Using The Balanced Equation $C_{10}H_{16} + 8Cl_2 \rightarrow 10C + 16HCl$, How Many Moles Of $Cl_2$ Would Be Needed To Produce 21.7 Mol Of $HCl$? Type Your Answer: _____ Mol

Introduction

Chemical reactions are the foundation of chemistry, and understanding the relationships between reactants and products is crucial in various fields, including chemistry, physics, and engineering. One of the essential tools in analyzing chemical reactions is the balanced chemical equation, which provides a clear picture of the reactants, products, and their stoichiometric relationships. In this article, we will explore the concept of balancing chemical equations and stoichiometry, and apply it to a specific problem involving the production of hydrogen chloride (HCl) from a given reaction.

What is a Balanced Chemical Equation?

A balanced chemical equation is a representation of a chemical reaction in which the number of atoms of each element is the same on both the reactant and product sides. This is achieved by adjusting the coefficients in front of the formulas of the reactants and products. A balanced equation is essential in understanding the stoichiometry of a reaction, which is the quantitative relationship between the reactants and products.

The Balanced Equation

The given balanced equation is:

$$C_{10}H_{16} + 8Cl_2 \rightarrow 10C + 16HCl$$

In this equation, 1 mole of $C_{10}H_{16}$ reacts with 8 moles of $Cl_2$ to produce 10 moles of $C$ and 16 moles of $HCl$.

Understanding Stoichiometry

Stoichiometry is the quantitative relationship between the reactants and products in a chemical reaction. It is based on the concept of the mole ratio, which is the ratio of the number of moles of one substance to the number of moles of another substance. In the balanced equation above, the mole ratio between $Cl_2$ and $HCl$ is 8:16 or 1:2.

Problem: Calculating Moles of $Cl_2$

We are given that 21.7 mol of $HCl$ is produced in a reaction. We need to calculate the number of moles of $Cl_2$ required to produce this amount of $HCl$.

Step 1: Identify the Mole Ratio

From the balanced equation, we know that 8 moles of $Cl_2$ produce 16 moles of $HCl$. Therefore, the mole ratio between $Cl_2$ and $HCl$ is 8:16 or 1:2.

Step 2: Calculate the Number of Moles of $Cl_2$

We can use the mole ratio to calculate the number of moles of $Cl_2$ required to produce 21.7 mol of $HCl$. Since the mole ratio is 1:2, we can set up a proportion:

$$\frac{8 \text{ mol } Cl_2}{16 \text{ mol } HCl} = \frac{x \text{ mol } Cl_2}{21.7 \text{ mol } HCl}$$

Solving for $x$, we get:

$$x = \frac{8 \text{ mol } Cl_2 \times 21.7 \text{ mol } HCl}{16 \text{ mol } HCl}$$

$$x = 8.55 \text{ mol } Cl_2$$

Therefore, 8.55 mol of $Cl_2$ would be needed to produce 21.7 mol of $HCl$.

Conclusion

In conclusion, balancing chemical equations and understanding stoichiometry are essential tools in analyzing chemical reactions. By applying these concepts to a specific problem, we can calculate the number of moles of a reactant required to produce a given amount of product. In this article, we used the balanced equation $C_{10}H_{16} + 8Cl_2 \rightarrow 10C + 16HCl$ to calculate the number of moles of $Cl_2$ required to produce 21.7 mol of $HCl$. The result shows that 8.55 mol of $Cl_2$ would be needed to produce this amount of $HCl$.

References

• Petrucci, R. H., Harwood, W. S., & Herring, F. G. (2006). General chemistry: Principles and modern applications. Pearson Prentice Hall.
• Atkins, P. W., & de Paula, J. (2006). Physical chemistry. Oxford University Press.

Additional Resources

• Khan Academy: Stoichiometry
• Chemistry LibreTexts: Stoichiometry
• MIT OpenCourseWare: 5.111 Principles of Chemical Science
  Balancing Chemical Equations and Stoichiometry: A Key to Understanding Chemical Reactions =====================================================

Q&A: Balancing Chemical Equations and Stoichiometry

In the previous article, we explored the concept of balancing chemical equations and stoichiometry, and applied it to a specific problem involving the production of hydrogen chloride (HCl) from a given reaction. In this article, we will answer some frequently asked questions related to balancing chemical equations and stoichiometry.

Q: What is the purpose of balancing a chemical equation?

A: The purpose of balancing a chemical equation is to ensure that the number of atoms of each element is the same on both the reactant and product sides. This is essential in understanding the stoichiometry of a reaction, which is the quantitative relationship between the reactants and products.

Q: How do I balance a chemical equation?

A: To balance a chemical equation, you need to adjust the coefficients in front of the formulas of the reactants and products. You can start by counting the number of atoms of each element on both sides of the equation and then adjusting the coefficients accordingly.

Q: What is stoichiometry?

A: Stoichiometry is the quantitative relationship between the reactants and products in a chemical reaction. It is based on the concept of the mole ratio, which is the ratio of the number of moles of one substance to the number of moles of another substance.

Q: How do I calculate the number of moles of a reactant required to produce a given amount of product?

A: To calculate the number of moles of a reactant required to produce a given amount of product, you need to use the mole ratio between the reactant and product. You can set up a proportion using the mole ratio and then solve for the number of moles of the reactant.

Q: What is the difference between a balanced equation and an unbalanced equation?

A: A balanced equation is an equation in which the number of atoms of each element is the same on both the reactant and product sides. An unbalanced equation is an equation in which the number of atoms of each element is not the same on both the reactant and product sides.

Q: Why is it important to balance a chemical equation?

A: It is essential to balance a chemical equation because it provides a clear picture of the reactants, products, and their stoichiometric relationships. This is crucial in understanding the quantitative relationships between the reactants and products in a chemical reaction.

Q: Can you give an example of a balanced equation?

A: Yes, the balanced equation for the combustion of methane is:

$$CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$$

In this equation, 1 mole of methane reacts with 2 moles of oxygen to produce 1 mole of carbon dioxide and 2 moles of water.

Q: Can you give an example of an unbalanced equation?

A: Yes, the unbalanced equation for the combustion of methane is:

$$CH_4 + O_2 \rightarrow CO_2 + H_2O$$

In this equation, the number of atoms of each element is not the same on both the reactant and product sides.

Conclusion

In conclusion, balancing chemical equations and understanding stoichiometry are essential tools in analyzing chemical reactions. By answering these frequently asked questions, we hope to have provided a better understanding of the concepts of balancing chemical equations and stoichiometry.

References

• Petrucci, R. H., Harwood, W. S., & Herring, F. G. (2006). General chemistry: Principles and modern applications. Pearson Prentice Hall.
• Atkins, P. W., & de Paula, J. (2006). Physical chemistry. Oxford University Press.

Additional Resources

• Khan Academy: Stoichiometry
• Chemistry LibreTexts: Stoichiometry
• MIT OpenCourseWare: 5.111 Principles of Chemical Science