The atomic mass of X is 30.69 u.
<h3>Further Explanation</h3>
Mass percent is the ratio of an element's mass to the mass of the compound. It is mathematically expressed as:
![\% \ mass \ of \ A \ = \frac{mass \ of \ element \ A}{mass \ of \ compound} \times 100](https://tex.z-dn.net/?f=%5C%25%20%5C%20mass%20%5C%20of%20%5C%20A%20%5C%20%3D%20%5Cfrac%7Bmass%20%5C%20of%20%5C%20element%20%5C%20A%7D%7Bmass%20%5C%20of%20%5C%20compound%7D%20%5Ctimes%20100)
In the problem, the mass percent of F is given and can be used to determine the atomic mass of element X. To do this, just set up the mass percent equation for F as shown below:
![mass \ \% \ of \ F = \frac{3 \times 18.998 \ u}{ X + 56.994 u}\\\\mass \% \ of \ F = \frac{56.994 \ u}{X + 56.994 \ u} = 65\%\\](https://tex.z-dn.net/?f=mass%20%5C%20%5C%25%20%5C%20of%20%5C%20F%20%3D%20%5Cfrac%7B3%20%5Ctimes%2018.998%20%5C%20u%7D%7B%20X%20%2B%2056.994%20u%7D%5C%5C%5C%5Cmass%20%5C%25%20%5C%20of%20%5C%20F%20%3D%20%5Cfrac%7B56.994%20%5C%20u%7D%7BX%20%2B%2056.994%20%5C%20u%7D%20%3D%2065%5C%25%5C%5C)
Solving for X,
![0.65 (X + 56.994) = 56.994\\0.65X \ + \ 37.0461 = 56.994\\0.65X = 19.9479\\\\\boxed {\boxed {X = 30.69 \ u}}](https://tex.z-dn.net/?f=0.65%20%28X%20%2B%2056.994%29%20%3D%2056.994%5C%5C0.65X%20%5C%20%2B%20%5C%2037.0461%20%3D%2056.994%5C%5C0.65X%20%3D%2019.9479%5C%5C%5C%5C%5Cboxed%20%7B%5Cboxed%20%7BX%20%3D%2030.69%20%5C%20u%7D%7D)
To check if the atomic mass of X is correct, use this value to calculate the %F. It is is equal to 65%, then the calculated value for X is correct.
![\% F \ = \frac{3 \times 18.998 u}{30.69u \ + 56.994 u} \times 100\\\\\%F \ = \frac{56.994u}{87.684u} \times 100\\\\\\boxed {\%F = 64.999\%}](https://tex.z-dn.net/?f=%5C%25%20F%20%5C%20%3D%20%5Cfrac%7B3%20%5Ctimes%2018.998%20u%7D%7B30.69u%20%5C%20%2B%2056.994%20u%7D%20%5Ctimes%20100%5C%5C%5C%5C%5C%25F%20%5C%20%3D%20%5Cfrac%7B56.994u%7D%7B87.684u%7D%20%5Ctimes%20100%5C%5C%5C%5C%5C%5Cboxed%20%7B%5C%25F%20%3D%2064.999%5C%25%7D)
Since substituting 30.69 as the atomic mass of X gives a mass % of 65 for F, then the calculated atomic mass is correct.
<h3>Learn More</h3>
- Learn more about empirical formula brainly.com/question/8516072
- Learn more about chemical formula brainly.com/question/4697698
- Learn more about percent composition brainly.com/question/11042307
Keywords: mass percent, empirical formula