Question

The following demonstration takes place in a two-step process: First, solid calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) reacts with liquid water to produce acetylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and aqueous calcium hydroxide. Second, the acetylene gas produced is then ignited with a match, causing the combustion reaction of acetylene with oxygen gas to produce gaseous carbon dioxide and gaseous water. Write the balanced equation for each reaction that is occurring.

Short answer

The balanced equations for both reactions are: First reaction: \(CaC_{2} (s) + 2 H_{2}O (l) \rightarrow C_{2}H_{2} (g) + Ca(OH)_{2} (aq)\) Second reaction: \(2 C_{2}H_{2} (g) + 5 O_{2} (g) \rightarrow 4 CO_{2} (g) + 2 H_{2}O (g)\)

Step-by-step solution

1. Identify the reactants and products of the first reaction

In the first reaction, solid calcium carbide (CaC2) reacts with liquid water (H2O) to produce acetylene gas (C2H2) and aqueous calcium hydroxide (Ca(OH)2).

2. Write the unbalanced first reaction equation

Next, write the unbalanced equation for the first reaction by placing the reactants on the left side of the equation and the products on the right side: CaC2 (s) + H2O (l) → C2H2 (g) + Ca(OH)2 (aq)

3. Balance the first reaction equation

To balance the first reaction, we need to make sure that the number of each type of atom on both sides of the equation is equal: CaC2 (s) + 2 H2O (l) → C2H2 (g) + Ca(OH)2 (aq)

4. Identify the reactants and products of the second reaction

In the second reaction, acetylene gas (C2H2) reacts with oxygen gas (O2) to produce carbon dioxide gas (CO2) and water vapor (H2O).

5. Write the unbalanced second reaction equation

Next, write the unbalanced equation for the second reaction by placing the reactants on the left side of the equation and the products on the right side: C2H2 (g) + O2 (g) → CO2 (g) + H2O (g)

6. Balance the second reaction equation

To balance the second reaction, we need to make sure that the number of each type of atom on both sides of the equation is equal: 2 C2H2 (g) + 5 O2 (g) → 4 CO2 (g) + 2 H2O (g) Now we have the balanced equations for both reactions: First reaction: CaC2 (s) + 2 H2O (l) → C2H2 (g) + Ca(OH)2 (aq) Second reaction: 2 C2H2 (g) + 5 O2 (g) → 4 CO2 (g) + 2 H2O (g)

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is respected within a chemical reaction. When we balance an equation, our goal is to have the same number of each type of atom on both sides of the equation. This simulates real-world reactions, where matter is neither created nor destroyed. For example, when calcium carbide reacts with water, the unbalanced equation is:
\( \text{CaC}_2 (s) + \text{H}_2\text{O} (l) \rightarrow \text{C}_2\text{H}_2 (g) + \text{Ca(OH)}_2 (aq) \).
By observing that there are two hydrogen atoms in the reactant side and four in the product side, we can balance the equation by adding a coefficient of two in front of the water molecule:
\( \text{CaC}_2 (s) + 2\text{H}_2\text{O} (l) \rightarrow \text{C}_2\text{H}_2 (g) + \text{Ca(OH)}_2 (aq) \).
Thus, the first reaction is properly balanced with an equal number of each atom on both sides, adhering to the fundamental law.

Chemical Reactions

Chemical reactions involve the transformation of one set of chemical substances to another. As evidenced by our example, calcium carbide reacting with water to produce acetylene and calcium hydroxide is a type of chemical reaction called a hydrolysis reaction. The process involves solid reactants and liquid reactants producing gaseous and aqueous products. Understanding the different states of matter and types of reactions can help students better visualize and predict products of reactions. By identifying the reactants and products, and the state of each, students can gain insights into how different substances interact at a molecular level.

Stoichiometry

Stoichiometry is the study of the quantitative relationships, or ratios, within chemical reactions. It serves as the mathematical backbone of chemistry, allowing us to predict how much product will form from given amounts of reactants. In balancing our equations, stoichiometry ensures that the mole ratios are maintained. With the balanced hydrolysis of calcium carbide, one mole of calcium carbide reacts with two moles of water, yielding one mole of acetylene gas and one mole of calcium hydroxide. In more complex reactions, stoichiometry can require balancing not just single atoms but polyatomic ions and molecules, as well as accounting for molar coefficients and ratios.

Combustion Reactions

Combustion reactions are a type of chemical reaction where a fuel reacts with an oxidant, releasing energy in the form of light or heat. In the given problem, we see the combustion of acetylene gas in the second step. The general form of a combustion reaction involving hydrocarbons is the fuel reacting with oxygen to form carbon dioxide and water, releasing energy. Balancing these equations requires careful attention to the oxygen molecules due to their diatomic nature. For acetylene, the balanced combustion reaction is:
\(2 \text{C}_2\text{H}_2 (g) + 5 \text{O}_2 (g) \rightarrow 4 \text{CO}_2 (g) + 2 \text{H}_2\text{O} (g)\)
. This equation indicates that two moles of acetylene gas react with five moles of oxygen gas to produce four moles of carbon dioxide gas and two moles of water vapor.