Chapter 8: Problem 77
Heptane, \(\mathrm{C}_{7} \mathrm{H}_{16}\), is one of the components of gasoline. Burning heptane in air yields carbon dioxide and water. Balance the equation for this reaction: \(\mathrm{C}_{7} \mathrm{H}_{16}(l)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)
Short Answer
Expert verified
The balanced chemical equation for the combustion of heptane is:
\(\mathrm{C}_{7} \mathrm{H}_{16}(l)+11\mathrm{O}_{2}(g) \rightarrow 7\mathrm{CO}_{2}(g)+8\mathrm{H}_{2} \mathrm{O}(g)\).
Step by step solution
01
Count the initial number of atoms for each element
Before balancing, we need to count the number of atoms for each element on both sides of the equation. On the left side of the equation, we have:
- 7 carbon atoms (C) from heptane: \(\mathrm{C}_7 \mathrm{H}_{16}(l)\)
- 16 hydrogen atoms (H) from heptane: \(\mathrm{C}_7 \mathrm{H}_{16}(l) \)
- 2 oxygen atoms (O) from oxygen gas: \(\mathrm{O}_{2}(g)\)
On the right side of the equation, we have:
- 1 carbon atom (C) from carbon dioxide: \(\mathrm{CO}_{2}(g)\)
- 2 hydrogen atoms (H) from water: \(\mathrm{H}_{2} \mathrm{O}(g) \)
- 3 oxygen atoms (O): 2 from carbon dioxide and 1 from water: \(\mathrm{CO}_{2}(g) + \mathrm{H}_{2} \mathrm{O}(g)\)
02
Balance the carbon atoms
We can balance the carbon atoms by changing the coefficient for carbon dioxide on the right side of the equation. Since there are 7 carbon atoms on the left side, we need:
\(7 \cdot \mathrm{CO}_{2}(g)\)
Now the equation is:
\(\mathrm{C}_{7} \mathrm{H}_{16}(l)+\mathrm{O}_{2}(g) \rightarrow 7\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)
03
Balance the hydrogen atoms
We can balance the hydrogen atoms by changing the coefficient for water on the right side of the equation. Since there are 16 hydrogen atoms on the left side, we need:
\( 8 \cdot \mathrm{H}_{2} \mathrm{O}(g)\)
Now the equation is:
\(\mathrm{C}_{7} \mathrm{H}_{16}(l)+\mathrm{O}_{2}(g) \rightarrow 7\mathrm{CO}_{2}(g)+8\mathrm{H}_{2} \mathrm{O}(g)\)
04
Balance the oxygen atoms
We have now balanced the carbon and hydrogen atoms. To balance the oxygen atoms, we need to adjust the coefficient for oxygen gas on the left side of the equation. On the right side, we have 14 oxygen atoms from carbon dioxide and 8 oxygen atoms from water, for a total of 22 oxygen atoms. Since oxygen gas (\(\mathrm{O}_{2}\)) contains 2 oxygen atoms, we need:
\(11 \cdot \mathrm{O}_{2}(g)\)
Now the balanced equation is:
\(\mathrm{C}_{7} \mathrm{H}_{16}(l)+11\mathrm{O}_{2}(g) \rightarrow 7\mathrm{CO}_{2}(g)+8\mathrm{H}_{2} \mathrm{O}(g)\)
The chemical equation for the combustion of heptane is now balanced, and the coefficients are the smallest whole numbers that satisfy the conservation of the elements.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Stoichiometry
Stoichiometry is a section of chemistry that involves using balanced chemical equations to calculate the quantities of reactants and products involved in a chemical reaction. For students grappling with this concept, crucial steps include understanding the molar relationships between substances and the ability to convert between moles, mass, and, in some cases, volume of gases.
To use stoichiometry in our heptane combustion example, a student would first need to identify the balanced chemical equation. This equation serves as a recipe, indicating how much of each reactant is needed to produce a certain amount of product. The coefficients in the balanced equation tell us the ratios of moles of reactants and products. Knowing these ratios allows us to predict how much CO2 and H2O will be produced from a known amount of heptane burnt, or conversely, how much heptane is needed to produce a desired amount of water and carbon dioxide.
To use stoichiometry in our heptane combustion example, a student would first need to identify the balanced chemical equation. This equation serves as a recipe, indicating how much of each reactant is needed to produce a certain amount of product. The coefficients in the balanced equation tell us the ratios of moles of reactants and products. Knowing these ratios allows us to predict how much CO2 and H2O will be produced from a known amount of heptane burnt, or conversely, how much heptane is needed to produce a desired amount of water and carbon dioxide.
Practical Application
To apply stoichiometry, you might be given the mass of heptane burned and asked to calculate the mass of water produced. You would convert the given mass of heptane to moles, use the molar ratios from the balanced equation, and then convert moles of water to grams using its molar mass.Combustion Reaction
A combustion reaction is a type of chemical reaction where a substance combines with oxygen and releases energy in the form of light or heat. The combustion of hydrocarbons like heptane is a common example, where the hydrocarbon reacts with oxygen to produce carbon dioxide and water.
In everyday life, we encounter combustion when burning fuels like gasoline in car engines or natural gas in home heating systems. For the combustion of heptane, an understanding of the process not only involves balancing the chemical equation but also recognizing the products of combustion and being aware that these reactions tend to be exothermic—releasing more energy than is consumed to initiate the reaction.
In everyday life, we encounter combustion when burning fuels like gasoline in car engines or natural gas in home heating systems. For the combustion of heptane, an understanding of the process not only involves balancing the chemical equation but also recognizing the products of combustion and being aware that these reactions tend to be exothermic—releasing more energy than is consumed to initiate the reaction.
Environmental Impact
While essential for energy production, combustion reactions also have environmental implications, such as the production of greenhouse gases. Therefore, studying these reactions can also lead to discussions about energy efficiency and alternative fuels.Chemical Reaction Balancing
Balancing chemical equations is critical in chemistry because it ensures that the Law of Conservation of Mass is satisfied, meaning that atoms are neither created nor destroyed in a chemical reaction.
When balancing equations, we adjust coefficients (the numbers placed before compounds) to ensure that the same number of each type of atom appears on both sides of the equation. In our heptane example, we adjusted coefficients to reflect that 7 carbon atoms and 16 hydrogen atoms from heptane must result in 7 molecules of carbon dioxide and 8 molecules of water, balancing out carbons and hydrogens.
When balancing equations, we adjust coefficients (the numbers placed before compounds) to ensure that the same number of each type of atom appears on both sides of the equation. In our heptane example, we adjusted coefficients to reflect that 7 carbon atoms and 16 hydrogen atoms from heptane must result in 7 molecules of carbon dioxide and 8 molecules of water, balancing out carbons and hydrogens.
Strategies for Balancing
A good strategy to start with is balancing elements that appear in only one reactant and one product. Afterwards, proceed to balance elements that are in more than one reactant or product. Finally, check and balance the oxygen atoms, as they are often found in multiple reactants and products, especially in combustion reactions.Conservation of Mass
The conservation of mass is a fundamental principle in chemistry stating that mass cannot be created or destroyed in a chemical reaction. This law implies that the mass of the reactants in a chemical reaction must equal the mass of the products.
In the context of a balanced chemical equation, this means that the number of atoms for each element must be the same on both sides of the reaction arrow. Balancing the equation for the combustion of heptane, we ensure that 7 carbons and 16 hydrogens on the reactant side result in the same number of atoms on the product side. The final step involved balancing the oxygen atoms to maintain conservation of mass throughout the entire reaction.
In the context of a balanced chemical equation, this means that the number of atoms for each element must be the same on both sides of the reaction arrow. Balancing the equation for the combustion of heptane, we ensure that 7 carbons and 16 hydrogens on the reactant side result in the same number of atoms on the product side. The final step involved balancing the oxygen atoms to maintain conservation of mass throughout the entire reaction.