Problem 96 - General Chemistry: Principles and Modern Applications

Question

A 0.7178 g sample of a hydrocarbon occupies a volume of \(390.7 \mathrm{mL}\) at \(65.0^{\circ} \mathrm{C}\) and \(99.2 \mathrm{kPa}\). When the sample is burned in excess oxygen, \(2.4267 \mathrm{g} \mathrm{CO}_{2}\) and \(0.4967 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) are obtained. What is the molecular formula of the hydrocarbon? Write a plausible structural formula for the molecule.

Step-by-Step Solution

Answer

The molecular formula of the compound is C3H8 and a plausible structural formula would be propane which satiates the octet rule for carbon atoms.

Step 1: Determining moles of the hydrocarbon

Use the ideal gas law, which is \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is number of moles, \(R\) is ideal gas constant and \(T\) is temperature. First, convert the temperature from Celsius to Kelvin \(T(K) = T(^{\circ} \mathrm{C}) + 273.15\). Convert pressure from kPa to atm. 1 atm = 101.325 kPa. We can substitute these values to obtain \(n\) (moles).

Step 2: Finding empirical formula

Carbon dioxide contains one carbon atom and water contains two hydrogen atoms. Determine the molar quantity using the provided masses of CO2 and H2O. Combined, these will give the empirical formula.

Step 3: Find the molecular formula

Calculate the molar masses of the compounds using the molar mass of carbon and hydrogen. The molar mass of carbon is 12 g/mol and hydrogen is 1 g/mol. Add them up to find the molecular formula.

Step 4: Draw a structural formula

To construct a plausible structure, the corresponding molecule should obey the octet rule for carbon atoms. Also, take into account that the molecule is a hydrocarbon, so it will only consist hydrogen and carbon atoms.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle used in chemistry to relate the physical properties of gases. It is expressed with the equation \( PV = nRT \). Here, \( P \) stands for pressure, \( V \) for volume, \( n \) is the number of moles of the gas, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. To solve for any unknown in the equation, the other variables must be known or measurable. For example:

• Pressure \( (P) \) is usually measured in atmospheres or kilopascals.
• Volume \( (V) \) must be in liters.
• Temperature \( (T) \) needs to be converted to the Kelvin scale to match the units used in the gas constant \( R \).

In this exercise,- Convert the given temperature from degrees Celsius to Kelvin by adding 273.15,- Convert pressure from kilopascals to atmospheres.By plugging these converted values into the equation, you can find the number of moles of the hydrocarbon gas in the sample.

Empirical Formula

The empirical formula is the simplest representation of the ratio of elements in a compound. It shows the lowest whole number ratio of atoms present. To determine the empirical formula from an experiment:1. Start with finding the moles of each element present in the compound.2. Use the masses of combustion products like \( CO_2 \) and \( H_2O \) to determine the amounts of carbon and hydrogen.3. Convert these amounts into moles: - Carbon from \( CO_2 \): The number of moles of carbon is the same as moles of \( CO_2 \). - Hydrogen from \( H_2O \): As each \( H_2O \) molecule has two hydrogen atoms, double the moles calculated.4. Simplify to the smallest whole number ratio to get the empirical formula.This basic framework helps identify the initial stoichiometry of the unknown compound.

Structural Formula

The structural formula provides a visual and detailed representation of a molecule. Unlike the molecular formula, which only shows the types and numbers of atoms, the structural formula shows how these atoms are connected. For hydrocarbons, the process involves: - Identifying possible bonding configurations that satisfy the valency rules. - Respecting the octet rule, where carbon forms four bonds. - Ensuring all hydrogen atoms form one bond each. Once the molecular formula of the hydrocarbon is determined, use it to visualize and draw the atom connections to conform to the standard structural configuration. It’s essential that the structure aligns with typical bonding patterns for hydrocarbons, indicating the distinctive arrangement of carbon-hydrogen bonds.

Hydrocarbon

Hydrocarbons are organic compounds composed exclusively of hydrogen and carbon atoms. They are the simplest form of organic molecules and serve as fundamental blocks in organic chemistry. There are various types of hydrocarbons, categorized primarily by:

• Saturation: Saturated hydrocarbons (alkanes) have only single bonds, while unsaturated (alkenes and alkynes) include double or triple bonds.
• Structure: Linear, branched, or cyclic forms that dictate physical and chemical properties.

Due to this structural variety, hydrocarbons can participate in numerous chemical reactions and serve as critical resources in producing fuels, oils, and many synthetic materials. In combustion reactions, like the one in the exercise, hydrocarbons react with oxygen to form carbon dioxide and water, illustrating their role as fuel sources and their broader significance in energy production and environmental science.