A Compound Is Composed Of $22.5 \%$ Phosphorus And $77.5 \%$ Chlorine. The Molecular Mass Of The Compound Is $137.32 \, \text{g/mol}$. What Is The Molecular Formula Of The Compound?A. $PCl_2$ B. $PCl_3$ C.

Introduction

In chemistry, determining the molecular formula of a compound is crucial in understanding its composition and properties. Given the percentage composition of a compound and its molecular mass, we can calculate the molecular formula using the concept of empirical formula and molecular mass. In this article, we will explore how to determine the molecular formula of a compound composed of phosphorus and chlorine.

Understanding the Problem

We are given a compound composed of $22.5 \%$ phosphorus and $77.5 \%$ chlorine, with a molecular mass of $137.32 \, \text{g/mol}$. Our goal is to determine the molecular formula of this compound.

Step 1: Calculate the Mass of Phosphorus and Chlorine in the Compound

To start, we need to calculate the mass of phosphorus and chlorine in the compound. Let's assume we have $100 \, \text{g}$ of the compound. The mass of phosphorus in the compound is $22.5 \%$ of $100 \, \text{g}$, which is $22.5 \, \text{g}$. Similarly, the mass of chlorine in the compound is $77.5 \%$ of $100 \, \text{g}$, which is $77.5 \, \text{g}$.

Step 2: Calculate the Number of Moles of Phosphorus and Chlorine

Next, we need to calculate the number of moles of phosphorus and chlorine in the compound. The atomic mass of phosphorus is $30.97 \, \text{g/mol}$, and the atomic mass of chlorine is $35.45 \, \text{g/mol}$. We can calculate the number of moles of phosphorus and chlorine using the formula:

$$\text{Number of moles} = \frac{\text{Mass of element}}{\text{Atomic mass of element}}$$

For phosphorus:

$$\text{Number of moles of phosphorus} = \frac{22.5 \, \text{g}}{30.97 \, \text{g/mol}} = 0.727 \, \text{mol}$$

For chlorine:

$$\text{Number of moles of chlorine} = \frac{77.5 \, \text{g}}{35.45 \, \text{g/mol}} = 2.19 \, \text{mol}$$

Step 3: Determine the Empirical Formula

The empirical formula of a compound is the simplest whole-number ratio of atoms of each element in the compound. To determine the empirical formula, we need to find the simplest whole-number ratio of phosphorus to chlorine.

We can do this by dividing the number of moles of phosphorus by the number of moles of chlorine:

$$\frac{\text{Number of moles of phosphorus}}{\text{Number of moles of chlorine}} = \frac{0.727 \, \text{mol}}{2.19 \, \text{mol}} = 0.332$$

To simplify the ratio, we can multiply both numbers by 3:

$$\frac{3 \times 0.727 \, \text{mol}}{3 \times 2.19 \, \text{mol}} = \frac{2.181 \, \text{mol}}{6.57 \, \text{mol}} = 0.332$$

However, we can simplify the ratio further by dividing both numbers by 0.332:

$$\frac{1 \, \text{mol}}{3 \, \text{mol}} = 0.333$$

This ratio is equivalent to 1:3, which means that for every 1 atom of phosphorus, there are 3 atoms of chlorine.

Step 4: Determine the Molecular Formula

The molecular formula of a compound is the actual number of atoms of each element in the compound. To determine the molecular formula, we need to multiply the empirical formula by a factor that gives us the molecular mass.

The molecular mass of the compound is $137.32 \, \text{g/mol}$, and the empirical formula mass is $30.97 \, \text{g/mol} + 3 \times 35.45 \, \text{g/mol} = 30.97 \, \text{g/mol} + 106.35 \, \text{g/mol} = 137.32 \, \text{g/mol}$.

Since the empirical formula mass is equal to the molecular mass, the molecular formula is the same as the empirical formula.

Conclusion

In conclusion, the molecular formula of the compound composed of $22.5 \%$ phosphorus and $77.5 \%$ chlorine is $PCl_3$.

Discussion

The molecular formula of a compound is crucial in understanding its composition and properties. By determining the molecular formula, we can predict the physical and chemical properties of the compound, such as its melting point, boiling point, and solubility.

In this article, we used the concept of empirical formula and molecular mass to determine the molecular formula of a compound composed of phosphorus and chlorine. We calculated the mass of phosphorus and chlorine in the compound, determined the number of moles of each element, and found the simplest whole-number ratio of phosphorus to chlorine. Finally, we multiplied the empirical formula by a factor that gave us the molecular mass to determine the molecular formula.

References

• Chemistry: An Atoms First Approach, by Steven S. Zumdahl
• General Chemistry: Principles and Modern Applications, by Linus Pauling

Further Reading

• Empirical Formula: A Simple Guide
• Molecular Formula: A Comprehensive Guide
• Determining the Molecular Formula of a Compound: A Step-by-Step Guide
  

Introduction

In our previous article, we explored how to determine the molecular formula of a compound composed of phosphorus and chlorine. We calculated the mass of phosphorus and chlorine in the compound, determined the number of moles of each element, and found the simplest whole-number ratio of phosphorus to chlorine. Finally, we multiplied the empirical formula by a factor that gave us the molecular mass to determine the molecular formula.

In this article, we will answer some frequently asked questions related to determining the molecular formula of a compound.

Q: What is the difference between empirical formula and molecular formula?

A: The empirical formula of a compound is the simplest whole-number ratio of atoms of each element in the compound, while the molecular formula is the actual number of atoms of each element in the compound.

Q: How do I determine the empirical formula of a compound?

A: To determine the empirical formula of a compound, you need to calculate the mass of each element in the compound, determine the number of moles of each element, and find the simplest whole-number ratio of the elements.

Q: What is the significance of the molecular mass in determining the molecular formula?

A: The molecular mass is crucial in determining the molecular formula of a compound. By multiplying the empirical formula by a factor that gives us the molecular mass, we can determine the molecular formula.

Q: Can I use the molecular formula to predict the physical and chemical properties of a compound?

A: Yes, the molecular formula can be used to predict the physical and chemical properties of a compound, such as its melting point, boiling point, and solubility.

Q: How do I determine the molecular formula of a compound if I don't know the molecular mass?

A: If you don't know the molecular mass of a compound, you can use other methods to determine the molecular formula, such as mass spectrometry or nuclear magnetic resonance (NMR) spectroscopy.

Q: Can I use the molecular formula to determine the percentage composition of a compound?

A: Yes, the molecular formula can be used to determine the percentage composition of a compound. By dividing the mass of each element in the compound by the molecular mass, you can calculate the percentage composition of the compound.

Q: What are some common mistakes to avoid when determining the molecular formula of a compound?

A: Some common mistakes to avoid when determining the molecular formula of a compound include:

• Not calculating the mass of each element in the compound
• Not determining the number of moles of each element
• Not finding the simplest whole-number ratio of the elements
• Not multiplying the empirical formula by a factor that gives us the molecular mass

Conclusion

In conclusion, determining the molecular formula of a compound is a crucial step in understanding its composition and properties. By answering some frequently asked questions related to determining the molecular formula, we hope to provide a better understanding of this concept.

Discussion

Determining the molecular formula of a compound is a complex process that requires careful calculation and analysis. By following the steps outlined in this article, you can determine the molecular formula of a compound and gain a deeper understanding of its composition and properties.

References

• Chemistry: An Atoms First Approach, by Steven S. Zumdahl
• General Chemistry: Principles and Modern Applications, by Linus Pauling

Further Reading

• Empirical Formula: A Simple Guide
• Molecular Formula: A Comprehensive Guide
• Determining the Molecular Formula of a Compound: A Step-by-Step Guide

Q&A

• Q: What is the difference between empirical formula and molecular formula? A: The empirical formula of a compound is the simplest whole-number ratio of atoms of each element in the compound, while the molecular formula is the actual number of atoms of each element in the compound.
• Q: How do I determine the empirical formula of a compound? A: To determine the empirical formula of a compound, you need to calculate the mass of each element in the compound, determine the number of moles of each element, and find the simplest whole-number ratio of the elements.
• Q: What is the significance of the molecular mass in determining the molecular formula? A: The molecular mass is crucial in determining the molecular formula of a compound. By multiplying the empirical formula by a factor that gives us the molecular mass, we can determine the molecular formula.
• Q: Can I use the molecular formula to predict the physical and chemical properties of a compound? A: Yes, the molecular formula can be used to predict the physical and chemical properties of a compound, such as its melting point, boiling point, and solubility.
• Q: How do I determine the molecular formula of a compound if I don't know the molecular mass? A: If you don't know the molecular mass of a compound, you can use other methods to determine the molecular formula, such as mass spectrometry or nuclear magnetic resonance (NMR) spectroscopy.
• Q: Can I use the molecular formula to determine the percentage composition of a compound? A: Yes, the molecular formula can be used to determine the percentage composition of a compound. By dividing the mass of each element in the compound by the molecular mass, you can calculate the percentage composition of the compound.
• Q: What are some common mistakes to avoid when determining the molecular formula of a compound? A: Some common mistakes to avoid when determining the molecular formula of a compound include:
• Not calculating the mass of each element in the compound
• Not determining the number of moles of each element
• Not finding the simplest whole-number ratio of the elements
• Not multiplying the empirical formula by a factor that gives us the molecular mass