What is the mass percentage of carbon (C) in methane (CH4)? (The molar mass of carbon is approximately 12 g/mol.)

Analysis

To find the mass percentage of an element in a compound, we need to compare the total mass of that specific element to the total molar mass of the entire compound, then multiply by 100.

Concept

The formula for mass percentage is:

Step-by-Step Solution

Step 1: Calculate the molar mass of Methane ($CH_4$)

• Atomic mass of Carbon (C) = 12 g/mol
• Atomic mass of Hydrogen (H) = 1 g/mol
• Molar mass of $CH_4 = (1 \times 12) + (4 \times 1)$
• Molar mass of $CH_4 = 12 + 4 = 16 \text{ g/mol}$

Step 2: Identify the total mass of Carbon in the compound

• There is only one atom of Carbon in $CH_4$.
• Total mass of Carbon = $12 \text{ g/mol}$

Step 3: Calculate the percentage

• $\text{Mass \% of C} = \left( \frac{12}{16} \right) \times 100\%$
• $\text{Mass \% of C} = 0.75 \times 100\%$
• $\text{Mass \% of C} = 75\%$

Conclusion

The calculation shows that Carbon makes up 75% of the mass of a methane molecule.

Exam Tip: When calculating mass percentages, always remember to count the number of atoms of the element present in the formula. For example, if the question asked for Hydrogen, you would use 4 (the mass of 4 H atoms) divided by 16, which would give you 25%.