Question

Balance these combustion reactions. (a) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{C}_{5} \mathrm{H}_{12}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{C}_{7} \mathrm{H}_{14} \mathrm{O}_{2}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Short answer

(a) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} + 6\mathrm{O}_2 \rightarrow 6 \mathrm{CO}_{2} + 6 \mathrm{H}_{2} \mathrm{O}\); (b) \(\mathrm{C}_{5} \mathrm{H}_{12} + 8\mathrm{O}_{2} \rightarrow 5 \mathrm{CO}_{2} + 6 \mathrm{H}_{2} \mathrm{O}\); (c) \(\mathrm{C}_{7} \mathrm{H}_{14} \mathrm{O}_{2} + 9\mathrm{O}_{2} \rightarrow 7 \mathrm{CO}_{2} + 7 \mathrm{H}_{2} \mathrm{O}\); (d) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2} + 2\mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2} + 2 \mathrm{H}_{2} \mathrm{O}\).

Step-by-step solution

Identify the elements to balance

In each combustion reaction, identify the elements that need to be balanced: carbon (C), hydrogen (H), and oxygen (O). Count the number of each element in the reactants and products for each reaction.

Balance carbon atoms

Start by balancing the carbon atoms for each reaction. Adjust the coefficient of carbon dioxide (\(\mathrm{CO}_{2}\)) in the products so that the number of carbon atoms matches those in the reactants.

Balance hydrogen atoms

Balance the hydrogen atoms by adjusting the coefficient of water (\(\mathrm{H}_{2}\mathrm{O}\)) in the products. Ensure the number of hydrogen atoms matches the number in the reactants.

Balance oxygen atoms

Count the total number of oxygen atoms in the balanced \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\) on the products side. Then, balance the oxygen atoms by adjusting the coefficient of \(\mathrm{O}_{2}\) in the reactants.

Verify the balance

Check each reaction to ensure all elements are balanced. Total atoms for each element should be the same on both sides of the equation.

Solution (a): Balance reaction of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)

Balanced Reaction: \[ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} + 6\mathrm{O}_2 \rightarrow 6 \mathrm{CO}_{2} + 6 \mathrm{H}_{2} \mathrm{O} \]

Solution (b): Balance reaction of \(\mathrm{C}_{5} \mathrm{H}_{12}\)

Balanced Reaction: \[ \mathrm{C}_{5} \mathrm{H}_{12} + 8\mathrm{O}_{2} \rightarrow 5 \mathrm{CO}_{2} + 6 \mathrm{H}_{2} \mathrm{O} \]

Solution (c): Balance reaction of \(\mathrm{C}_{7} \mathrm{H}_{14} \mathrm{O}_{2}\)

Balanced Reaction: \[ \mathrm{C}_{7} \mathrm{H}_{14} \mathrm{O}_{2} + 9\mathrm{O}_{2} \rightarrow 7 \mathrm{CO}_{2} + 7 \mathrm{H}_{2} \mathrm{O} \]

Solution (d): Balance reaction of \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\)

Balanced Reaction: \[ \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2} + 2\mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \]

Key concepts

Balancing Chemical Equations

Balancing chemical equations is about ensuring that the same number of each type of atom appears on both sides of the equation. This is crucial because chemical reactions must follow the law of conservation of mass, meaning no atoms are lost or gained in a reaction. To balance an equation:

• Identify all elements in the reaction.
• Count the number of atoms of each element in both reactants and products.
• Adjust the coefficients (numbers in front of molecules) to make the number of atoms equal on both sides.

This task might seem tedious, but it’s much like solving a puzzle. Start with elements that appear only once on each side or those that appear in complex compounds last.

• Common approach involves balancing metals first, nonmetals second, and hydrogens and oxygens last.
• Re-check every step to ensure all elements are balanced and adjust as needed.

Being methodical and practicing frequently helps improve your balancing skills.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the ratios of substances. These ratios, called stoichiometric coefficients, help in figuring out how much of a chemical is consumed or produced in a reaction.Key steps in using stoichiometry include:

• Convert masses to moles using molar masses from the periodic table.
• Use the stoichiometric coefficients from the balanced equation to set up mole ratios.
• Calculate the required amount of reactants or desired amount of products.

This is essential for predicting the amounts in a reaction and ensuring that chemicals are used efficiently. It’s widely used in experiments and industry to scale up reactions safely and economically.

• Example: In \[ ext{C}_6 ext{H}_{12} ext{O}_6 + 6 ext{O}_2 ightarrow 6 ext{CO}_2 + 6 ext{H}_2 ext{O}, \]1 mole of glucose reacts with 6 moles of oxygen to produce 6 moles of carbon dioxide and 6 moles of water.

Chemical Reactions

Chemical reactions involve the transformation of substances into one or more different substances. These transformations can often be observed as color changes, temperature shifts, or gas production. The substances initially involved are called reactants, while the resulting substances are known as products. Key characteristics of chemical reactions:

• They conserve atoms: all atoms present in the reactants are accounted for in the products.
• The bonds between atoms in the reactants are broken, and new bonds form to create the products.
• Energy is either absorbed or released during the process (endothermic vs. exothermic reactions).

For combustion reactions specifically:

• Involve a fuel and an oxidant (often oxygen), producing energy, usually as heat and light.
• Common examples include burning wood or gasoline, integral in engines and power plants.

Understanding chemical reactions helps in controlling and using them for beneficial purposes, from generating energy to creating new materials.

Oxidation Reactions

Oxidation reactions are a type of chemical reaction where a substance loses electrons. They go hand-in-hand with reduction reactions, where another substance gains those electrons. Together, they are called redox reactions.In terms of combustion:

• The fuel undergoes oxidation by losing electrons to oxygen, typically forming oxides like CO₂ and H₂O.
• These reactions release energy, making them vital in processes like metabolism and powering engines.

Recognizing oxidation involves:

• Increase in oxidation state of the substance.
• Gain of oxygen or loss of hydrogen atoms.

Understanding oxidation is crucial because it has practical applications in batteries, rusting of metals, and even blueprints for sustainable energy solutions.

• Example from reaction: In \[ ext{C}_2 ext{H}_4 ext{O}_2 + ext{O}_2 ightarrow ext{CO}_2 + ext{H}_2 ext{O}, \]ethanol (\( ext{C}_2 ext{H}_4 ext{O}_2 \)) is oxidized to carbon dioxide and water.

Emphasizing the electron transfer helps in understanding the inherent energy changes during the reaction.