrm{H}_{3} \mathrm{PO}_{4}\)). Products have 3 calcium, 8 oxygen, and 2 phosphorus (from \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}\)), and 12 hydrogen and 6 oxygen (from \(6 \mathrm{H}_{2} \mathrm{O}\)). The elements match on both sides, indicating a balanced equation.

Verify Equation (c)

The given equation is: \[\mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\] Count the atoms: On the reactant side, there is 1 magnesium and 2 oxygen atoms; on the product side, 2 magnesium atoms and 2 oxygen atoms. Balance the magnesium by rewriting: \[2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{MgO}(s)\] Now, there are 2 magnesium and 2 oxygen atoms on each side. The equation is balanced.

Verify Equation (d)

The given equation is: \[\mathrm{K}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{KOH}(aq)+\mathrm{H}_{2}(g)\] Count the atoms: On the reactant side, there is 1 potassium, 2 hydrogen, and 1 oxygen; on the product side, 1 potassium, 1 oxygen, and 3 hydrogen (from \(\mathrm{KOH}\) and \(\mathrm{H}_{2}\)). Balance the hydrogen by rewriting: \[2 \mathrm{K}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{KOH}(aq)+\mathrm{H}_{2}(g)\] Now, there are 2 potassium, 4 hydrogen, and 2 oxygen on each side. The equation is balanced.

Key concepts

Chemical Reactions

Chemical reactions happen when substances interact and transform into new substances. This process involves the breaking and forming of chemical bonds between atoms. Understanding how these transformations occur is fundamental to chemistry. When a chemical reaction takes place, the original substances, called reactants, undergo changes that result in new substances known as products.
A key indicator of a chemical reaction is an observable change, which can include color change, temperature change, gas production, or the formation of a precipitate. By observing these changes, we can understand more about the substances involved and the power behind those transformations.

Stoichiometry

Stoichiometry is like a recipe for chemical reactions. It helps us figure out the precise amounts of reactants and products involved. This involves using the balanced chemical equation to determine the relative quantities of substances.
For students, learning stoichiometry is crucial. It enables them to predict how much product a certain quantity of reactants will produce or how much reactant is needed to form a desired amount of product.

• It involves using molar ratios, which are derived from the coefficients of substances in a balanced chemical equation.
• These ratios allow chemists to calculate the exact amounts of participants in a reaction.
• Mastering stoichiometry is like having the key to understanding and correctly predicting chemical interactions.

Chemical Equations

Chemical equations are shorthand descriptions of chemical reactions. They display reactants transforming into products.
A correct chemical equation should be balanced, reflecting the conservation of mass where atoms must be equal on both sides of the equation. This means that the amount of each element remains the same before and after the reaction.

• Balancing these equations is essential as it ensures no atoms are lost or gained during the reaction.
• Each type of atom is conserved, and the total mass of reactants equals the total mass of products.

When an equation is unbalanced, that indicates a need for adjustment, using coefficients to equalize the number of atoms for each element on both sides.

Educational Chemistry

Educational chemistry revolves around making complex scientific concepts comprehensible for learners at different levels. This branch of science education focuses on engaging learners through simplified explanations and interactive techniques.
Chemistry education serves as a foundation for diverse scientific understanding, from everyday phenomena to advanced scientific research. Providing clear and engaging educational content helps students cultivate a genuine fascination for chemistry.

• This field encourages the development of problem-solving skills via exercises like balancing equations, which enhance logical thinking and analytical abilities.
• It also inspires curiosity, motivating students to explore deeper into the subject matter.
• The ultimate goal is to demystify chemistry, turning it from an intimidating subject into an exciting and approachable discipline.