Problem 90 - General Chemistry: Principles and Modern Applications

Question

What is the molecular formula of a hydrocarbon containing \(n\) carbon atoms and only one double bond? Can such a hydrocarbon yield a greater mass of \(\mathrm{H}_{2} \mathrm{O}\) than \(\mathrm{CO}_{2}\) when burned in an excess of oxygen?

Step-by-Step Solution

Answer

The molecular formula of a hydrocarbon with \(n\) carbon atoms and one double bond is \(C_{n}H_{2n}\). It cannot yield a greater mass of \(H_{2}O\) compared to \(CO_{2}\) when burned in excess oxygen.

Step 1: Determine the Molecular Formula

The structure of a hydrocarbon with only one double bond is known as an alkene. The general formula for alkenes is \(C_{n}H_{2n}\). Therefore, for a hydrocarbon with \(n\) carbon atoms and one double bond, the molecular formula would be \(C_{n}H_{2n}\).

Step 2: Write Down the Balanced Combustion Reaction

The general balanced equation for complete combustion of hydrocarbons with oxygen is \[ C_{n}H_{2n} + \frac{3n}{2} O_{2} \rightarrow nCO_{2} + nH_{2}O \] Every mole of \(C_{n}H_{2n}\) reacts with \(\frac{3n}{2}\) moles of \(O_{2}\) to produce \(n\) moles of \(CO_{2}\) and \(n\) moles of \(H_{2}O\).

Step 3: Mass Comparison of CO2 and H2O

Now, let's apply the law of Conservation of Mass to analyze the reaction. From the balanced equation, it is clear that 1 mole of hydrocarbon yields the same number of moles of \(CO_{2}\) as \(H_{2}O\). However, the molar mass of \(H_{2}O\)(18.015 g/mol) is less than the molar mass of \(CO_{2}\)(44.01 g/mol). Therefore, the mass of \(H_{2}O\) produced is less than the mass of \(CO_{2}\) produced in the combustion reaction.

Key Concepts

Understanding Hydrocarbons

Hydrocarbons are organic compounds composed solely of carbon and hydrogen atoms. They are the simplest type of organic molecules and serve as the building blocks for more complex compounds. Hydrocarbons can be classified into different categories based on the type of bonding between the carbon atoms. For instance, they can be alkanes, alkenes, or alkynes, each having distinct properties and formulae. This diversity allows hydrocarbons to be used in a wide range of applications, including fuels and raw materials for the chemical industry.
Alkanes are saturated hydrocarbons with single bonds, whereas alkenes, such as the one in the problem, are unsaturated and contain at least one double bond. Due to their bonding characteristics, alkenes have a general formula of \(C_{n}H_{2n}\), with the number of hydrogen atoms always being double the number of carbon atoms. Understanding these formulas is essential when determining the specific type of hydrocarbon in chemical problems.

What Happens in a Combustion Reaction?

A combustion reaction is a chemical process wherein a substance combines with oxygen, releasing energy in the form of heat and light. It’s commonly used to describe the burning of hydrocarbons where the main products are carbon dioxide \(CO_2\) and water \(H_2O\).
A complete combustion of a hydrocarbon ensures that all carbon atoms are converted into carbon dioxide and all hydrogen atoms into water. The balanced equation for the combustion of an alkene \(C_{n}H_{2n}\) looks like this:

• \(C_{n}H_{2n} + \frac{3n}{2} O_2 \rightarrow nCO_2 + nH_2O\)

Here, 1 mole of the alkene produces \(n\) moles each of \(CO_2\) and \(H_2O\). The balanced equation is crucial because it respects the Law of Conservation of Mass, ensuring the mass of reactants equals the mass of products.

Exploring the Alkene

Alkenes are fascinating hydrocarbons characterized by the presence of at least one carbon-carbon double bond. This double bond introduces a degree of unsaturation, affecting their reactivity and structure. As described by the molecular formula \(C_{n}H_{2n}\), alkenes differ from alkanes (single bonds only) by having two fewer hydrogen atoms for the same number of carbon atoms.
This structural characteristic gives alkenes their unique physical and chemical properties, including:

• Higher reactivity compared to alkanes due to the double bond.
• Ability to undergo addition reactions, where atoms are added to the carbon atoms of the double bond.
• Being used as starting materials in the manufacture of plastics and other materials.

The problem looks at an alkene’s combustion and highlights that, while it can produce both \(CO_2\) and \(H_2O\), the mass of water produced will always be less than that of carbon dioxide due to their different molar masses.