Question

Methane \(\left(\mathrm{CH}_{4}\right)\) is the main component of marsh gas. Heating methane in the presence of sulfur produces carbon disulfide and hydrogen sulfide as the only products. a. Write the balanced chemical equation for the reaction of methane and sulfur. b. Calculate the theoretical yield of carbon disulfide when \(120 . \mathrm{g}\) of methane is reacted with an equal mass of sulfur.

Short answer

The balanced chemical equation for the reaction between methane and sulfur is given by: \(\mathrm{CH}_{4} + 4\mathrm{S} \rightarrow \mathrm{CS}_{2} + 2\mathrm{H}_{2}\mathrm{S}\). When 120 g of methane is reacted with an equal mass of sulfur, the theoretical yield of carbon disulfide is 20.04 g.

Step-by-step solution

Write the balanced chemical equation for the reaction.

The chemical equation can be written as: \[ \mathrm{CH}_{4} + \mathrm{S} \rightarrow \mathrm{CS}_{2} + 2\mathrm{H}_{2}\mathrm{S} \] To balance this equation, we need to add coefficients in-front of the reactants and products until we find equal numbers of atoms of each type on both sides. So the balanced chemical equation is: \[ \mathrm{CH}_{4} + 4\mathrm{S} \rightarrow \mathrm{CS}_{2} + 2\mathrm{H}_{2}\mathrm{S} \]

Determine the limiting reactant.

We are given that we have 120 g of methane and 120 g of sulfur. To find the limiting reactant, we must first determine the number of moles of each reactant. We have: - Methane: molar mass = 12.01 g/mol (for C) + 4 * 1.01 g/mol (for H) = 16.04 g/mol - Sulfur: molar mass = 32.07 g/mol Now, we can calculate the number of moles of each reactant: Methane: n = m/M = 120 g / 16.04 g/mol = 7.48 mol Sulfur: n = m/M = 120 g / 32.07 g/mol = 3.74 mol Now, we need to compare the mole ratios. From the balanced chemical equation, the ratio of methane to sulfur is 1:4. So, let's divide the number of moles by their coefficients in the balanced equation: - Methane: n/1 = 7.48 / 1 = 7.48 - Sulfur: n/4 = 3.74 / 4 = 0.935 Since sulfur has the smallest value (0.935), it is the limiting reactant.

Calculate the theoretical yield of carbon disulfide.

To calculate the theoretical yield of carbon disulfide, we will use the mole ratio from the balanced chemical equation and the number of moles of the limiting reactant (sulfur). In this case, the ratio of sulfur to carbon disulfide is 4:1. So, the number of moles of carbon disulfide produced will be: n(CS2) = 0.935 * (1 mol CS2 / 4 mol S) = 0.234 mol CS2 Now, we must convert moles of carbon disulfide back to grams using the molar mass: m(CS2) = n(CS2) * M(CS2) = 0.234 mol CS2 * (12.01 g/mol C + 2 * 32.07 g/mol S) = 20.04 g CS2 Hence, the theoretical yield of carbon disulfide is 20.04 g when 120 g of methane is reacted with an equal mass of sulfur.

Key concepts

Chemical Reaction Balancing

Chemical reaction balancing is a fundamental skill in chemistry that ensures the law of conservation of mass is upheld. During a chemical reaction, atoms aren't created or destroyed; they are simply rearranged. To balance a reaction, one must ensure that there are equal numbers of each type of atom on both the reactant and product sides of the chemical equation.

To start, write down the unbalanced equation with all of the reactants and products. Then, adjust the coefficients—the numbers in front of the chemical formulas—to balance the atoms. It is vital to remember that you can only change the coefficients and not the subscripts in the chemical formulas, as altering the subscripts would change the compounds themselves. Begin with elements that appear only once on each side and leave hydrogen and oxygen for last, as they are often found in multiple compounds within the reaction.

Practical Tips

• Check each type of atom or polyatomic ion to see if they're balanced.
• If there are odd numbers of atoms, you may need to double some coefficients.
• After every adjustment, recount the atoms until the equation is balanced.

Limiting Reactant Calculation

The limiting reactant in a chemical reaction is the substance that is completely consumed first, stopping the reaction from proceeding, since there is no material left to react. To identify the limiting reactant, first, list the amount of each reactant in moles. You cannot directly compare masses since different substances have different molar masses.

The stoichiometric coefficients from the balanced equation give the precise ratios in which reactants combine. Dividing the molar amount of each reactant by its coefficient provides a way to determine which ratio is lower. The reactant with the lower value is the limiting reactant because it will run out first, based on the stoichiometric proportions. Understanding the limiting reactant is key, as it dictates the maximum amount of product that can be formed – known as the theoretical yield.

Helpful Hints:

• Always convert reactant amounts to moles before making comparisons.
• Remember to use the coefficients from the balanced equation to determine the ratio.
• Consider using a ratio or proportion method to clearly see which reactant is limiting.

Stoichiometry

Stoichiometry is a section of chemistry that involves using the quantitative relationship between reactants and products in a chemical reaction. This concept is critical for predicting the amounts of products formed or the amounts of reactants needed. Stoichiometric calculations often incorporate the concepts of molar ratios, limiting reactants, and theoretical yield. Different steps in stoichiometry include converting mass to moles, using molar ratios from the balanced equation to find the corresponding moles of another substance, and converting moles back to mass.

The theoretical yield is an important outcome of stoichiometric calculations; it denotes the maximum amount of product expected, assuming everything reacts perfectly. It is calculated by using the number of moles of the limiting reactant and the balanced equation to find the amount of product that could be formed under ideal conditions.

Quick Tips:

• Balance the equation before performing stoichiometric calculations.
• Use the molar ratios from the balanced equation to interconvert between reactants and products.
• To find theoretical yield, start with the limiting reactant's quantity in moles, then use the stoichiometry to find the moles (and ultimately the mass) of the product.