Question

In which of the following compounds is the percent composition of carbon closest to 63 percent? A. Acetone B. Ethanol C. C3H8 D. Methanol

Short answer

Acetone

Step-by-step solution

Write the chemical formula of each compound

List the chemical formulas for Acetone (C3H6O), Ethanol (C2H6O), Propane (C3H8), and Methanol (CH4O).

Calculate the molar masses

Determine the molar masses of each compound using the atomic masses of carbon (C: 12.01 g/mol), hydrogen (H: 1.01 g/mol), and oxygen (O: 16.00 g/mol).Acetone: 3(12.01) + 6(1.01) + 16.00 = 58.08 g/molEthanol: 2(12.01) + 6(1.01) + 16.00 = 46.08 g/molPropane: 3(12.01) + 8(1.01) = 44.11 g/molMethanol: 1(12.01) + 4(1.01) + 16.00 = 32.05 g/mol

Calculate the mass of carbon in each compound

Find the total mass of carbon in each compound.Acetone: 3 * 12.01 = 36.03 gEthanol: 2 * 12.01 = 24.02 gPropane: 3 * 12.01 = 36.03 gMethanol: 1 * 12.01 = 12.01 g

Calculate the percent composition of carbon

Use the formula \(\frac{\text{Mass of Carbon}}{\text{Total Molar Mass}} \times 100 \) to calculate the percent composition of carbon in each compound.Acetone: \(\frac{36.03}{58.08} \times 100 = 62.03\%\)Ethanol: \(\frac{24.02}{46.08} \times 100 = 52.11\%\)Propane: \(\frac{36.03}{44.11} \times 100 = 81.68\%\)Methanol: \(\frac{12.01}{32.05} \times 100 = 37.47\%\)

Compare the percent compositions

Compare the percent compositions calculated to find which compound is closest to 63% carbon. Acetone has 62.03% carbon, Ethanol has 52.11% carbon, Propane has 81.68% carbon, and Methanol has 37.47% carbon. Acetone is the closest at 62.03%.

Key concepts

Molar Masses

Molar mass is the mass of one mole of a given substance, measured in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. To find the molar mass of a compound, you need to know the atomic masses of the individual elements.
For example, the atomic mass of carbon (C) is 12.01 g/mol, hydrogen (H) is 1.01 g/mol, and oxygen (O) is 16.00 g/mol.
Consider acetone (C3H6O), which has 3 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom. The molar mass of acetone is calculated as follows:

• 3 carbon atoms: 3 × 12.01 = 36.03 g/mol
• 6 hydrogen atoms: 6 × 1.01 = 6.06 g/mol
• 1 oxygen atom: 1 × 16.00 = 16.00 g/mol

When you add these together, you get the total molar mass: 36.03 + 6.06 + 16.00 = 58.08 g/mol.

Chemical Formulas

Chemical formulas represent the types and numbers of atoms in a molecule. They use the element symbols from the periodic table and subscript numbers to indicate the quantity of each element.
For instance, the chemical formula for acetone is C3H6O. This means it contains:

• 3 carbon (C) atoms
• 6 hydrogen (H) atoms
• 1 oxygen (O) atom

Similarly, propane has the chemical formula C3H8, indicating it has 3 carbon atoms and 8 hydrogen atoms. These formulas are crucial for calculating molar masses and understanding the composition of compounds.

Percent Composition Calculations

Percent composition is the percentage by mass of each element in a compound. It helps to understand the proportion of each element in the substance. The formula for calculating percent composition is: \(\frac{\text{Mass of Element}}{\text{Total Molar Mass}} \times 100\)
Let's calculate the percent composition of carbon in acetone: The molar mass of carbon in acetone is 36.03 g (from 3 carbon atoms). We already determined the total molar mass of acetone as 58.08 g/mol.
Using the formula: \(\frac{36.03}{58.08} \times 100 = 62.03\text{\text{%}}\)
This tells us that carbon makes up approximately 62.03% of acetone by mass. By comparing the percent compositions of various compounds, one can determine which compound has a composition closest to a given percentage.