Problem 56 - Chemistry The Molecular Nature of Matter

Question

How many moles of \(S\) are needed to combine with 0.225 mol Al to give \(\mathrm{Al}_{2} \mathrm{~S}_{3}\) ?

Step-by-Step Solution

Answer

0.3375 moles of Sulfur (S) are needed.

Step 1: Understand the Chemical Reaction

Looking at the balanced chemical equation for the combination of Aluminum (Al) and Sulfur (S) to form Aluminum Sulfide \(\mathrm{Al}_{2}\mathrm{S}_{3}\) helps in understanding how the reactants combine in fixed ratios according to their stoichiometry. The balanced equation is: \[2\mathrm{Al} + 3\mathrm{S} \rightarrow \mathrm{Al}_{2}\mathrm{S}_{3}\] This equation shows that 2 moles of Al reacts with 3 moles of S to form one mole of \(\mathrm{Al}_{2}\mathrm{S}_{3}\).

Step 2: Calculate the Moles of S

Since the mole ratio of Al to S in the formation of \(\mathrm{Al}_{2}\mathrm{S}_{3}\) is 2:3, we can use the given amount of Al to find the required amount of S. \[\frac{0.225\, \text{mol Al}\times3\, \text{mol S}}{2\, \text{mol Al}} = 0.3375\, \text{mol S}\] Therefore, 0.3375 moles of S are needed to react with 0.225 moles of Al.

Key Concepts

Understanding Chemical Reactions

A chemical reaction is the process by which substances, called reactants, are transformed into different substances, known as products. During a chemical reaction, the bonds between atoms in the reactants are broken, and new bonds are formed to create the products. The law of conservation of mass requires that the mass of the reactants equals the mass of the products; therefore, a chemical equation representing the reaction must be balanced, meaning the same number of each type of atom is present on both sides of the equation.

For example, in the reaction between aluminum (Al) and sulfur (S) to form aluminum sulfide (\r\(\text{Al}_{2}\text{S}_{3}\)), aluminum and sulfur combine in a specific stoichiometric ratio. This ratio is determined by the chemical formula of the products they form and is critical in telling us how much of each reactant is needed to form a certain amount of product.

Balancing Equations

Balancing equations is the cornerstone of stoichiometry. It's a systematic process of ensuring that the number of atoms for each element is equal on both sides of a chemical equation. This balance ensures that the law of conservation of mass is upheld. To balance an equation, you can only change the coefficients (the numbers in front of molecules), not the subscripts (the numbers that are part of the chemical formulas).

Looking at our example of the synthesis of aluminum sulfide, we start with the skeletal equation: \r\(2\mathrm{Al} + 3\mathrm{S} \rightarrow \mathrm{Al}_{2}\mathrm{S}_{3}\). The coefficients here, 2 and 3 for aluminum and sulfur respectively, give us the balanced equation indicating that two moles of aluminum react with three moles of sulfur to produce one mole of aluminum sulfide. Learning to balance equations is instrumental for solving stoichiometry problems.

The Mole Ratio in Stoichiometry

The mole ratio is the proportion of reactants and products involved in a chemical reaction, expressed in moles. It is derived from the coefficients of a balanced chemical equation and is utilized to calculate the amounts of reactants needed or products formed. In the equation \r\(2\mathrm{Al} + 3\mathrm{S} \rightarrow \mathrm{Al}_{2}\mathrm{S}_{3}\), the mole ratio of Al to S is 2:3, meaning two moles of aluminum are required for every three moles of sulfur.

In the given exercise, we applied the mole ratio to determine that 0.3375 moles of sulfur are required for 0.225 moles of aluminum. Understanding mole ratios allows you to scale reactions up or down and calculate the required amounts of substances for any given chemical reaction, which is crucial in both laboratory and industrial settings.