Question

Balance each of the following skeletal equations: (a) \(\mathrm{Al}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{AlCl}_{3}(s)\) (b) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \longrightarrow\) \(\mathrm{PbCrO}_{4}(a q)+\mathrm{KNO}_{3}(a q)\) (c) \(\mathrm{Li}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{LiOH}(a q)+\mathrm{H}_{2}(g)\) (d) \(\mathrm{C}_{6} \mathrm{H}_{14}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

The balanced equations are: (a) \(\mathrm{Al}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{AlCl}_{3}(s)\), (b) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \longrightarrow \mathrm{PbCrO}_{4}(a q)+2\mathrm{KNO}_{3}(a q)\), (c) \(2\mathrm{Li}(s)+2\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2\mathrm{LiOH}(a q)+\mathrm{H}_{2}(g)\), and (d) \(\mathrm{C}_{6} \mathrm{H}_{14}(g)+9\mathrm{O}_{2}(g) \longrightarrow 6\mathrm{CO}_{2}(g)+7\mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-step solution

Balancing Equation a

This equation \(\mathrm{Al}(s) + \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{AlCl}_{3}(s)\) is already balanced, as there is one Al atom and three Cl atoms on both sides of the equation.

Balancing Equation b

Balancing the lead and chromium first: \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \longrightarrow \mathrm{PbCrO}_{4}(a q)+\mathrm{KNO}_{3}(a q)\) \n Now balance the nitrate ions: \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \longrightarrow \mathrm{PbCrO}_{4}(a q)+2\mathrm{KNO}_{3}(a q)\) \n Lastly, balance the potassium ions: \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2\mathrm{K}_{2} \mathrm{CrO}_{4}(a q) \longrightarrow \mathrm{PbCrO}_{4}(a q)+2\mathrm{KNO}_{3}(a q)\)

Balancing Equation c

\(\mathrm{Li}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2\mathrm{LiOH}(a q)+\mathrm{H}_{2}(g)\) ensures one Lithium and two Oxygen are on both sides, but there are four Hydrogen atoms on the product side now. Balance the Hydrogen atoms: \(\mathrm{2Li}(s)+\mathrm{2H}_{2} \mathrm{O}(l) \longrightarrow 2\mathrm{LiOH}(a q)+\mathrm{H}_{2}(g)\)

Balancing Equation d

Balance the Carbon atoms first: \(\mathrm{C}_{6} \mathrm{H}_{14}(g)+\mathrm{O}_{2}(g) \longrightarrow 6\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) \n Balance the Hydrogen atoms next: \(\mathrm{C}_{6} \mathrm{H}_{14}(g)+\mathrm{O}_{2}(g) \longrightarrow 6\mathrm{CO}_{2}(g)+7\mathrm{H}_{2} \mathrm{O}(g)\) \n Finally balance the Oxygen atoms: \(\mathrm{C}_{6} \mathrm{H}_{14}(g)+9\mathrm{O}_{2}(g) \longrightarrow 6\mathrm{CO}_{2}(g)+7\mathrm{H}_{2} \mathrm{O}(g)\)

Key concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It serves as a vital tool in chemistry, helping us understand how atoms and molecules interact to form different substances. The main goal of stoichiometry is to ensure that we maintain a balance of the elements involved in a reaction. It relies on the concept that in a balanced equation, the amount of each element is the same on both sides of the equation. This relationship makes it possible to predict the amount of products formed from given amounts of reactants. Key principles of stoichiometry include:

• Mole ratios, which are derived from the coefficients of a balanced equation.
• Conversion between moles, mass, and volume.
• Use of the ideal gas law when dealing with gaseous substances.

By understanding stoichiometry, we can precisely measure how much of each substance is needed in a reaction, ensuring that the reaction proceeds with maximum efficiency and minimal waste.

Chemical Reaction

A chemical reaction is a process through which substances, known as reactants, are transformed into different substances called products. This transformation involves the breaking and forming of chemical bonds, leading to changes in energy and structure. Understanding chemical reactions is crucial because they are at the core of both natural processes and industrial manufacturing. Here are some aspects to consider:

• Reactants and products are represented by chemical formulas.
• The reaction may involve heat, light, electricity, or catalysts.
• Chemical reactions can be classified into various types, such as synthesis, decomposition, combustion, and more.

In any given chemical reaction, it is important to understand the roles of the different substances involved and the conditions under which the reaction occurs for predicting the outcomes effectively.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions, showing the reactants and products with their respective quantities. A balanced chemical equation obeys the law of conservation of mass and accurately represents how matter is conserved. To craft such an equation, follow these steps:

• Write the unbalanced equation, using correct formulas for all reactants and products.
• Balance each element one at a time, using coefficients to equalize the number of atoms on both sides.
• Check your work by verifying that the total number of atoms for each element is equal on both sides.

Balanced chemical equations are essential for conducting stoichiometric calculations and for understanding the proportions involved in the reaction.

Law of Conservation of Mass

The law of conservation of mass is a fundamental principle in chemistry which states that mass is neither created nor destroyed in any ordinary chemical reaction. This means the mass of the reactants must equal the mass of the products. In practical terms, it implies that:

• The total number of atoms for each element must be the same before and after a reaction.
• This principle is crucial when balancing chemical equations.
• Any discrepancies in mass indicate an unaccounted error, often requiring recalibration or reevaluation of the chemical equation.

The law of conservation of mass is critical for accurately predicting the quantities required and produced in chemical reactions, ensuring that chemical processes remain efficient and sustainable.