Question

Write the balanced chemical equation for the complete combustion of heptene, \(\mathrm{C}_{7} \mathrm{H}_{14}\). In combustion, heptene reacts with oxygen to produce carbon dioxide and water. What is the mole ratio that would enable you to calculate the number of moles of oxygen needed to react exactly with a given number of moles of heptene? What mole ratios would you use to calculate how many moles of each product form from a given number of moles of heptene?

Short answer

The balanced chemical equation for the complete combustion of heptene (\(\mathrm{C}_{7} \mathrm{H}_{14}\)) is: \[\mathrm{C}_{7} \mathrm{H}_{14} + 14 \mathrm{O}_{2} \rightarrow 7 \mathrm{CO}_{2} + 7 \mathrm{H}_{2}\mathrm{O}\] The mole ratio of oxygen to heptene is 14:1, meaning 14 moles of \(\mathrm{O}_{2}\) are needed for each mole of \(\mathrm{C}_{7} \mathrm{H}_{14}\). Furthermore, the mole ratios for the products are 7:1 for both \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\), meaning 7 moles of \(\mathrm{CO}_{2}\) and 7 moles of \(\mathrm{H}_{2}\mathrm{O}\) are produced for each mole of \(\mathrm{C}_{7} \mathrm{H}_{14}\).

Step-by-step solution

Write the unbalanced chemical equation

We first write the unbalanced chemical equation for the combustion of heptene: C7H14 + O2 → CO2 + H2O

Balance the chemical equation

In order to balance the equation, we need to adjust the coefficients of each compound so that the number of atoms of each element is balanced on both sides of the equation. C7H14 + O2 → 7CO2 + 7H2O Now, we have 7 carbon atoms (from 7CO2) and 14 hydrogen atoms (from 7H2O) on the product side, but the number of oxygen atoms is not balanced yet. Since we have 14 oxygen atoms from CO2 and another 14 from H2O, we need 28 oxygen atoms on the reactant side. So our balanced equation becomes: C7H14 + 14O2 → 7CO2 + 7H2O

Find the mole ratio of oxygen to heptene

From the balanced equation, we can see that 1 mole of heptene (C7H14) reacts with 14 moles of oxygen (O2). The mole ratio of oxygen to heptene is: 14O2 : 1C7H14

Find the mole ratios of CO2 and H2O to heptene

We can also see the mole ratios of the products, CO2 and H2O, to heptene from the balanced equation: For CO2: 7CO2 : 1C7H14 For H2O: 7H2O : 1C7H14 To summarize the mole ratios, we have: - 14 moles of O2 are needed for each mole of C7H14. - 7 moles of CO2 are produced for each mole of C7H14. - 7 moles of H2O are produced for each mole of C7H14. These mole ratios can be used to calculate the amount of reactants and products in any given reaction involving the combustion of heptene.

Key concepts

Combustion Reaction

When we talk about a combustion reaction, we are referring to a chemical process where a substance (typically a hydrocarbon) reacts with oxygen to produce heat and light. This type of reaction is exothermic, meaning it releases energy. In the specific case of heptene, which is a hydrocarbon with the formula \(\mathrm{C}_{7} \mathrm{H}_{14}\), its combustion involves oxygen (\(\mathrm{O}_2\)) to produce carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)).

The balanced equation from the example provides a clear picture of the reaction:\[\mathrm{C}_7\mathrm{H}_{14} + 14\mathrm{O}_2 \rightarrow 7\mathrm{CO}_2 + 7\mathrm{H}_2\mathrm{O}\]
This means that for the complete combustion of one mole of heptene, fourteen moles of oxygen are necessary and this combustion will produce seven moles each of carbon dioxide and water.

Mole Ratio Calculation

The mole ratio is a key component of chemical equations as it shows the proportional relationship between the amounts in moles of any two substances involved in a chemical reaction. From the balanced equation provided earlier, we can derive the mole ratios necessary for calculations in a reaction involving heptene. For instance, the mole ratio of oxygen to heptene is 14 to 1, indicating that it takes 14 moles of oxygen to completely react with 1 mole of heptene.

For products, we refer to the balanced equation to establish their mole ratios to heptene. For carbon dioxide and water, the ratios are 7 to 1 with respect to heptene, respectively. These ratios are pivotal for stoichiometric calculations because they allow us to convert between moles of different substances within a chemical reaction.

Chemical Stoichiometry

Chemical stoichiometry is an area of chemistry that involves quantitatively analyzing the relationships expressed as mole ratios in balanced chemical equations. Stoichiometry is integral for predicting the amounts of products and reactants involved in a chemical reaction. In the context of the heptene combustion reaction, stoichiometry can be utilized to determine the volume of oxygen required to react with a certain quantity of heptene or the amount of carbon dioxide and water produced from this reaction.

These estimates are achievable by applying the mole ratios laid out in the balanced equation. If, for example, one needed to find out the number of moles of water produced from the combustion of 5 moles of heptene, the mole ratio \(7\mathrm{H}_2\mathrm{O} : 1\mathrm{C}_7\mathrm{H}_{14}\) would indicate that 35 moles of water (\(7 \times 5\)) would result. Such calculations are critical in fields like environmental science and engineering, where precise measurements can impact the design of combustion systems and the control of emissions.