Question

Select the chemical equation that is correctly balanced. (A) \(\mathrm{Mg}+\mathrm{Cl}_2 \rightarrow 2 \mathrm{MgCl}\) (B) \(\mathrm{CH}_4+\mathrm{O}_2 \rightarrow \mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2\) (C) \(2 \mathrm{Al}+3 \mathrm{Cl}_2 \rightarrow 2 \mathrm{AlCl}_3\) (D) \(2 \mathrm{Na}+\mathrm{O}_2 \rightarrow \mathrm{Na}_2 \mathrm{O}\)

Short answer

The correctly balanced chemical equation is (C) \(2 \mathrm{Al}+3 \mathrm{Cl}_2 \rightarrow 2 \mathrm{AlCl}_3\).

Step-by-step solution

Testing equation (A)

In equation (A): \(\mathrm{Mg}+\mathrm{Cl}_2 \rightarrow 2 \mathrm{MgCl}\), we will count the number of elements on both sides: Reactants: 1 Mg and 2 Cl Products: 2 Mg and 2 Cl Since the number of Mg atoms is not equal on both sides, this equation is not balanced correctly.

Testing equation (B)

In equation (B): \(\mathrm{CH}_4+\mathrm{O}_2 \rightarrow \mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2\), we will count the number of elements on both sides: Reactants: 1 C, 4 H, and 2 O Products: 2 H, 1 C, 1 O, and 2 O Since the number of O atoms is not equal on both sides, this equation is not balanced correctly.

Testing equation (C)

In equation (C): \(2 \mathrm{Al}+3 \mathrm{Cl}_2 \rightarrow 2 \mathrm{AlCl}_3\), we will count the number of elements on both sides: Reactants: 2 Al and 6 Cl Products: 2 Al and 6 Cl Since the number of Al and Cl atoms is equal on both sides, this equation appears to be balanced correctly. However, we must still test equation (D) before making a final decision.

Testing equation (D)

In equation (D): \(2 \mathrm{Na}+\mathrm{O}_2 \rightarrow \mathrm{Na}_2 \mathrm{O}\), we will count the number of elements on both sides: Reactants: 2 Na and 2 O Products: 2 Na and 1 O Since the number of O atoms is not equal on both sides, this equation is not balanced correctly. Based on the analysis of each equation, the correct answer is: (C) \(2 \mathrm{Al}+3 \mathrm{Cl}_2 \rightarrow 2 \mathrm{AlCl}_3\) since it is the only equation with the same number of atoms for each element on both the reactant and product sides.

Key concepts

Stoichiometry

Exploring the realm of stoichiometry is akin to learning the language of chemistry. It's the quantitative study of the relationships between reactants and products in chemical reactions. Imagine you are baking cookies, and your recipe is exact: for every cup of sugar, you need two cups of flour. Stoichiometry works with similar ratios, but instead of cups of ingredients, chemists deal with moles of substances.

For instance, to fully comprehend an equation like equation (C), which relates to aluminum and chlorine forming aluminum chloride, one must be able to interpret the coefficients as 'mole ratios'. This means '2 moles of Al react with 3 moles of Cl₂ to produce 2 moles of AlCl₃'. These ratios allow for the prediction of how much product will form from given amounts of reactants, and vice versa, which is essential for applications like pharmaceuticals manufacturing or environmental engineering where precise chemical composition is critical.

Chemical Reactions

Chemical reactions are the transformative events of chemistry where reactants convert into products. Engaging with chemical reactions is like observing a dance where participants swap partners; atoms are the dancers and the bonds are their hands connecting them.

Each reaction has its unique choreography depicted in a chemical equation. For example, equation (C) describes a dance between aluminum atoms and chlorine molecules resulting in pairs of aluminum chloride. Learning to read these equations is pivotal in chemistry. The variety of reactions is vast - from simple combinations like the formation of water, \( 2 \mathrm{H}_2 + \mathrm{O}_2 \rightarrow 2 \mathrm{H}_2 \mathrm{O} \), to complex organic chemistry syntheses. Mastering the understanding of chemical reactions not only allows students to predict the outcome of mixing certain chemicals but also to manipulate the conditions to control the reaction rate and yield.

Conservation of Mass

The principle of conservation of mass is a cornerstone of science, famously articulated by Lavoisier as 'Nothing is lost, nothing is created, everything is transformed.' In the context of chemical equations, this principle dictates that the mass of the reactants must equal the mass of the products.

When balancing chemical equations like those in the exercise, the conservation of mass is the rule we follow to ensure the number of atoms for each element remains unchanged from reactants to products. This is not just an academic exercise but a reflection of the physical consistency of matter. It means that when balancing equation (A), if we start with one magnesium atom and two chlorine atoms, we must end with the same tally of atoms. In practice, for industries like chemical manufacturing or waste treatment, obeying the conservation of mass is critical for predicting yield and ensuring that processes are efficient and environmentally compliant.