{ AC_2H_6 + BO_2 \rightarrow CH_2O + DCO_2 \}$What Are The Values Of ${$ A \$}$, ${$ B \$}$, ${$ C \$}$, And ${$ D \$}$ Respectively?

Introduction

Balancing chemical equations is a crucial concept in chemistry that helps us understand the stoichiometry of chemical reactions. It involves determining the correct proportions of reactants and products in a chemical reaction. In this article, we will focus on balancing the given chemical equation: ${ aC_2H_6 + bO_2 \rightarrow cH_2O + dCO_2 }$. We will break down the steps to find the values of $a$, $b$, $c$, and $d$.

Understanding the Chemical Equation

The given chemical equation is:

{ aC_2H_6 + bO_2 \rightarrow cH_2O + dCO_2 \}

This equation represents the combustion of ethane ($C_2H_6$) in the presence of oxygen ($O_2$) to produce water ($H_2O$) and carbon dioxide ($CO_2$).

Step 1: Counting the Atoms

To balance the chemical equation, we need to count the number of atoms of each element on both the reactant and product sides.

• On the reactant side, we have:
  • $a$ molecules of $C_2H_6$, each containing 2 carbon atoms and 6 hydrogen atoms.
  • $b$ molecules of $O_2$, each containing 2 oxygen atoms.
• On the product side, we have:
  • $c$ molecules of $H_2O$, each containing 2 hydrogen atoms and 1 oxygen atom.
  • $d$ molecules of $CO_2$, each containing 1 carbon atom and 2 oxygen atoms.

Step 2: Balancing Carbon Atoms

Let's start by balancing the carbon atoms. We have 2 carbon atoms in each molecule of $C_2H_6$ and 1 carbon atom in each molecule of $CO_2$. To balance the carbon atoms, we need to multiply the number of molecules of $CO_2$ by 2.

{ aC_2H_6 + bO_2 \rightarrow cH_2O + 2dCO_2 \}

Step 3: Balancing Hydrogen Atoms

Next, let's balance the hydrogen atoms. We have 6 hydrogen atoms in each molecule of $C_2H_6$ and 2 hydrogen atoms in each molecule of $H_2O$. To balance the hydrogen atoms, we need to multiply the number of molecules of $H_2O$ by 3.

{ aC_2H_6 + bO_2 \rightarrow 3cH_2O + 2dCO_2 \}

Step 4: Balancing Oxygen Atoms

Finally, let's balance the oxygen atoms. We have 2 oxygen atoms in each molecule of $O_2$ and 1 oxygen atom in each molecule of $H_2O$ and 2 oxygen atoms in each molecule of $CO_2$. To balance the oxygen atoms, we need to multiply the number of molecules of $O_2$ by 7/2 and the number of molecules of $H_2O$ by 7/2.

{ aC_2H_6 + \frac{7}{2}bO_2 \rightarrow 3cH_2O + 2dCO_2 \}

However, we cannot have a fraction of a molecule, so we need to multiply the entire equation by 2 to eliminate the fraction.

{ 2aC_2H_6 + 7bO_2 \rightarrow 6cH_2O + 4dCO_2 \}

Conclusion

In conclusion, the balanced chemical equation is:

{ 2aC_2H_6 + 7bO_2 \rightarrow 6cH_2O + 4dCO_2 \}

To find the values of $a$, $b$, $c$, and $d$, we need to know the specific conditions of the reaction, such as the amount of reactants used and the temperature at which the reaction occurs. However, in general, we can say that the values of $a$, $b$, $c$, and $d$ are:

• $a = 2$
• $b = 7/2$
• $c = 3$
• $d = 2$

Note that the values of $a$, $b$, $c$, and $d$ may vary depending on the specific conditions of the reaction.

References

• Petrucci, R. H., Harwood, W. S., Herring, F. G., & Madura, J. D. (2007). General chemistry: Principles and modern applications. Pearson Prentice Hall.
• Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.

Further Reading

• Balancing chemical equations: A step-by-step guide
• Stoichiometry: The art of counting atoms
• Chemical reactions: A brief introduction
  Balancing Chemical Equations: A Q&A Guide =====================================================

Introduction

Balancing chemical equations is a crucial concept in chemistry that helps us understand the stoichiometry of chemical reactions. In our previous article, we discussed the steps to balance the given chemical equation: ${ aC_2H_6 + bO_2 \rightarrow cH_2O + dCO_2 }$. In this article, we will answer some frequently asked questions about balancing chemical equations.

Q: What is the purpose of balancing chemical equations?

A: The purpose of balancing chemical equations is to ensure that the number of atoms of each element is the same on both the reactant and product sides. This helps us understand the stoichiometry of the reaction and predict the amount of products formed.

Q: How do I know if a chemical equation is balanced?

A: A chemical equation is balanced if the number of atoms of each element is the same on both the reactant and product sides. You can check if a chemical equation is balanced by counting the number of atoms of each element on both sides.

Q: What are the steps to balance a chemical equation?

A: The steps to balance a chemical equation are:

1. Count the number of atoms of each element on both the reactant and product sides.
2. Balance the atoms of each element one by one, starting with the elements that appear only once on each side.
3. Use coefficients to balance the atoms of each element.
4. Check if the equation is balanced by counting the number of atoms of each element on both sides.

Q: How do I know which element to balance first?

A: You should balance the elements that appear only once on each side first. This is because these elements have the fewest number of atoms, making it easier to balance them.

Q: Can I balance a chemical equation by trial and error?

A: Yes, you can balance a chemical equation by trial and error. However, this method can be time-consuming and may not always lead to the correct solution. It's better to use a systematic approach to balance a chemical equation.

Q: What are some common mistakes to avoid when balancing chemical equations?

A: Some common mistakes to avoid when balancing chemical equations include:

• Not counting the number of atoms of each element on both sides.
• Not using coefficients to balance the atoms of each element.
• Not checking if the equation is balanced after making changes.
• Not considering the physical and chemical properties of the reactants and products.

Q: How do I know if a chemical equation is correct?

A: A chemical equation is correct if it meets the following criteria:

• The number of atoms of each element is the same on both the reactant and product sides.
• The equation is consistent with the physical and chemical properties of the reactants and products.
• The equation is consistent with the laws of thermodynamics.

Conclusion

Balancing chemical equations is a crucial concept in chemistry that helps us understand the stoichiometry of chemical reactions. By following the steps outlined in this article, you can balance chemical equations with ease. Remember to count the number of atoms of each element on both sides, balance the atoms of each element one by one, and check if the equation is balanced after making changes.

References

• Petrucci, R. H., Harwood, W. S., Herring, F. G., & Madura, J. D. (2007). General chemistry: Principles and modern applications. Pearson Prentice Hall.
• Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.

Further Reading

• Balancing chemical equations: A step-by-step guide
• Stoichiometry: The art of counting atoms
• Chemical reactions: A brief introduction