What is the mass of 0.042 moles C8H18? a. 0.0178 b. 0.370 c. 0.500 d. 4.80 e. 921
The Correct Answer and Explanation is:
To find the mass of 0.042 moles of C₈H₁₈ (octane), we use the formula: Mass=Moles×Molar Mass\text{Mass} = \text{Moles} \times \text{Molar Mass}
Step 1: Determine the molar mass of C₈H₁₈
Octane has 8 carbon atoms and 18 hydrogen atoms.
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.008 g/mol
Molar Mass of C₈H₁₈=(8×12.01)+(18×1.008)=96.08+18.144=114.224 g/mol\text{Molar Mass of C₈H₁₈} = (8 \times 12.01) + (18 \times 1.008) = 96.08 + 18.144 = 114.224 \, \text{g/mol}
Step 2: Multiply by number of moles
Mass=0.042 mol×114.224 g/mol≈4.80 g\text{Mass} = 0.042 \, \text{mol} \times 114.224 \, \text{g/mol} \approx 4.80 \, \text{g}
Correct Answer: d. 4.80
Explanation
To solve this problem, we apply a fundamental concept in chemistry: the relationship between moles and mass. Moles serve as a bridge between the number of particles in a substance and its measurable mass. The formula for converting moles to mass is: Mass (g)=Moles×Molar Mass (g/mol)\text{Mass (g)} = \text{Moles} \times \text{Molar Mass (g/mol)}
Here, we’re given 0.042 moles of C₈H₁₈, which is octane, a common hydrocarbon found in gasoline. Our task is to convert this quantity to grams. To do this, we must first calculate the molar mass of octane.
Octane consists of 8 carbon atoms and 18 hydrogen atoms. Using the periodic table, we find that the atomic mass of carbon is approximately 12.01 g/mol and that of hydrogen is about 1.008 g/mol. The molar mass of octane is then the sum of the masses of its constituent atoms: (8×12.01)+(18×1.008)=114.224 g/mol(8 \times 12.01) + (18 \times 1.008) = 114.224 \, \text{g/mol}
With the molar mass known, we multiply by the number of moles: 0.042 mol×114.224 g/mol=4.80 g0.042 \, \text{mol} \times 114.224 \, \text{g/mol} = 4.80 \, \text{g}
Thus, 0.042 moles of octane has a mass of 4.80 grams, making option d the correct answer. This type of calculation is essential in stoichiometry, allowing chemists to relate quantities of substances in reactions.
