Given The Equation Representing A Reaction:$\[ 2C + 3H_2 \rightarrow C_2H_6 \\]What Is The Number Of Moles Of \[$ C \$\] That Must Completely React To Produce 2.0 Moles Of \[$ C_2H_6 \$\]?1. \[$ \quad 1.0 \, \text{mol}
Understanding the Chemical Equation
The given equation represents a chemical reaction between carbon (C) and hydrogen gas (H2) to produce ethane (C2H6). The equation is:
This equation indicates that 2 moles of carbon react with 3 moles of hydrogen gas to produce 1 mole of ethane.
Balancing the Chemical Equation
To balance the equation, we need to ensure that the number of atoms of each element is the same on both the reactant and product sides. In this case, the equation is already balanced, but we can verify it by counting the number of atoms of each element:
Reactants:
- Carbon (C): 2 atoms
- Hydrogen (H): 6 atoms
Products:
- Carbon (C): 2 atoms
- Hydrogen (H): 6 atoms
The equation is indeed balanced, and we can proceed to the next step.
Stoichiometry and Mole Ratios
Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. In this case, we are interested in finding the number of moles of carbon that must completely react to produce 2.0 moles of ethane.
To do this, we need to use the mole ratio between carbon and ethane. From the balanced equation, we can see that 2 moles of carbon react to produce 1 mole of ethane. Therefore, the mole ratio between carbon and ethane is:
We can use this mole ratio to find the number of moles of carbon that must react to produce 2.0 moles of ethane.
Calculating the Number of Moles of Carbon
Let's use the mole ratio to set up a proportion:
where x is the number of moles of carbon that must react.
We can cross-multiply and solve for x:
Therefore, the number of moles of carbon that must completely react to produce 2.0 moles of ethane is:
Conclusion
In conclusion, the number of moles of carbon that must completely react to produce 2.0 moles of ethane is 4.0 moles. This can be calculated using the mole ratio between carbon and ethane, which is 2 moles of carbon per 1 mole of ethane.
Additional Examples and Applications
This concept of stoichiometry and mole ratios has numerous applications in chemistry and other fields. For example, in the production of fuels, the amount of reactants needed to produce a certain amount of product can be calculated using mole ratios.
In addition, this concept can be applied to other chemical reactions, such as the combustion of fuels, the synthesis of chemicals, and the analysis of biological systems.
References
- Petrucci, R. H., Harwood, W. S., & Herring, F. G. (2016). General chemistry: Principles and modern applications. Pearson Education.
- Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
Glossary
- Mole ratio: The ratio of the number of moles of one substance to the number of moles of another substance in a chemical reaction.
- Stoichiometry: The branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions.
- Balanced equation: A chemical equation in which the number of atoms of each element is the same on both the reactant and product sides.
Balancing Chemical Equations and Stoichiometry: A Comprehensive Guide ===========================================================
Q&A: Balancing Chemical Equations and Stoichiometry
Q: What is the difference between a balanced equation and an unbalanced equation?
A: A balanced equation is a chemical equation in which the number of atoms of each element is the same on both the reactant and product sides. An unbalanced equation, on the other hand, is a chemical equation in which the number of atoms of one or more elements is not the same on both the reactant and product sides.
Q: How do I balance a chemical equation?
A: To balance a chemical equation, you need to ensure that the number of atoms of each element is the same on both the reactant and product sides. You can do this by adding coefficients (numbers in front of the formulas of reactants or products) to the equation. The coefficients should be such that the number of atoms of each element is the same on both sides.
Q: What is stoichiometry?
A: Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. It involves calculating the amount of reactants needed to produce a certain amount of product, and vice versa.
Q: How do I calculate the number of moles of a substance needed to produce a certain amount of product?
A: To calculate the number of moles of a substance needed to produce a certain amount of product, you need to use the mole ratio between the substance and the product. The mole ratio is the ratio of the number of moles of one substance to the number of moles of another substance in a chemical reaction.
Q: What is the mole ratio?
A: The mole ratio is the ratio of the number of moles of one substance to the number of moles of another substance in a chemical reaction. It is used to calculate the amount of reactants needed to produce a certain amount of product.
Q: How do I calculate the number of moles of a substance produced from a certain amount of reactant?
A: To calculate the number of moles of a substance produced from a certain amount of reactant, you need to use the mole ratio between the reactant and the product. The mole ratio is the ratio of the number of moles of one substance to the number of moles of another substance in a chemical reaction.
Q: What is the difference between a limiting reactant and an excess reactant?
A: A limiting reactant is a reactant that is present in a smaller amount than required to react completely with the other reactants. An excess reactant, on the other hand, is a reactant that is present in a larger amount than required to react completely with the other reactants.
Q: How do I determine the limiting reactant in a chemical reaction?
A: To determine the limiting reactant in a chemical reaction, you need to compare the mole ratio of the reactants to the mole ratio of the products. The reactant that is present in the smallest amount relative to the products is the limiting reactant.
Q: What is the significance of stoichiometry in chemistry?
A: Stoichiometry is significant in chemistry because it allows us to calculate the amount of reactants needed to produce a certain amount of product, and vice versa. It is also used to determine the limiting reactant in a chemical reaction, which is essential in designing and optimizing chemical processes.
Q: How do I apply stoichiometry in real-world scenarios?
A: Stoichiometry is applied in various real-world scenarios, such as in the production of fuels, the synthesis of chemicals, and the analysis of biological systems. It is also used in the design and optimization of chemical processes, such as in the production of pharmaceuticals and the treatment of wastewater.
Q: What are some common mistakes to avoid when balancing chemical equations and applying stoichiometry?
A: Some common mistakes to avoid when balancing chemical equations and applying stoichiometry include:
- Not balancing the equation correctly
- Not using the correct mole ratio
- Not considering the limiting reactant
- Not accounting for the excess reactant
Q: How do I practice balancing chemical equations and applying stoichiometry?
A: You can practice balancing chemical equations and applying stoichiometry by:
- Solving problems and exercises in your textbook or online resources
- Working on practice problems and quizzes
- Participating in online forums and discussion groups
- Seeking help from your instructor or teaching assistant
Conclusion
In conclusion, balancing chemical equations and applying stoichiometry are essential skills in chemistry that require practice and attention to detail. By understanding the concepts and principles of stoichiometry, you can apply them in various real-world scenarios and make informed decisions in your career and personal life.