Question

Ethane and acetylene are two gaseous hydrocarbons. Chemical analyses show that in one sample of ethane, \(2.65 \mathrm{~g}\) of carbon are combined with \(0.665 \mathrm{~g}\) of hydrogen, and in one sample of acetylene, \(4.56 \mathrm{~g}\) of carbon are combined with \(0.383 \mathrm{~g}\) of hydrogen. (a) Are these results consistent with the law of multiple proportions? (b) Write reasonable molecular formulas for these compounds.

Short answer

Yes, they exhibit a simple ratio; reasonable formulas are \(\text{C}_2\text{H}_6\) for ethane and \(\text{C}_2\text{H}_2\) for acetylene.

Step-by-step solution

Calculate Ratios for Ethane

For ethane, we need to find the ratio of the mass of carbon to the mass of hydrogen. Given: \(2.65\, \text{g of carbon}\) and \(0.665\, \text{g of hydrogen}\). The ratio is calculated as: \[\text{Ratio for Ethane} = \frac{2.65}{0.665}\approx 3.98\]

Calculate Ratios for Acetylene

For acetylene, find the ratio similarly. Given: \(4.56\, \text{g of carbon}\) and \(0.383\, \text{g of hydrogen}\). The ratio is: \[\text{Ratio for Acetylene} = \frac{4.56}{0.383}\approx 11.9\]

Apply the Law of Multiple Proportions

The law of multiple proportions states that if two elements form more than one compound, the ratios of the masses of the second element which combine with a fixed mass of the first element will be simple. To check this, we compare the two ratios: \[\frac{11.9}{3.98} \approx 2.99 \approx 3\]This is a simple whole number ratio, confirming consistency with the law.

Propose Molecular Formulas

Considering the calculated ratios and common hydrocarbons, ethane and acetylene should have molecular formulas matching common patterns in carbon systems. Ethane has the formula \(\text{C}_2\text{H}_6\), and acetylene, with a higher carbon-to-hydrogen ratio, has the formula \(\text{C}_2\text{H}_2\).

Key concepts

Ethane

Ethane is a simple hydrocarbon with a chemical formula of \( ext{C}_2 ext{H}_6\). It is part of a category of organic compounds known as alkanes, which have single bonds between carbon atoms.
This compound is commonly found in natural gas and is colorless and odorless under normal conditions.
In the instance of ethane, chemical analysis revealed a ratio of carbon to hydrogen mass of approximately 3.98. This ratio provides insights into its molecular structure, where two carbon atoms bond with six hydrogen atoms, forming its chemical formula.
Ethane plays a significant role in the petrochemical industry as it can be cracked into ethylene, a precursor to a variety of plastic materials.

Acetylene

Acetylene is another hydrocarbon with the molecular formula \( ext{C}_2 ext{H}_2\). It belongs to the alkyne family, known for having a triple bond between carbon atoms.
This gas is utilized in industries for welding and cutting metals due to its ability to burn at high temperatures. The analysis of acetylene showed a carbon-to-hydrogen mass ratio of about 11.9, considerably higher than that of ethane.
This high ratio reflects its distinct molecular structure, where a stronger carbon-to-carbon triple bond exists, explaining the reduced hydrogen presence. Understanding the structure and properties of acetylene helps in comprehending its applications and behavior under different conditions.

Molecular Formulas

Molecular formulas are vital as they indicate the types and numbers of atoms in a molecule. For instance, ethane's molecular formula \( ext{C}_2 ext{H}_6\) tells us it contains two carbon atoms and six hydrogen atoms.
Acetylene's molecular formula \( ext{C}_2 ext{H}_2\) reveals it has two carbon atoms and two hydrogen atoms, highlighting the differences between these hydrocarbons.
Molecular formulas are not only essential for understanding the composition of molecules but also for predicting their physical and chemical properties. They allow chemists to deduce how these molecules may react, interact, or change under various conditions.

Hydrocarbons

Hydrocarbons are organic compounds consisting entirely of hydrogen and carbon atoms. They form the basis of crude oil, natural gas, coal, and other energy resources.
Common categories include alkanes, alkenes, and alkynes, based on the types of bonds between carbon atoms. Ethane is an alkane, with single bonds, while acetylene is an alkyne, with triple bonds.
These structural differences affect the hydrocarbons' chemical properties and applications, such as fuel efficiency, flame temperature, and reactivity. Understanding these properties is crucial in fields like energy production and chemical synthesis.

Chemical Analysis

Chemical analysis involves examining substances to understand their composition and quantities of various elements. In the case of ethane and acetylene, chemical analysis determined the mass ratios of carbon to hydrogen.
These precise measurements are fundamental in verifying the law of multiple proportions, which shows that ratios of masses are simple whole numbers when elements form different compounds.
Such analysis informs the determination of molecular formulas and helps predict how these substances might behave chemically, aiding both scientific understanding and practical applications in areas like materials science and environmental study.