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Chapter 3: Problem 47

A compound whose empirical formula is \(\mathrm{XF}_{3}\) consists of \(65 \%\) F by mass. What is the atomic mass of X?

Short Answer

Expert verified
The atomic mass of element X in the compound \(\mathrm{XF}_{3}\) is approximately 30.54 g/mol.

Step by step solution

01

Calculate the mass of F in \(\mathrm{XF}_{3}\)

Since \(\mathrm{XF}_{3}\) consists of 65% F by mass, it means that the remaining mass (100%-65%=35%) will be element X. We can assume a total mass of 100 grams for the compound, which would give us 65 grams of F and 35 grams of X. Now, we move on to the following steps.
02

Calculate moles of F

To find the moles of F in the compound, we will use the molar mass of F, which is approximately 19 g/mol. Moles of F = Mass of F / Molar mass of F = 65 g / 19 g/mol = \( \frac{65}{19} \) moles.
03

Calculate the ratio of X to F in moles

Since the empirical formula is \(\mathrm{XF}_{3}\), this means there are 3 moles of F per mole of X. We can use this information to find the moles of X in the compound. Moles of X = \( \frac{1}{3} \times \frac{65}{19} \) = \( \frac{65}{57} \) moles.
04

Calculate the atomic mass of X

Now that we have the moles of X and mass of X, we can find the atomic mass of X using the formula: Atomic mass of X = Mass of X / Moles of X Atomic mass of X = \( \frac{35 \text{ g}}{\frac{65}{57} \text{ moles}} \) Atomic mass of X = \( 35 \times \frac{57}{65} \) Atomic mass of X ≈ 30.54 g/mol Thus, the atomic mass of element X is approximately 30.54 g/mol.

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Most popular questions from this chapter

Determine the empirical and molecular formulas of each of the following substances: (a) Styrene, a compound substance used to make Styrofoam \(^{\circledast}\) cups and insulation, contains \(92.3 \% \mathrm{C}\) and \(7.7 \% \mathrm{H}\) by mass and has a molar mass of \(104 \mathrm{~g} / \mathrm{mol}\) (b) Caffeine, a stimulant found in coffee, contains \(49.5 \% \mathrm{C}\), \(5.15 \% \mathrm{H}, 28.9 \% \mathrm{~N},\) and \(16.5 \% \mathrm{O}\) by mass and has a molar mass of \(195 \mathrm{~g} / \mathrm{mol}\) (c) Monosodium glutamate (MSG), a flavor enhancer in certain foods, contains \(35.51 \%\) C, \(4.77 \%\) H, \(37.85 \%\) O, \(8.29 \% \mathrm{~N},\) and \(13.60 \% \mathrm{Na},\) and has a molar mass of \(169 \mathrm{~g} / \mathrm{mol}\)

The allowable concentration level of vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl},\) in the atmosphere in a chemical plant is \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\). How many moles of vinyl chloride in each liter does this represent? How many molecules per liter?

Balance the following equations: (a) $\mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Li}_{3} \mathrm{~N}(s)$ (b) $\mathrm{TiCl}_{4}(l)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{TiO}_{2}(s)+\mathrm{HCl}(a q)$ (c) $\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$ (d) $\mathrm{AlCl}_{3}(s)+\mathrm{Ca}_{3} \mathrm{~N}_{2}(s) \longrightarrow \mathrm{AlN}(s)+\mathrm{CaCl}_{2}(s)$

Determine the formula weights of each of the following com- pounds: (a) nitric acid, \(\mathrm{HNO}_{3} ;\) (b) \(\mathrm{KMnO}_{4} ;\) (c) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} ;\) (d) quartz, \(\mathrm{SiO}_{2} ;\) (e) gallium sulfide, (f) chromium(III) sulfate, (g) phosphorus trichloride.

What is the mass, in kilograms, of an Avogadro's number of people, if the average mass of a person is \(160 \mathrm{lb}\) ? How does this compare with the mass of Earth, \(5.98 \times 10^{24} \mathrm{~kg}\) ?
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