How Many Moles of Carbon Dioxide Will be Produced When Burning Ethane?
Burning ethane in the presence of oxygen is a common chemical process that produces carbon dioxide and water vapor as byproducts. This article will guide you through the process of calculating the amount of carbon dioxide produced from a given amount of ethane, using balanced chemical equations and basic stoichiometric principles.
The Balanced Chemical Equation for Ethane Combustion
It is well-established that ethane undergoes complete combustion in the presence of oxygen to produce carbon dioxide and water. The general form of the balanced chemical equation for the combustion of ethane is:
1 C?H? 7/2 O? → 2 CO? 3 H?O
From this equation, we can see that one mole of ethane will produce two moles of carbon dioxide. This relationship is fundamental to our calculations.
Now, let's consider a specific scenario where we have 4 moles of ethane. Using the balanced equation, we can determine the amount of carbon dioxide produced.
Step-by-Step Calculation
To find the moles of carbon dioxide produced from 4 moles of ethane, we start by setting up a proportion based on the coefficients in the balanced equation.
According to the balanced equation:
2 moles of C?H? produce 4 moles of CO?.
Therefore, for 4 moles of C?H?, the amount of CO? produced (x) can be calculated using the following proportion:
If 2 moles of C?H? produce 4 moles of CO?, then 4 moles of C?H? will produce x moles of CO?.
Using the ratio:
$$frac{4 text{ moles CO?}}{2 text{ moles C?H?}} frac{x text{ moles CO?}}{4 text{ moles C?H?}}$$
Cross-multiplying gives:
2x 16
Thus:
x 8
Therefore, burning 4 moles of ethane in the presence of oxygen will produce 8 moles of carbon dioxide.
Further Examples and Applications
Understanding the stoichiometry of ethane combustion is not only crucial for chemists but also important for various real-world applications, such as studying air pollution and developing efficient fuel systems.
Consider another example where 2.4 moles of ethane are combusted. Based on the stoichiometric ratio of 1:2, 2.4 moles of ethane will produce:
2.4 moles of C?H? → 2.4 × 2 moles of CO? 4.8 moles of CO?
Therefore, the number of moles of carbon dioxide produced is 4.8 moles.
The first step in solving such problems is to write down the balanced chemical equation:
C?H? 7/2 O? → 2 CO? 3 H?O
The ratio of ethane to carbon dioxide is 1:2. Given this, 2.4 moles of ethane will yield:
2.4 × 2 4.8 moles of CO?
Understanding the Reaction Stoichiometry
Let's delve deeper into the process of balancing the chemical equation for the combustion of ethane:
To balance the equation:
Balance the carbons: We start by balancing the carbons in both the reactants and products. Balance the hydrogens: Next, we balance the hydrogens by equating the number of hydrogen atoms on both sides of the equation. Balance the oxygens: Finally, we ensure that the number of oxygen atoms on both sides of the equation is the same. This might involve using fractional coefficients, as shown in the balanced equation.In the given scenario, we calculate the moles of ethane and then use the stoichiometric ratio to determine the moles of carbon dioxide produced. For instance, given 6.0 grams of ethane, we convert it to moles:
$$frac{6.0 text{ g}}{30.07 text{ g/mol}} 0.2 text{ moles}$$
Given the balanced equation and the stoichiometry, we produce 0.4 moles of CO? (2:1 ratio), which translates to:
0.4 moles of CO?
This corresponds to a mass of:
0.4 moles × 44.01 g/mol 17.6 g of CO?
Therefore, the amount of carbon dioxide produced is directly proportional to the amount of ethane burned, as demonstrated by the key stoichiometric principles and the balanced chemical equation.
In conclusion, the balanced chemical equation for the combustion of ethane is fundamental to understanding the production of carbon dioxide. By mastering these principles, you can confidently calculate the amount of carbon dioxide produced in various scenarios, ensuring a deeper understanding of chemical reactions and their environmental impacts.