Problem 27 - Chemistry Matter and Change

Question

Analyze Tetraphosphorus trisulphide \(\left(P_{4} S_{3}\right)\) is used in the match heads of some matches. It is produced in the reaction \(8 \mathrm{P}_{4}+3 \mathrm{S}_{8} \rightarrow 8 \mathrm{P}_{4} \mathrm{S}_{3}\) . Determine which of the following statements are incorrect, and rewrite the incorrect statements to make them correct. \begin{equation} \begin{array}{l}{\text { a. } 4 \text { mol } P_{4} \text { reacts with } 1.5 \text { mol } S_{8} \text { to form } 4 \text { mol } P_{4} S_{3} \text { . }} \\\ {\text { b. Sulfur is the limiting reactant when } 4 \text { mol } P_{4} \text { and } 4 \text { mol } S_{8} \text { react. }} \\ {\text { c. } 6 \text { mol } P_{4} \text { reacts with } 6 \text { mol } S_{8} \text { forming } 1320 \text { g } P_{4} S_{3} \text { . }}\end{array} \end{equation}

Step-by-Step Solution

Answer

Statements (b) is incorrect; phosphorus, not sulfur, is limiting.

Step 1: Understand the Chemical Reaction

The balanced equation for the reaction is \(8 \mathrm{P}_{4} + 3 \mathrm{S}_{8} \rightarrow 8 \mathrm{P}_{4} \mathrm{S}_{3}\). This indicates the mole ratio is 8:3:8 for \(\mathrm{P}_4\), \(\mathrm{S}_8\), and \(\mathrm{P}_4 \mathrm{S}_3\) respectively.

Step 2: Evaluate Statement (a)

Statement (a) claims that 4 mol \(P_{4}\) reacts with 1.5 mol \(S_{8}\) to form 4 mol \(P_{4}S_{3}\). The simplified mole ratio of the given reaction is 8:3:8 or 8:3, which simplifies in half to 4:1.5. This confirms that statement (a) is correct.

Step 3: Evaluate Statement (b)

Statement (b) says sulfur is the limiting reactant when 4 mol \(P_{4}\) and 4 mol \(S_{8}\) react. Check the mole ratios: for 4 mol \(P_{4}\), you need \(\frac{3}{8} \times 4 = 1.5\) mol \(S_8\). Here, we have 4 mol \(S_8\), so \(\mathrm{P}_4\) is needed more than available \(\mathrm{S}_8\), making it the limiting reactant. Statement (b) is incorrect.

Step 4: Correct Statement (b)

Since \(\mathrm{P}_4\) needs more \(\mathrm{S}_8\) than available, the correct statement is: "Phosphorus is the limiting reactant when 4 mol \(P_4\) and 4 mol \(S_8\) react."

Step 5: Evaluate Statement (c)

Statement (c) mentions 6 mol \(P_{4}\) reacts with 6 mol \(S_{8}\) forming 1320 g \(P_{4}S_{3}\). Calculate: needed \(S_8\) for 6 mol \(P_4\) is \(\frac{3}{8} \times 6 = 2.25\) mol. Since both \(\mathrm{P}_4\) and \(\mathrm{S}_8\) are in surplus, neither is limiting. Let's verify the product mass: \(\mathrm{molar\ weight\ of\ } P_4S_3 \text{ is } 4(30.97)+3(32.07) = 220.09\text{ g/mol}\). So, for 6 mol: \(6 \times 220.09 = 1320.54\text{ g}\). This confirms that statement (c) is correct.

Key Concepts

Limiting Reactant

In a chemical reaction, the limiting reactant is the substance that is entirely consumed first, determining the amount of product that can be formed. Once the limiting reactant is used up, the reaction stops, even if other reactants are still available.
This concept is crucial in chemistry because it allows us to predict the maximum possible yield of a chemical reaction based on the reactants we start with.
In the given exercise, statement (b) incorrectly identifies sulfur as the limiting reactant. The chemical equation requires 1.5 mol of \( S_8 \) for 4 mol of \( P_4 \). However, when you start with 4 mol of both reactants, phosphorus \( (P_4) \) becomes the limiting reactant because it needs more sulfur than is available.

Mole Ratio

The mole ratio of reactants and products in a balanced chemical equation is an essential aspect of chemical reaction analysis. This ratio is derived from the coefficients of the substances in the balanced equation.
For example, in the reaction \( 8 \mathrm{P}_4 + 3 \mathrm{S}_8 \rightarrow 8 \mathrm{P}_4 \mathrm{S}_3 \), the mole ratio is 8:3:8. This ratio tells us how many moles of \( P_4 \) and \( S_8 \) will react to produce the \( P_4S_3 \).
In statement (a), the use of 4 mol \( P_4 \) and 1.5 mol \( S_8 \) aligns correctly with the simplified mole ratio of 4:1.5, confirming that it is correct. Proper understanding of mole ratios helps in calculating how much of each reactant is needed and how much product can be formed.

Balanced Chemical Equation

A balanced chemical equation is crucial because it represents the conservation of mass in a chemical reaction. Each side of the equation must have the same number of atoms of each element.
This process ensures that the equation correctly reflects the actual reaction occurring. In our example, \( 8 \mathrm{P}_4 + 3 \mathrm{S}_8 \rightarrow 8 \mathrm{P}_4 \mathrm{S}_3 \) is already balanced since the number of phosphate and sulfur atoms are equal on both sides.
Balancing an equation helps identify the mole ratio of reactants to products, crucial for accurate chemical stoichiometry calculations.

Chemical Stoichiometry

Chemical stoichiometry involves calculating the quantities of reactants and products involved in a chemical reaction. It is based on the balanced chemical equation and the mole ratios derived from it.
Stoichiometry allows chemists to make predictions about the outcome of chemical reactions, including how much of each product will be formed and how each reactant will be consumed.
In statement (c), stoichiometry is used to determine whether the mass of \( P_4S_3 \) produced is correct. The calculation confirms that 6 mol \( P_4 \) reacting with 6 mol \( S_8 \) will indeed produce approximately 1320 g of \( P_4S_3 \), using the molar mass of \( P_4S_3 \), which is 220.09 g/mol. This verification shows the importance of stoichiometry in ensuring accurate predictions and understanding of chemical reactions.