Question

Calculate the mass of carbon in grams, the percent carbon by mass, and the number of individual carbon atoms present in each of the following samples. a. \(7.819 \mathrm{~g}\) of carbon suboxide, \(\mathrm{C}_{3} \mathrm{O}_{2}\) b. \(1.53 \times 10^{21}\) molecules of carbon monoxide c. 0.200 mole of phenol, \(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}\)

Short answer

In each sample, the mass of carbon, percent carbon by mass, and number of individual carbon atoms are: a. Carbon suboxide \(\mathrm{C}_{3} \mathrm{O}_{2}\): - Mass of carbon: 4.855 g - Percent carbon by mass: 62.10% - Number of carbon atoms: \(2.43 \times 10^{23}\) atoms b. Carbon monoxide: - Mass of carbon: 0.0305 g - Percent carbon by mass: 42.91% - Number of carbon atoms: \(1.53 \times 10^{21}\) atoms c. Phenol \(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}\): - Mass of carbon: 14.41 g - Percent carbon by mass: 76.56% - Number of carbon atoms: \(7.21 \times 10^{23}\) atoms

Step-by-step solution

Part a: Calculating mass of carbon in C3O2 sample

First, determine the molar mass of carbon suboxide (C3O2): Molar mass of C3O2 = (3 × Molar mass of C) + (2 × Molar mass of O) Molar mass of C3O2 = (3 × 12.01 g/mol) + (2 × 16.00 g/mol) Molar mass of C3O2 = 58.03 g/mol Now calculate the moles of C3O2 in the 7.819 g sample: moles of C3O2 = mass of C3O2 / molar mass of C3O2 moles of C3O2 = 7.819 g / 58.03 g/mol moles of C3O2 ≈ 0.1347 mol Now, calculate the mass of carbon in the 7.819 g sample of C3O2: Mass of carbon = (moles of C3O2) × (3 × Molar mass of C) Mass of carbon ≈ 0.1347 mol × (3 × 12.01 g/mol) Mass of carbon ≈ 4.855 g

Part a: Calculating percent carbon by mass in C3O2 sample

Percent carbon by mass = (Mass of carbon / Mass of C3O2 sample) × 100% Percent carbon by mass = (4.855 g / 7.819 g) × 100% Percent carbon by mass ≈ 62.10%

Part a: Calculating number of carbon atoms in C3O2 sample

Number of carbon atoms = (Moles of C3O2) × (3 × Avogadro's number) Number of carbon atoms ≈ 0.1347 mol × (3 × 6.022 × 10^23 atoms/mol) Number of carbon atoms ≈ 2.43 × 10^23 atoms

Part b: Calculating the mass of carbon in CO sample

Molar mass of carbon monoxide (CO) = Molar mass of C + Molar mass of O Molar mass of CO = 12.01 g/mol + 16.00 g/mol Molar mass of CO = 28.01 g/mol Now calculate the moles of CO in the 1.53 × 10^21 molecules sample: moles of CO = number of CO molecules / Avogadro's number moles of CO = (1.53 × 10^21 molecules) / (6.022 × 10^23 molecules/mol) moles of CO ≈ 0.00254 mol Now, calculate the mass of carbon in the CO sample: Mass of carbon = (moles of CO) × (Molar mass of C) Mass of carbon ≈ 0.00254 mol × 12.01 g/mol Mass of carbon ≈ 0.0305 g

Part b: Calculating percent carbon by mass in CO sample

Percent carbon by mass = (Mass of carbon / Mass of CO) × 100% Mass of CO = (0.00254 mol) × (28.01 g/mol) ≈ 0.0711 g Percent carbon by mass = (0.0305 g / 0.0711 g) × 100% Percent carbon by mass ≈ 42.91%

Part b: Calculating number of carbon atoms in CO sample

Number of carbon atoms = (Moles of CO) × (Avogadro's number) Number of carbon atoms ≈ 0.00254 mol × 6.022 × 10^23 atoms/mol Number of carbon atoms ≈ 1.53 × 10^21 atoms

Part c: Calculating mass of carbon in C6H6O sample

Molar mass of phenol (C6H6O) = (6 × Molar mass of C) + (6 × Molar mass of H) + Molar mass of O Molar mass of C6H6O = (6 × 12.01 g/mol) + (6 × 1.01 g/mol) + 16.00 g/mol Molar mass of C6H6O = 94.11 g/mol Now calculate the mass of the phenol sample: Mass of phenol = (0.200 mol) × (94.11 g/mol) Mass of phenol = 18.82 g Now, calculate the mass of carbon in the 0.200 mol sample of C6H6O: Mass of carbon = (0.200 mol) × (6 × Molar mass of C) Mass of carbon = 0.200 mol × (6 × 12.01 g/mol) Mass of carbon = 14.41 g

Part c: Calculating percent carbon by mass in C6H6O sample

Percent carbon by mass = (Mass of carbon / Mass of C6H6O sample) × 100% Percent carbon by mass = (14.41 g / 18.82 g) × 100% Percent carbon by mass ≈ 76.56%

Part c: Calculating number of carbon atoms in C6H6O sample

Number of carbon atoms = (Moles of C6H6O) × (6 × Avogadro's number) Number of carbon atoms = 0.200 mol × (6 × 6.022 × 10^23 atoms/mol) Number of carbon atoms ≈ 7.21 × 10^23 atoms

Key concepts

Mole Concept

The mole concept is essential in chemistry for understanding the quantity of substances involved in chemical reactions. A mole (mol) is a unit that represents a specific number of particles, usually atoms or molecules. This helps chemists convert between the mass of a substance and the number of particles it contains.

Imagine having a dozen eggs. Instead of saying 12 eggs, you say one dozen. Similarly, a mole is like a 'chemical dozen', only much larger. One mole is equal to Avogadro’s number, which is approximately \(6.022 \times 10^{23}\) particles.

For example, in the given exercise, the moles of carbon compounds like carbon suboxide (C\(_3\)O\(_2\)), carbon monoxide (CO), and phenol (C\(_6\)H\(_6\)O) are calculated. This helps determine how many particles or atoms are involved in each sample, bridging the macroscopic world of grams and the microscopic world of atoms.

Percent Composition

Percent composition is an analysis of how much of each element is present within a compound based on mass. It's important for understanding the makeup of a compound to predict how it will behave in reactions.

To calculate the percent composition of an element in a compound, first find the mass of that element in one mole of the compound, then divide it by the total molar mass of the compound. Multiply the result by 100 to convert it to a percentage.

In the example from the exercise, the percent carbon by mass is calculated for carbon suboxide, carbon monoxide, and phenol. For instance, in the carbon suboxide sample, the mass of carbon compared to its total mass gives a percent composition of approximately 62.10%. This shows how much of the compound's mass comes from carbon, vital for understanding its properties and behavior during reactions.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, used to quantify the number of atoms, ions, or molecules in a given mole of substance. Named after Amedeo Avogadro, this number is approximately \(6.022 \times 10^{23}\).

Consider it as a bridge between the atomic scale and the macro scale. Using Avogadro's number, chemists can convert between the number of atoms or molecules and the amount of substance in moles. Thus, it's crucial for understanding the scale of reactions and the size of substances being handled.

In the provided exercise, Avogadro's number was used to calculate the number of carbon atoms in samples of carbon suboxide, carbon monoxide, and phenol. For instance, the carbon atoms in the carbon suboxide were found to be approximately \(2.43 \times 10^{23}\), illustrating how many particles are in a sample of known mass or moles.