Problem 3 - Chemistry and Chemical Reactivity

Question

Which of the following is an alkane? Which could be a cycloalkane? (a) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (b) \(\mathrm{C}_{5} \mathrm{H}_{10}\) (c) \(\mathrm{C}_{14} \mathrm{H}_{30}\) (d) \(\mathrm{C}_{7} \mathrm{H}_{8}\)

Step-by-Step Solution

Answer

(c) \(\mathrm{C}_{14}\mathrm{H}_{30}\) is an alkane, (b) \(\mathrm{C}_{5}\mathrm{H}_{10}\) could be a cycloalkane.

Step 1: Determine the General Formula for Alkanes

Alkanes are saturated hydrocarbons with the general formula \(C_nH_{2n+2}\). This means that for every \(n\) carbon atoms, there should be \(2n+2\) hydrogen atoms. Check if any of the given compounds fit this formula.

Step 2: Check Each Option for Alkane

- **(a)** \(\mathrm{C}_2\mathrm{H}_4\): For \(n=2\), \(2n+2=6\), but the compound has 4 hydrogens. Not an alkane.- **(b)** \(\mathrm{C}_5\mathrm{H}_{10}\): For \(n=5\), \(2n+2=12\), but the compound has 10 hydrogens. Not an alkane.- **(c)** \(\mathrm{C}_{14}\mathrm{H}_{30}\): For \(n=14\), \(2n+2=30\), matches perfectly. This is an alkane.- **(d)** \(\mathrm{C}_7\mathrm{H}_8\): For \(n=7\), \(2n+2=16\), but the compound has 8 hydrogens. Not an alkane.

Step 3: Determine the General Formula for Cycloalkanes

Cycloalkanes are cyclic saturated hydrocarbons with the general formula \(C_nH_{2n}\). This indicates that for every \(n\) carbon atoms, there should be \(2n\) hydrogen atoms. Check if any of the remaining compounds fit this formula.

Step 4: Check Each Option for Cycloalkane

- **(a)** \(\mathrm{C}_2\mathrm{H}_4\): For \(n=2\), \(2n=4\), matches perfectly. This could be a cycloalkane (though typically cycloalkanes have at least 3 carbons, this fits the formula for a small ring compound).- **(b)** \(\mathrm{C}_5\mathrm{H}_{10}\): For \(n=5\), \(2n=10\), matches perfectly. This is a cycloalkane.- **(d)** \(\mathrm{C}_7\mathrm{H}_8\): For \(n=7\), \(2n=14\), does not match. Not a cycloalkane.

Key Concepts

Understanding Alkanes

Alkanes are a fundamental class of hydrocarbons, which are compounds consisting only of carbon and hydrogen. Often referred to as saturated hydrocarbons, alkanes have their carbon atoms connected by single bonds, resulting in a straight or branched chain. Imagine them as the most basic building blocks in organic chemistry. They are named with the suffix '-ane' and their simplest form is methane, represented as \(\ = 1, H_4\).
 

• Alkanes follow a straightforward formula: \(C_nH_{2n+2}\).
• This means for any given number of carbon atoms \(n\), the number of hydrogen atoms is \(2n+2\).
• Since they are saturated, alkanes generally do not react with many chemicals, except under certain conditions - like burning or with very strong acids.

An example from the provided exercise is option (c) \(\mathrm{C}_{14} \mathrm{H}_{30}\), where \(n=14\) and fits perfectly into the formula \(C_nH_{2n+2}\), identifying it as an alkane.

Exploring Cycloalkanes

Cycloalkanes present an interesting twist to the simple alkane chain — they form rings. As cyclic saturated hydrocarbons, cycloalkanes have all single bonds, similar to alkanes, but the carbon atoms form a loop. Think of it like taking a straight necklace and connecting the ends together; it becomes a bracelet. Cycloalkanes are important in the study of chemistry for their unique properties and occurrence in nature.
 

• The general formula for cycloalkanes is \(C_nH_{2n}\).
• Since they form rings, the 2 ends of the chain join together, reducing the hydrogen count by two.
• They usually have at least 3 carbon atoms to form a stable ring structure.

In the exercise, both (a) \(\mathrm{C}_2\mathrm{H}_4\) and (b) \(\mathrm{C}_5\mathrm{H}_{10}\) fit the formula \(C_nH_{2n}\). Hence, they could be cycloalkanes, with (b) being more typical due to its 5 carbon atoms forming a more stable ring.

Deciphering Chemical Formulas

Chemical formulas are like a language for chemists. They let us know exactly what atoms make up a molecule, and how many of each there are. Learning to read them means you can understand the essential composition and geometry of molecules, even without seeing them.
 

• Chemical formulas for hydrocarbons typically begin with 'C', standing for carbon, followed by 'H' for hydrogen.
• Subscripts (small numbers) next to each symbol indicate how many of those atoms are in the molecule.
• By examining these formulas, we can deduce whether a hydrocarbon is saturated or unsaturated, linear or cyclic.

For instance, examining \(\mathrm{C}_{5} \mathrm{H}_{10}\) and recognizing it matches the \(C_nH_{2n}\) formula tells us it might be a cycloalkane. Understanding the meaning behind these characters and numbers allows us to predict the potential behavior and reactivity of a compound.