Question

Calculate the number of moles of carbon atoms present in each of the following samples. a. \(1.271 \mathrm{g}\) of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) b. \(3.982 \mathrm{g}\) of 1,4 -dichlorobenzene, \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2}\) c. 0.4438 g of carbon suboxide, \(\mathrm{C}_{3} \mathrm{O}_{2}\) d. \(2.910 \mathrm{g}\) of methylene chloride, \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\)

Short answer

The number of moles of carbon atoms in each sample is as follows: a. Ethanol: 0.0552 mol b. 1,4-dichlorobenzene: 0.1626 mol c. Carbon suboxide: 0.02376 mol d. Methylene chloride: 0.0343 mol

Step-by-step solution

a. Ethanol, C2H5OH

Step 1: Determine the molar mass of ethanol: Molar mass of C2H5OH = (2 × 12.01 g/mol) + (6 × 1.01 g/mol) + (1 × 16.00 g/mol) = 46.07 g/mol Step 2: Calculate the number of moles of ethanol: Number of moles = mass of sample / molar mass = 1.271 g / 46.07 g/mol = 0.0276 mol Step 3: Determine the number of carbon atoms in ethanol: Ethanol has 2 carbon atoms. Step 4: Calculate the number of moles of carbon atoms: Number of moles of carbon atoms = 0.0276 mol × 2 = 0.0552 mol

b. 1,4-dichlorobenzene, C6H4Cl2

Step 1: Determine the molar mass of 1,4-dichlorobenzene: Molar mass of C6H4Cl2 = (6 × 12.01 g/mol) + (4 × 1.01 g/mol) + (2 × 35.45 g/mol) = 147.00 g/mol Step 2: Calculate the number of moles of 1,4-dichlorobenzene: Number of moles = mass of sample / molar mass = 3.982 g / 147.00 g/mol = 0.0271 mol Step 3: Determine the number of carbon atoms in 1,4-dichlorobenzene: 1,4-dichlorobenzene has 6 carbon atoms. Step 4: Calculate the number of moles of carbon atoms: Number of moles of carbon atoms = 0.0271 mol × 6 = 0.1626 mol

c. Carbon suboxide, C3O2

Step 1: Determine the molar mass of carbon suboxide: Molar mass of C3O2 = (3 × 12.01 g/mol) + (2 × 16.00 g/mol) = 56.03 g/mol Step 2: Calculate the number of moles of carbon suboxide: Number of moles = mass of sample / molar mass = 0.4438 g / 56.03 g/mol = 0.00792 mol Step 3: Determine the number of carbon atoms in carbon suboxide: Carbon suboxide has 3 carbon atoms. Step 4: Calculate the number of moles of carbon atoms: Number of moles of carbon atoms = 0.00792 mol × 3 = 0.02376 mol

d. Methylene chloride, CH2Cl2

Step 1: Determine the molar mass of methylene chloride: Molar mass of CH2Cl2 = (1 × 12.01 g/mol) + (2 × 1.01 g/mol) + (2 × 35.45 g/mol) = 84.93 g/mol Step 2: Calculate the number of moles of methylene chloride: Number of moles = mass of sample / molar mass = 2.910 g / 84.93 g/mol = 0.0343 mol Step 3: Determine the number of carbon atoms in methylene chloride: Methylene chloride has 1 carbon atom. Step 4: Calculate the number of moles of carbon atoms: Number of moles of carbon atoms = 0.0343 mol × 1 = 0.0343 mol

Key concepts

Molar Mass

The concept of molar mass is crucial when dealing with chemical reactions and compositions. It represents the mass of one mole of a substance, expressed in grams per mole (g/mol). Each element has a unique atomic mass which can be found on the periodic table. The molar mass of a compound is calculated by summing up the atomic masses of all the atoms present in the molecule. For instance, the molar mass of ethanol (\(C_2H_5OH\)) is 46.07 g/mol. This value is obtained by adding the mass of 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom. Calculating molar mass allows you to convert between mass and moles, a fundamental concept in chemistry.

Ethanol

Ethanol, also known as ethyl alcohol, is a common chemical compound with the molecular formula \(C_2H_5OH\). It is a volatile, flammable, colorless liquid that is widely used in alcoholic beverages, as a solvent, and in various industrial applications.
Ethanol consists of 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom, contributing to its molar mass of 46.07 g/mol. Understanding the structure and composition of ethanol is important when calculating the number of moles or when dealing with reactions where ethanol is a reactant or product. For example, if you have 1.271 grams of ethanol, you can determine the number of moles of ethanol by dividing the mass by the molar mass, resulting in approximately 0.0276 moles.

1,4-Dichlorobenzene

1,4-Dichlorobenzene is an aromatic compound with the molecular formula \(C_6H_4Cl_2\). It is commonly used as a moth repellent and deodorizer. In terms of chemical structure, it consists of a benzene ring with two chlorine atoms substituted at the 1st and 4th positions, making it a dichloro derivative of benzene.
It has a molar mass of 147.00 g/mol, determined by the mass of its 6 carbon atoms, 4 hydrogen atoms, and 2 chlorine atoms. When performing chemical calculations, such as finding the moles in a sample, knowing these details is essential. For instance, 3.982 grams of 1,4-dichlorobenzene corresponds to 0.0271 moles based on its molar mass.

Carbon Suboxide

Carbon suboxide, with the formula \(C_3O_2\), is a lesser-known compound characterized by a linear structure where carbon atoms are bonded sequentially with oxygen atoms. It appears as a colorless gas and is considered a reactive intermediate in organic syntheses.
To determine the molar mass of carbon suboxide, you sum the masses of its 3 carbon atoms and 2 oxygen atoms, resulting in 56.03 g/mol. This knowledge helps in converting the mass of a sample, like 0.4438 grams of carbon suboxide, to moles, which would be roughly 0.00792 moles. Recognizing its composition aids in various chemical calculations involving carbon content and stoichiometry.

Methylene Chloride

Methylene chloride, or dichloromethane, is a volatile compound with the chemical formula \(CH_2Cl_2\). It is frequently used as a solvent in the production of paint strippers, degreasers, and other products due to its excellent solvent properties.
To determine its molar mass, you calculate the sum of the atomic masses of 1 carbon atom, 2 hydrogen atoms, and 2 chlorine atoms, resulting in 84.93 g/mol. Understanding its molar mass is key to practical applications in chemistry, such as determining the number of moles in a given mass. For instance, 2.910 grams of methylene chloride equates to 0.0343 moles. By knowing how to convert between mass and moles, students gain valuable skills in handling real-world chemical problems.