Problem 33 - Introductory Chemistry Atoms First

Question

Consider the following chemical equation: \(\mathrm{C}_{2} \mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) (a) Balance this chemical equation by inspection. (b) Translate the balanced equation into words. The compound \(\mathrm{C}_{2} \mathrm{H}_{2}\) is called acetylene and is used as a fuel for torches that cut through steel.

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction between acetylene and oxygen is \(2 \mathrm{C}_{2} \mathrm{H}_{2}+5 \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2}\mathrm{O}+4 \mathrm{CO}_{2}\). In words, two molecules of acetylene react with five molecules of oxygen to produce two molecules of water and four molecules of carbon dioxide.

Step 1: Balance the given chemical equation

To balance the chemical equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation. Given equation: \(\mathrm{C}_{2} \mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow \mathrm{H}_{2}\mathrm{O}+\mathrm{CO}_{2}\) Balanced equation: \(2 \mathrm{C}_{2} \mathrm{H}_{2}+5 \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2}\mathrm{O}+4 \mathrm{CO}_{2}\) In the balanced equation, we can see that we have the same number of carbon, hydrogen, and oxygen atoms on both sides: - 4 carbon atoms in 2 C₂H₂ molecules and 4 carbon atoms in 4 CO₂ molecules - 4 hydrogen atoms in 2 C₂H₂ molecules and 4 hydrogen atoms in 2 H₂O molecules - 10 oxygen atoms in 5 O₂ molecules and 10 oxygen atoms in 2 H₂O and 4 CO₂ molecules.

Step 2: Translate the balanced equation into words

Now that we have balanced the chemical equation, we can translate it into words describing the reaction. Balanced equation: \(2 \mathrm{C}_{2} \mathrm{H}_{2}+5 \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2}\mathrm{O}+4 \mathrm{CO}_{2}\) In words: Two molecules of acetylene (C₂H₂) react with five molecules of oxygen (O₂) to produce two molecules of water (H₂O) and four molecules of carbon dioxide (CO₂). This reaction describes the combustion of acetylene in the presence of oxygen, which releases energy in the form of heat and light. This makes it suitable for use as a fuel in cutting torches, as stated in the problem.

Key Concepts

Stoichiometry

Stoichiometry is the quantitative aspect of chemistry that establishes the relationships between the substances involved in chemical reactions. It involves calculations that allow us to predict the amounts of products and reactants that are involved in a chemical reaction based on the coefficients of the balanced chemical equation.

Consider the balanced combustion reaction of acetylene:
\(2 \text{C}_{2}\text{H}_{2} + 5 \text{O}_{2} \rightarrow 2 \text{H}_{2}\text{O} + 4 \text{CO}_{2}\). Here stoichiometry tells us exactly how much oxygen is needed to react completely with acetylene and how much water and carbon dioxide will be formed. These stoichiometric calculations are essential in a variety of real-world applications, from pharmaceuticals to environmental engineering.

Combustion Reaction

A combustion reaction is a chemical change where a substance combines with oxygen to produce heat and light. It's a specific type of exothermic reaction, which involves the release of energy. In the context of our chemical equation, the substance acetylene \(\text{C}_{2}\text{H}_{2}\) combusts when exposed to oxygen \(\text{O}_{2}\), creating water \(\text{H}_{2}\text{O}\) and carbon dioxide \(\text{CO}_{2}\).

Understanding the intricacies of a combustion reaction is crucial, especially when it's used in welding and metalwork where controlling the flame and heat output is vital. The reaction is heavily reliant on both the correct stoichiometric ratio of reactants and sufficient oxygen to sustain the burning.

Chemical Nomenclature

Chemical nomenclature involves the systematic naming of chemical compounds. It provides a standardized way to communicate the particularities of chemical substances and their reactions. For instance, \(\text{C}_{2}\text{H}_{2}\) is the chemical formula for acetylene, a compound name that indicates a molecule composed of two carbon atoms and two hydrogen atoms.

In the balanced equation, \(2 \text{C}_{2}\text{H}_{2} + 5 \text{O}_{2} \rightarrow 2 \text{H}_{2}\text{O} + 4 \text{CO}_{2}\), 'acetylene' and 'oxygen' are the reactants, while 'water' and 'carbon dioxide' are the products. Acetylene is used as a fuel in torches for cutting steel due to the energy released when it burns with oxygen. The use of these standardized names in chemical nomenclature helps to prevent confusion and ensure clarity when discussing or writing about chemical reactions.