Problem 11 - Chemistry Matter and Change

Question

Methane and sulfur react to produce carbon disulfide \(\left(\mathrm{CS}_{2}\right),\) a liquid often used in the production of cellophane. ___\(\mathrm{CH}_{4}(\mathrm{g})+\) ___ \(\mathrm{S}_{8}(\mathrm{s}) \rightarrow\) ___\(\mathrm{cs}_{2}(\mathrm{l})\) + ___ \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) \begin{equation} \begin{array}{l}{\text { a. Balance the equation. }} \\ {\text { b. Calculate the moles of } \mathrm{CS}_{2} \text { produced when } 1.50 \mathrm{mol} \mathrm{S}_{8} \text { is used. }} \\ {\text { c. How many moles of } \mathrm{H}_{2} \mathrm{S} \text { is produced? }}\end{array} \end{equation}

Step-by-Step Solution

Answer

The balanced equation is \( 4\text{CH}_4 + \text{S}_8 \rightarrow 4\text{CS}_2 + 8\text{H}_2S \). Using 1.50 mol of \( \text{S}_8 \), 6.00 mol \( \text{CS}_2 \) and 12.00 mol \( \text{H}_2S \) are produced.

Step 1: Write the Unbalanced Equation

The chemical reaction given is: \( \text{CH}_4(g) + \text{S}_8(s) \rightarrow \text{CS}_2(l) + \text{H}_2S(g) \). This equation is a starting point to determine how the atoms need to be balanced.

Step 2: Balance Sulfur Atoms

Start by balancing the sulfur (S) atoms. \( \text{S}_8 \) contains 8 sulfur atoms and \( \text{CS}_2 \) contains 2 sulfur atoms each. To balance the sulfur, we'll need 4 \( \text{CS}_2 \) on the product side. The equation becomes: \( \text{CH}_4(g) + \text{S}_8(s) \rightarrow 4\text{CS}_2(l) + \text{H}_2S(g) \).

Step 3: Balance Carbon and Hydrogen Atoms

Next, balance the carbon atoms by recognizing that each \( \text{CH}_4 \) supplies 1 carbon to \( \text{CS}_2 \). We need 4 carbons, so we use 4 \( \text{CH}_4 \): \( 4\text{CH}_4(g) + \text{S}_8(s) \rightarrow 4\text{CS}_2(l) + \text{H}_2S(g) \).

Step 4: Balance Hydrogen Atoms

For hydrogen, each \( \text{CH}_4 \) has 4 hydrogen atoms. With 4 \( \text{CH}_4 \), there are 16 hydrogen atoms. Since each \( \text{H}_2S \) contains 2 hydrogen atoms, we need 8 \( \text{H}_2S \): \( 4\text{CH}_4(g) + \text{S}_8(s) \rightarrow 4\text{CS}_2(l) + 8\text{H}_2S(g) \).

Step 5: Balanced Equation

The balanced chemical equation is: \[ 4\text{CH}_4(g) + \text{S}_8(s) \rightarrow 4\text{CS}_2(l) + 8\text{H}_2S(g). \]

Step 6: Calculate Moles of CS\(_2\) Produced

The balanced equation shows 1 mole of \( \text{S}_8 \) produces 4 moles of \( \text{CS}_2 \). Using 1.50 moles of \( \text{S}_8 \), the moles of \( \text{CS}_2 \) produced is: \( 1.50 \text{ moles } \text{S}_8 \times \frac{4 \text{ moles } \text{CS}_2}{1 \text{ mole } \text{S}_8} = 6.00 \text{ moles } \text{CS}_2. \)

Step 7: Calculate Moles of H\(_2\)S Produced

From the balanced equation, 1 mole of \( \text{S}_8 \) produces 8 moles of \( \text{H}_2S \). Therefore, using 1.50 moles of \( \text{S}_8 \), the moles of \( \text{H}_2S \) produced is: \( 1.50 \text{ moles } \text{S}_8 \times \frac{8 \text{ moles } \text{H}_2S}{1 \text{ mole } \text{S}_8} = 12.00 \text{ moles } \text{H}_2S. \)

Key Concepts

Stoichiometry

Stoichiometry helps us understand the quantitative relationships in a chemical reaction. It's like the math behind chemistry, telling us how much of each reactant is needed and how much product we can expect. Underlying these calculations is the concept that matter is conserved in a chemical reaction. This means the total number of atoms of each element remains the same, before and after the reaction.

To calculate stoichiometry in a reaction like the one between methane and sulfur to produce carbon disulfide and hydrogen sulfide, we rely on a balanced chemical equation. This equation acts like a recipe, telling us the proportions of each reactant and product. In this exercise, the stoichiometric calculations were made using the ratios:

• 1 mole of \( S_8 \) produces 4 moles of \( CS_2 \).
• 1 mole of \( S_8 \) produces 8 moles of \( H_2S \).

This means when 1.50 moles of \( S_8 \) are used, they will yield 6.00 moles of \( CS_2 \) and 12.00 moles of \( H_2S \).

Stoichiometry allows chemists to plan reactions efficiently and economically by predicting how much of each substance will be involved.

Chemical Equation Balancing

Balancing a chemical equation is crucial because it ensures that the law of conservation of mass is upheld. In other words, no atoms are lost or gained during the reaction, they are merely rearranged. A balanced chemical equation will have the same number of each type of atom on both sides.

For example, in the reaction where methane (\( CH_4 \)) and sulfur (\( S_8 \)) produce carbon disulfide (\( CS_2 \)) and hydrogen sulfide (\( H_2S \)), balancing starts by looking at one type of atom—often whichever appears the least numbers of times in compounds, in this case, sulfur.

Steps to balance include:

• Balancing sulfur first as it involves complex multi-atom molecules (\( S_8 \) and \( CS_2 \)).
• Next carbon atoms were balanced by recognizing each \( CH_4 \) introduces a carbon atom to \( CS_2 \).
• Finally, hydrogen atoms are balanced, ensuring the total hydrogens on both sides are equal.

The balanced equation reflects all these steps and ensures a proper stoichiometric relationship.

Understanding chemical equation balancing is fundamental to predicting the outcomes of chemical reactions effectively.

Mole Concept

The mole is a central concept in chemistry, making it easier to express amounts of a substance. It connects the microscopic world of atoms and molecules to the macroscopic world we can observe. One mole equals Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) entities (atoms, molecules).

In this exercise, the mole concept was used to convert between the number of molecules participating in the reaction and the mass or volume of substances we measure in labs. It forms the basis of stoichiometry calculations.

To visualize:

• 1.50 moles of \( S_8 \) signifies \( 1.50 \times 6.022 \times 10^{23} \) molecules of \( S_8 \).
• With stoichiometry, from this number of sulfur molecules, we calculate the production of 6.00 moles of \( CS_2 \) and 12.00 moles of \( H_2S \).

Reactions are quantified through the mole, making it the bridge between the experiments we perform and the reactions on a molecular scale.

This makes the mole concept a powerful tool for chemists, allowing accurate measurements and predictions about reactions.