Problem 3 - Chemistry and Chemical Reactivity

Question

The equation for the reaction of phosphorus and chlorine is \(\mathrm{P}_{4}(\mathrm{s})+6 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{PCl}_{3}(\ell) .\) If you use 8000 molecules of \(P_{4}\) in this reaction how many molecules of \(\mathrm{Cl}_{2}\) are required to consume the \(\mathrm{P}_{4}\) completely?

Step-by-Step Solution

Answer

48,000 molecules of \( \mathrm{Cl}_{2} \) are required.

Step 1: Understand Mole Ratio

The balanced chemical equation is \( \mathrm{P}_{4}(\mathrm{s}) + 6 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{PCl}_{3}(\ell) \). From this, note that 1 molecule of \( \mathrm{P}_{4} \) reacts with 6 molecules of \( \mathrm{Cl}_{2} \). This gives us a mole ratio of 1:6 between \( \mathrm{P}_{4} \) and \( \mathrm{Cl}_{2} \).

Step 2: Calculate Required Molecules

Since 1 molecule of \( \mathrm{P}_{4} \) requires 6 molecules of \( \mathrm{Cl}_{2} \), for 8000 molecules of \( \mathrm{P}_{4} \), the number of \( \mathrm{Cl}_{2} \) molecules required is calculated as follows: \( 6 \times 8000 = 48000 \) molecules of \( \mathrm{Cl}_{2} \).

Step 3: Verify Calculation

To ensure accuracy, double-check that we have calculated 6 molecules of \( \mathrm{Cl}_{2} \) per molecule of \( \mathrm{P}_{4} \). Multiply 8000 by 6 again: \( 8000 \times 6 = 48000 \). This confirms that the required amount is correct.

Key Concepts

Mole Ratio

Understanding the concept of mole ratio is crucial in stoichiometry. Mole ratio refers to the proportionate relationship between the amounts in moles of reactants and products involved in a chemical reaction as represented by a balanced chemical equation. It is derived directly from the coefficients of the reactants and products.

• In the chemical equation featuring phosphorus and chlorine, \[ \mathrm{P}_{4}( ext{s}) + 6 \mathrm{Cl}_{2}( ext{g}) \rightarrow 4 \mathrm{PCl}_{3}( ext{l}) \]1 mole of \( \mathrm{P}_{4} \) reacts with 6 moles of \( \mathrm{Cl}_{2} \).
• This ratio is a key part of calculations in chemical equations, allowing us to determine how many moles of one substance are required to react completely with a given amount of another substance.

It is used to calculate how quantities of chemicals relate to each other in a reaction, providing essential insight into the required and resulting amounts of each substance in a molecule-based calculation.

Chemical Equations

Chemical equations present a way to describe chemical reactions using symbols for the elements and formulas for compounds. They are essential for understanding how substances interact and transform in reactions.

• The balanced chemical equation for the reaction between phosphorus and chlorine helps establish the stoichiometric relationships: \[ \mathrm{P}_{4}( ext{s}) + 6 \mathrm{Cl}_{2}( ext{g}) \rightarrow 4 \mathrm{PCl}_{3}( ext{l}) \]
• Each component in the equation is essential, from the reactants \(\mathrm{P}_{4} \) and \(\mathrm{Cl}_{2} \), to the product, \(\mathrm{PCl}_{3} \).
• The equation must be balanced, meaning the number of atoms for each element should be the same on both the reactant and product sides, maintaining the Law of Conservation of Mass.

Chemical equations provide a framework for predicting the outcomes of reactions such as the quantities of products produced or reactants needed.

Molecular Calculations

Molecular calculations in chemistry involve determining the amounts of molecules needed or produced in a reaction. These calculations rely heavily on understanding mole ratios and using them to predict chemical quantities.

• To calculate the number of chlorine molecules required to completely react with a given number of phosphorus molecules, we utilize the mole ratio from the balanced equation.
• For example, when given 8000 molecules of \(\mathrm{P}_{4} \), one can calculate the needed \(\mathrm{Cl}_{2} \) molecules by multiplying 8000 by 6 (since the mole ratio is 1:6).
• This results in 48000 molecules of \(\mathrm{Cl}_{2} \) needed to ensure complete reaction with the phosphorus molecules.

These calculations are central to stoichiometry, providing essential data for predicting how many molecules of reactants are necessary or products will form in chemical reactions.