Problem 61 - Chemistry Matter and Change

Question

Welding If 5.50 mol of calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) reacts with an excess of water, how many moles of acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right),\) a gas used in welding, will be produced? $$\mathrm{CaC}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})+\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})$$

Step-by-Step Solution

Answer

When 5.50 mol of calcium carbide (CaC₂) reacts with an excess of water, 5.50 mol of acetylene (C₂H₂) will be produced.

Step 1: Write down the balanced chemical equation

We have been given the balanced chemical equation: \( \ CaC_2(s) + 2 H_2O(l) \rightarrow Ca(OH)_2(aq) + C_2H_2(g) \)

Step 2: Identify the given and required substances

We are given 5.50 mol of calcium carbide (CaC₂) and we need to find the moles of acetylene (C₂H₂).

Step 3: Determine the mole-to-mole ratio

According to the balanced chemical equation, 1 mol of calcium carbide (CaC₂) reacts with 2 mol of water (H₂O) to produce 1 mol of calcium hydroxide (Ca(OH)₂) and 1 mol of acetylene (C₂H₂). Thus, the mole-to-mole ratio is 1:1 between calcium carbide and acetylene.

Step 4: Calculate the moles of acetylene produced

Since the mole-to-mole ratio between calcium carbide and acetylene is 1:1, the moles of acetylene produced will be equal to the moles of calcium carbide supplied. Moles of acetylene (C₂H₂) = Moles of calcium carbide (CaC₂) = 5.50 mol

Step 5: Write the final answer

When 5.50 mol of calcium carbide (CaC₂) reacts with an excess of water, 5.50 mol of acetylene (C₂H₂) will be produced.

Key Concepts

Mole Concept

The mole concept is a fundamental tool in chemistry. It allows chemists to count and quantify substances on a large scale. You can think of a mole much like a dozen: just as a dozen refers to 12 items, a mole refers to a very large number of particles, typically atoms or molecules. This number is Avogadro's number, approximately \( 6.022 \times 10^{23} \). Using the mole concept, we can easily communicate how much of a substance we are working with in terms of number of particles, without dealing with the impossibly large figures you would expect when counting individual molecules.

In our exercise, we are using the mole concept to establish a relationship between calcium carbide and acetylene. Knowing the number of moles of calcium carbide enables us to use stoichiometry to determine the number of moles of acetylene produced. This is possible because the chemical equation provides a mole-to-mole ratio, which is crucial for accurately predicting the amount of product formed from a given reactant.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. During this process, reactants turn into products as depicted by a chemical equation. We start with certain materials (reactants) and end with different substances (products). This reaction process is driven by the principles of conservation of mass and energy.

In the given chemical reaction, calcium carbide reacts with water to produce calcium hydroxide and acetylene gas. This type of reaction is notable because it converges reactants into entirely different compounds, illustrating the dynamic nature of chemical reactions. The transformation from the solid calcium carbide and liquid water into new products shows the alteration of bonding and formation of new substances.

Balanced Chemical Equation

A balanced chemical equation represents the conservation of mass, showing that the number of each type of atom is the same on both sides of the equation. This balance is achieved by using coefficients before the chemical formulas to indicate the relative quantities of reactants and products.

The balanced chemical equation for the reaction in our exercise is:

• \( CaC_2(s) + 2 H_2O(l) \rightarrow Ca(OH)_2(aq) + C_2H_2(g) \)

This equation reveals important stoichiometric details about the reaction. It shows that one molecule of calcium carbide reacts with two molecules of water to form one molecule of calcium hydroxide and one molecule of acetylene. This 1:2:1:1 ratio ensures the equation is balanced in terms of both mass and atoms, allowing chemists to predict the amounts of products that can be produced from a given amount of reactants.