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].
