Problem 102 - General Chemistry: Principles and Modern Applications

Question

A compound with the same hydrogen-to-carbon ratio as cyclobutane is (a) \(\mathrm{C}_{4} \mathrm{H}_{10} ;\) (b) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{3}\) (c) \(\mathrm{CH}_{3} \mathrm{C}=\mathrm{CCH}_{3} ;\) (d) \(\mathrm{C}_{6} \mathrm{H}_{6}\).

Step-by-Step Solution

Answer

None of the options has the same hydrogen-to-carbon ratio as cyclobutane.

Step 1: Calculate the Hydrogen-to-Carbon Ratio of Cyclobutane

The molecular formula of cyclobutane is \(C_4H_8\). The hydrogen-to-carbon ratio is therefore \(8/4 = 2\). This means there are twice as many hydrogen atoms as there are carbon atoms in cyclobutane.

Step 2: Check the Hydrogen-to-Carbon Ratio in each Option

Calculate the hydrogen-to-carbon ratio for each compound given in the options and compare it with that of cyclobutane.\n(a) \(\mathrm{C}_{4} \mathrm{H}_{10}\) has a ratio of \(10/4 = 2.5\)\n(b) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{3}\) has a ratio of \(6/4 = 1.5\)\n(c) \(\mathrm{CH}_{3} \mathrm{C}=\mathrm{CCH}_{3}\) has a ratio of \(6/4 = 1.5\)\n(d) \(\mathrm{C}_6H_6\) has a ratio of \(6/6 = 1\)

Step 3: Select the Compound with the Same Hydrogen-to-Carbon Ratio as Cyclobutane

After comparing the hydrogen-to-carbon ratio in each option to that of cyclobutane, it can be concluded that none of the options has the same ratio as cyclobutane. Therefore, none of the given options (a), (b), (c), or (d) has the same hydrogen-to-carbon ratio as cyclobutane.

Key Concepts

Cyclobutane

Cyclobutane is a type of organic compound known as a cycloalkane. It's composed of a carbon ring structure with four carbon atoms, each bonded to two hydrogen atoms. The molecular formula for cyclobutane is \(C_4H_8\). This formula indicates that it contains four carbon atoms and eight hydrogen atoms. Cyclobutane is notable for its hydrogen-to-carbon ratio, which is a key characteristic in identifying similar compounds. In cyclobutane, the ratio is 2:1, meaning there are two hydrogen atoms for every one carbon atom. This proportion is crucial when comparing it to other compounds in order to find ones with similar ratios.

Molecular Formula

A molecular formula is a concise way of expressing information about the atoms that constitute a particular chemical compound. It shows the number and type of atoms present, using element symbols and numeric subscripts.
For example, the molecular formula for cyclobutane is \(C_4H_8\). The subscript \'4\' next to carbon indicates that there are four carbon atoms, while \'8\' next to hydrogen shows there are eight hydrogen atoms.
Calculating the hydrogen-to-carbon ratio from these subscripts is simple: divide the number of hydrogen atoms by the number of carbon atoms. For cyclobutane, this division (\(8/4\)) yields a ratio of 2. Understanding molecular formulas is essential in chemistry for categorizing compounds and predicting their properties.

Organic Compounds

Organic compounds are a vast category of compounds generally characterized by the presence of carbon atoms. These compounds are foundational for life and encompass a wide range of materials including, but not limited to, plastics, fuels, and biomolecules. Carbon's ability to form stable, covalent bonds with itself as well as with many other elements (most commonly hydrogen, oxygen, and nitrogen) is at the core of organic chemistry.
Compounds like cyclobutane fall within this category. Organic chemists often study different families of organic compounds to understand their structures, bonding, and reactivity. Cyclobutane is specifically part of the cycloalkanes, known for their carbon-ring structures. Understanding these families helps in comparing and contrasting chemical behaviors and properties.

Chemical Ratios

Chemical ratios, such as the hydrogen-to-carbon ratio, are vital in chemistry for understanding the composition and properties of compounds. These ratios help chemists predict how compounds will react chemically.
The hydrogen-to-carbon ratio indicates the relative amounts of hydrogen and carbon in a molecular structure. For cyclobutane, the ratio is calculated as \( \frac{8}{4} = 2 \). Ratios help to quickly assess similarities and differences between compounds.
When asked to compare cyclobutane's ratio with other compounds, it’s about determining if another compound maintains the same proportion of hydrogen to carbon. Chemical ratios also play a role in the naming and classification of compounds, providing insight into potential reactivity and stability.