Questions: Which element has a mass percent composition of 54.50% in Vitamin C, C6H8O6?

Which element has a mass percent composition of 54.50% in Vitamin C, C6H8O6?
Transcript text: Mass percent composition involves calculating the percentage of mass, for each of the individual elements, in a given substance. Mass percent composition is calculated according to the following equation: % of an element $=\frac{\text { (number of atoms of element) (atomic mass of element) }}{\text { atomic mass of chemical }} \times 100 \%$ The percentages for each of the individual elements will then add up to $100 \%$. Which element has a mass percent composition of $54.50 \%$ in Vitamin $\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}$ ?
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Solution

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Solution Steps

Step 1: Determine the Molar Mass of Vitamin C

First, we need to calculate the molar mass of Vitamin C, \( \text{C}_6\text{H}_8\text{O}_6 \).

  • Carbon (C): 6 atoms × 12.01 g/mol = 72.06 g/mol
  • Hydrogen (H): 8 atoms × 1.008 g/mol = 8.064 g/mol
  • Oxygen (O): 6 atoms × 16.00 g/mol = 96.00 g/mol

Adding these together gives the molar mass of Vitamin C:

\[ \text{Molar mass of } \text{C}_6\text{H}_8\text{O}_6 = 72.06 + 8.064 + 96.00 = 176.124 \, \text{g/mol} \]

Step 2: Calculate Mass Percent of Each Element

Next, we calculate the mass percent of each element in Vitamin C using the formula:

\[ \% \text{ of element} = \frac{\text{(number of atoms of element) (atomic mass of element)}}{\text{molar mass of compound}} \times 100\% \]

Mass Percent of Carbon (C)

\[ \% \text{C} = \frac{6 \times 12.01}{176.124} \times 100\% = \frac{72.06}{176.124} \times 100\% \approx 40.91\% \]

Mass Percent of Hydrogen (H)

\[ \% \text{H} = \frac{8 \times 1.008}{176.124} \times 100\% = \frac{8.064}{176.124} \times 100\% \approx 4.58\% \]

Mass Percent of Oxygen (O)

\[ \% \text{O} = \frac{6 \times 16.00}{176.124} \times 100\% = \frac{96.00}{176.124} \times 100\% \approx 54.51\% \]

Final Answer

The element with a mass percent composition of \(54.50\%\) in Vitamin C is Oxygen (O).

\[ \boxed{\text{O}} \]

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