Question

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

Short answer

a. The balanced equation is: CH4(g) + 4S8(s) -> CS2(l) + 8H2S(g) b. When 1.50 mol S8 is used, 0.375 moles of CS2 are produced. c. When 1.50 mol S8 is used, 3.00 moles of H2S are produced.

Step-by-step solution

Balance the chemical equation

First, let's balance the equation: CH4(g) + S8(s) -> CS2(l) + H2S(g) A balanced equation must have the same number of atoms of each element on both sides. We can start by inserting coefficients to balance the equation. In this case, the correct balanced equation is: CH4(g) + 4S8(s) -> CS2(l) + 8H2S(g) Now the equation is balanced.

Calculate moles of CS2 produced

From the balanced equation, the stoichiometry indicates that 1 mol of CH4 reacts with 4 mols of S8 to produce 1 mol of CS2. Therefore, the molar ratio of S8 to CS2 is 4:1. We are given that 1.50 mol S8 is used. To find the moles of CS2 produced, we can set up a proportion using the stoichiometric coefficients from the balanced equation: \( \frac{1\, mol\, CS_{2}}{4\, mol\, S_{8}} = \frac{x}{1.50\, mol\, S_{8}} \) Where 'x' represents the moles of CS2 produced. Now we can solve for 'x': \( x = \frac{1.50\, mol\, S_{8}}{4} \) \( x = 0.375\, mol\, CS_{2} \) So, 0.375 moles of CS2 are produced.

Calculate moles of H2S produced

From the balanced equation, the stoichiometry indicates that 1 mol of CH4 reacts with 4 mols of S8 to produce 8 mols of H2S. Therefore, the molar ratio of S8 to H2S is 4:8 or 1:2. We are given that 1.50 mol S8 is used. To find the moles of H2S produced, we can set up a proportion using the stoichiometric coefficients from the balanced equation: \( \frac{2\, mol\, H_{2}S}{1\, mol\, S_{8}} = \frac{y}{1.50\, mol\, S_{8}} \) Where 'y' represents the moles of H2S produced. Now we can solve for 'y': \( y = \frac{1.50\, mol\, S_{8}}{0.5} \) \( y = 3.00\, mol\, H_{2}S \) So, 3.00 moles of H2S are produced. In conclusion: a. The balanced equation is: CH4(g) + 4S8(s) -> CS2(l) + 8H2S(g) b. When 1.50 mol S8 is used, 0.375 moles of CS2 are produced. c. When 1.50 mol S8 is used, 3.00 moles of H2S are produced.

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. It's a vital concept because it allows scientists and students to predict the amounts of substances consumed and produced during reactions, ensuring reactions are carried out efficiently and economically.

In the context of the problem involving methane (CH₄) and sulfur (S₈), stoichiometry helps balance the chemical equation and determine the amount of carbon disulfide (CS₂) and hydrogen sulfide (H₂S) produced from a given amount of reactants. The balanced equation provided acts as a recipe for the reaction, detailing exactly how much of each reactant is needed to produce a certain amount of product. The stoichiometric coefficients in the balanced equation—1 mole of CH₄ to 4 moles of S₈ and 8 moles of H₂S—serve as conversion factors, enabling us to transition from moles of one substance to moles of another.

Mole Concept

The mole concept is a fundamental building block in chemistry, because it provides a bridge between the atomic world and the macroscopic world we live in. One mole of any substance contains Avogadro's number of particles, which is approximately 6.022 x 10²³ particles. This concept allows chemists to work with the submicroscopic particles that we cannot see.

To compute the quantity of a substance in moles, which is exactly what's needed in the exercise for CS₂ and H₂S, the molar masses of the substances are typically used. Here, however, the molar ratios derived from the balanced equation are the sole focus. Thanks to the mole concept, we can quantify chemical elements and compounds, making it possible to use stoichiometry to solve the problem, whether we are looking at a laboratory experiment or an industrial scale reaction.

Chemical Reactions

Chemical reactions encompass the transformation of reactants into products through breaking and forming chemical bonds. Each reaction is accompanied by energy changes and is guided by the laws of conservation of mass and energy. In our exercise, the reaction between methane and sulfur to produce carbon disulfide and hydrogen sulfide is one such chemical transformation.

A critical aspect of chemical reactions is the requirement that they are balanced. This reflects the conservation of mass, meaning the total mass of the reactants must equal the total mass of the products. By balancing the chemical equation, it is ensured that there are equal numbers of each type of atom on both sides of the equation. This balance is also essential for performing stoichiometry calculations accurately, as seen in the step-by-step solution to the exercise. Being able to interpret and balance chemical reactions is a key skill in chemistry that allows us to predict the outcomes of reactions and to understand the changes at a molecular level.