A 100.0 g sample is found to contain 77.6 g Xe and 22.4 g F.

What is the percent by mass of Xe in the sample?

A. [tex]$0.776 \%$[/tex]
B. [tex]$22.4 \%$[/tex]
C. [tex]$0.224 \%$[/tex]
D. [tex]$77.6 \%$[/tex]



Answer :

To determine the percent by mass of Xenon (Xe) in the sample, we follow these steps:

1. Identify the given values:
- Mass of Xe in the sample: [tex]\( 77.6 \)[/tex] grams
- Total mass of the sample: [tex]\( 100.0 \)[/tex] grams

2. Calculate the percent by mass:
The percent by mass of a component in a sample is calculated using the formula:

[tex]\[ \text{Percent by mass} = \left( \frac{\text{Mass of the component}}{\text{Total mass of the sample}} \right) \times 100 \][/tex]

3. Substitute the given values into the formula:
- Mass of the component (Xe) = [tex]\( 77.6 \)[/tex] grams
- Total mass of the sample = [tex]\( 100.0 \)[/tex] grams

[tex]\[ \text{Percent by mass of Xe} = \left( \frac{77.6}{100.0} \right) \times 100 \][/tex]

4. Perform the division:
[tex]\[ \frac{77.6}{100.0} = 0.776 \][/tex]

5. Multiply by 100 to convert to a percentage:
[tex]\[ 0.776 \times 100 = 77.6\% \][/tex]

Therefore, the percent by mass of Xenon (Xe) in the sample is [tex]\( 77.6\% \)[/tex].

Reviewing the options provided:
- [tex]\( 0.776\% \)[/tex]
- [tex]\( 22.4\% \)[/tex]
- [tex]\( 0.224\% \)[/tex]
- [tex]\( 77.6\% \)[/tex]

The correct answer is [tex]\( 77.6\% \)[/tex].