Problem 23 - Chemistry: The Central Science in SI Units, Global Edition

Question

Give the molecular formula of a hydrocarbon containing five carbon atoms that is (a) an alkane, \((\mathbf{b})\) a cycloalkane, (c) an alkene,(d) an alkyne.

Step-by-Step Solution

Answer

The molecular formulas for the hydrocarbons with five carbon atoms are: (a) Alkane: \(C_5H_{12}\), (b) Cycloalkane: \(C_5H_{10}\), (c) Alkene: \(C_5H_{10}\), and (d) Alkyne: \(C_5H_8\). Note that the alkene and cycloalkane have the same molecular formula but different structures.

Step 1: Alkane #

For an alkane, the general molecular formula is CnH2n+2, where n represents the number of carbon atoms. We have n = 5, so the molecular formula for the alkane will be C5H(2(5)+2). Calculating the number of hydrogen atoms, 2(5) + 2 = 12 So, the molecular formula for the alkane with five carbon atoms is C5H12.

Step 2: Cycloalkane #

For a cycloalkane, the general molecular formula is CnH2n, where n represents the number of carbon atoms. We have n = 5, so the molecular formula for the cycloalkane will be C5H(2(5)). Calculating the number of hydrogen atoms, 2(5) = 10 So, the molecular formula for the cycloalkane with five carbon atoms is C5H10.

Step 3: Alkene #

For an alkene, the general molecular formula is CnH2n, where n represents the number of carbon atoms. We have n = 5, so the molecular formula for the alkene will be C5H(2(5)). Calculating the number of hydrogen atoms, 2(5) = 10 So, the molecular formula for the alkene with five carbon atoms is C5H10. Note that it has the same molecular formula as the cycloalkane, but the structures will be different because alkenes have a double bond.

Step 4: Alkyne #

For an alkyne, the general molecular formula is CnH2n-2, where n represents the number of carbon atoms. We have n = 5, so the molecular formula for the alkyne will be C5H(2(5)-2). Calculating the number of hydrogen atoms, 2(5) - 2 = 8 So, the molecular formula for the alkyne with five carbon atoms is C5H8.

Key Concepts

Alkane

Alkanes are the simplest type of hydrocarbon compounds. They are composed entirely of single bonds, which makes them saturated hydrocarbons (meaning they have the maximum number of hydrogen atoms possible for that carbon structure). The general molecular formula for an alkane is \( C_nH_{2n+2} \). This formula signifies that for \( n \) carbon atoms, the compound will have \( 2n + 2 \) hydrogen atoms. Alkanes are also known as paraffins.

• Saturated hydrocarbons
• Single bonds only
• Commonly found in fuels such as methane, ethane, propane, and butane

For a hydrocarbon with five carbon atoms (n = 5), the molecular formula of an alkane would be \( C_5H_{12} \). You simply plug the value of \( n \) into the formula:\[C_nH_{2n+2} = C_5H_{2(5)+2} = C_5H_{12}\]This means there are 12 hydrogen atoms bonded to the five carbon atoms.

Cycloalkane

Cycloalkanes are a type of alkanes where carbon atoms form a ring structure. Unlike linear or branched alkanes, cycloalkanes adopt a cycle shape which alters their molecular formula, making it \( C_nH_{2n} \). This formula indicates that there are two fewer hydrogen atoms compared to their straight-chain counterparts, because each end carbon connects to close a ring.

• Saturated hydrocarbons
• Carbons form a ring structure
• Simplest example is cyclopropane (\( C_3H_6 \))

For a five-membered carbon ring (n = 5), the molecular formula for a cycloalkane would be \( C_5H_{10} \). The calculation looks like this:\[C_nH_{2n} = C_5H_{2(5)} = C_5H_{10}\]The structure forms a closed loop, like a pentagon.

Alkene

Alkenes are hydrocarbons that contain carbon-carbon double bonds, making them unsaturated, as they do not hold the maximum possible hydrogen atoms per carbon. The presence of double bonds means that their general molecular formula is \( C_nH_{2n} \), the same as cycloalkanes but due to different structural features. Alkenes are more reactive than alkanes due to the presence of these double bonds.

• Unsaturated hydrocarbons
• Contains one or more double bonds
• Examples include ethene (ethylene), propene

In the case of a hydrocarbon with five carbon atoms, the molecular formula for an alkene is the same as for a cycloalkane, \( C_5H_{10} \):\[C_nH_{2n} = C_5H_{2(5)} = C_5H_{10}\]The double bond can be positioned along various points in the chain of carbons, affecting the compound's properties and reactions.

Alkyne

Alkynes are hydrocarbons characterized by carbon-carbon triple bonds, which make them highly unsaturated. Triple bonds imply a strong bond between carbon atoms but allow for fewer hydrogen atoms. The general molecular formula for alkynes is \( C_nH_{2n-2} \). The presence of triple bonds not only affects their molecular geometry but makes them significantly more reactive than alkanes and alkenes.

• Unsaturated hydrocarbons
• Contains one or more triple bonds
• Examples include acetylene (ethyne), propyne

For a five-carbon alkyne, the molecular formula is \( C_5H_8 \):\[C_nH_{2n-2} = C_5H_{2(5)-2} = C_5H_8\]This reduction in hydrogen atoms occurs as the triple bond forms, distinguishing alkynes from alkenes and affecting their chemical reactions and properties.