Question

Analyze Tetraphosphorus trisulphide \(\left(\mathrm{P}_{4} \mathrm{S}_{3}\right)\) 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. a. 4 mol \(P_{4}\) reacts with 1.5 mol \(S_{8}\) to form 4 mol \(P_{4} S_{3}\) b. Sulfur is the limiting reactant when 4 \(\mathrm{mol} \mathrm{P}_{4}\) and 4 \(\mathrm{mol} \mathrm{S}_{8}\) react. c. 6 mol \(P_{4}\) reacts with 6 mol \(S_{8},\) forming 1320 \(\mathrm{g} \mathrm{P}_{4} \mathrm{S}_{3}\)

Short answer

a. Correct statement. b. Incorrect statement, corrected statement: "Phosphorus is the limiting reactant when 4 mol \(P_{4}\) and 4 mol \(S_{8}\) react." c. Correct statement.

Step-by-step solution

1. Understanding the balanced chemical equation

The balanced chemical equation for this reaction is: \[8 \mathrm{P}_{4} + 3 \mathrm{S}_{8} \rightarrow 8 \mathrm{P}_{4}\mathrm{S}_{3}\] This means that 8 moles of \(\mathrm{P}_{4}\) react with 3 moles of \(\mathrm{S}_{8}\) to produce 8 moles of \(\mathrm{P}_{4}\mathrm{S}_{3}\). Now we will analyze each statement and determine if they are correct or incorrect.

2. Analyzing statement a

Statement a: 4 mol \(\mathrm{P}_{4}\) reacts with 1.5 mol \(\mathrm{S}_{8}\) to form 4 mol \(\mathrm{P}_{4}\mathrm{S}_{3}\). Based on the balanced chemical equation, 8 moles of \(\mathrm{P}_{4}\) react with 3 moles of \(\mathrm{S}_{8}\) to form 8 moles of \(\mathrm{P}_{4}\mathrm{S}_{3}\). To verify if the given statement is correct, we can divide the balanced chemical equation by 2: \(4 \mathrm{P}_{4} + 1.5 \mathrm{S}_{8} \rightarrow 4 \mathrm{P}_{4}\mathrm{S}_{3}\) So, statement a is correct.

3. Analyzing statement b

Statement b: Sulfur is the limiting reactant when 4 mol \(\mathrm{P}_{4}\) and 4 mol \(\mathrm{S}_{8}\) react. Since 8 mol of \(\mathrm{P}_{4}\) react with 3 mol of \(\mathrm{S}_{8}\) to form 8 mol of \(\mathrm{P}_{4}\mathrm{S}_{3}\), the molar ratio of \(\mathrm{P}_{4}\) to \(\mathrm{S}_{8}\) should be 8:3. When 4 mol of \(\mathrm{P}_{4}\) and 4 mol of \(\mathrm{S}_{8}\) are present, we can calculate the mole ratio: Mole ratio of \(\mathrm{P}_{4}\) to \(\mathrm{S}_{8}\) = \(\frac{4}{4}\) = 1:1 The mole ratio required for the complete reaction is 8:3, but in this case, the ratio is 1:1, which indicates that \(\mathrm{P}_{4}\) is the limiting reactant, not $\mathrm{S}_{ 8}$. So, statement b is incorrect. The corrected statement would be: "Phosphorus is the limiting reactant when 4 mol \(\mathrm{P}_{4}\) and 4 mol \(\mathrm{S}_{8}\) react."

4. Analyzing statement c

Statement c: 6 mol \(\mathrm{P}_{4}\) reacts with 6 mol \(\mathrm{S}_{8}\), forming 1320 g \(\mathrm{P}_{4}\mathrm{S}_{3}\). First, we need to determine the limiting reactant. Since the required molar ratio of \(\mathrm{P}_{4}\) to \(\mathrm{S}_{8}\) is 8:3, the mole ratio in this scenario is: Mole ratio of \(\mathrm{P}_{4}\) to \(\mathrm{S}_{8}\) = \(\frac{6}{6}\) = 1:1 Again, phosphorus (\(\mathrm{P}_{4}\)) is the limiting reactant. Since the limiting reactant is \(\mathrm{P}_{4}\), we can calculate the moles of \(\mathrm{P}_{4}\mathrm{S}_{3}\) that will be formed based on the moles of \(\mathrm{P}_{4}\): \(6\,\text{mol}\, \mathrm{P}_{4}\) * \(\frac{1\,\text{mol}\, \mathrm{P}_{4}\mathrm{S}_{3}}{1\,\text{mol}\, \mathrm{P}_{4}}\) = 6 mol \(\mathrm{P}_{4}\mathrm{S}_{3}\) Now let's find the molecular weight of \(\mathrm{P}_{4}\mathrm{S}_{3}\): - \(\mathrm{P}_{4}\): 4 * 30.97 g/mol (molar mass of phosphorus) = 123.88 g/mol - \(\mathrm{S}_{3}\): 3 * 32.06 g/mol (molar mass of sulfur) = 96.18 g/mol - \(\mathrm{P}_{4}\mathrm{S}_{3}\): 123.88 g/mol + 96.18 g/mol = 220.06 g/mol Finally, we can calculate the grams of \(\mathrm{P}_{4}\mathrm{S}_{3}\) formed: \(6\,\text{mol}\, \mathrm{P}_{4}\mathrm{S}_{3}\) * 220.06 g/mol = 1320.36 g Since the value of 1320 g in the statement is close enough to the calculated value of 1320.36 g, we can consider statement c as correct. In summary: a. Correct statement. b. Incorrect statement, corrected statement: "Phosphorus is the limiting reactant when 4 mol \(\mathrm{P}_{4}\) and 4 mol \(\mathrm{S}_{8}\) react." c. Correct statement.

Key concepts

Limiting Reactant

In chemical reactions, the limiting reactant is the substance that is totally consumed first and limits the amount of product that can be formed. It's like the ingredient in a recipe that runs out first, stopping you from making more of the dish, even if you have plenty of the other ingredients left.

To identify the limiting reactant, you compare the mole ratio of the reactants used in the reaction with the mole ratio given by the balanced chemical equation. If the actual mole ratio of reactants does not match the ratio required by the balanced equation, the reactant in the lesser amount (considering the required mole ratio) will be the limiting reactant. In our exercise, when analyzing statements b and c, we determined the limiting reactant by considering the mole ratios given and comparing them to the balanced chemical equation's requirements.

Understanding Limiting Reactants through Exercise Statements

For instance, statement b was revised to 'Phosphorus is the limiting reactant when 4 mol \(\mathrm{P}_{4}\) and 4 mol \(\mathrm{S}_{8}\) react,' because the mole ratio of 1:1 does not match the balanced equation's mole ratio of 8:3.

Mole Ratio

The mole ratio in chemistry is an essential concept that compares the amounts of any two substances involved in a chemical reaction. It is determined from the coefficients of a balanced chemical equation and is used to calculate how much reactant is needed or how much product can be made.

In our exercise, when working through the chemical equation for the production of Tetraphosphorus trisulphide, we utilized the mole ratio to assess the statements provided. The balanced equation indicates a mole ratio of 8 moles of \(\mathrm{P}_{4}\) to 3 moles of \(\mathrm{S}_{8}\) that react to form 8 moles of \(\mathrm{P}_{4}\mathrm{S}_{3}\). Therefore, any given combination of \(\mathrm{P}_{4}\) and \(\mathrm{S}_{8}\) moles can be evaluated against this ratio to predict whether the given statement is correct or not.

Exercise Application of Mole Ratio

In statement a, the mole ratio of 4:1.5 matches the required ratio when divided by two, making the statement correct. However, in statement b, the mole ratio of 1:1 indicates an excess of sulfur, thus requiring the correction that phosphorus is the limiting reactant.

Molecular Weight

Molecular weight, also known as molecular mass, is the weight of a single molecule of a compound and is expressed in atomic mass units (amu). It is calculated by summing the atomic weights of all atoms in the molecule, which are found on the periodic table. Understanding molecular weight is crucial when converting between moles of a substance and the corresponding mass in grams.

In the context of our exercise, calculating the molecular weight of Tetraphosphorus trisulphide (\(\mathrm{P}_{4}\mathrm{S}_{3}\)) was necessary to verify statement c about the mass of the product formed from a reaction involving 6 moles of \(\mathrm{P}_{4}\) and \(\mathrm{S}_{8}\). By adding the atomic weights of phosphorus and sulfur atoms in the compound, we found the molecular weight to be crucial for converting moles of \(\mathrm{P}_{4}\mathrm{S}_{3}\) to grams.

Exercise Calculation of Molecular Weight

Using the molecular weight of 220.06 g/mol for \(\mathrm{P}_{4}\mathrm{S}_{3}\), we calculated the mass of the product and found the statement c to be approximately correct, highlighting the practical application of molecular weight in stoichiometry.