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Chapter 3: Problem 109

A piece of gold (Au) foil measuring \(0.25 \mathrm{mm} \times\) \(15 \mathrm{mm} \times 15 \mathrm{mm}\) is treated with fluorine gas. The treatment converts all the gold in the foil to \(1.400 \mathrm{g}\) of a gold fluoride. What is the formula and name of the fluoride? The density of gold is \(19.3 \mathrm{g} / \mathrm{cm}^{3}\)

Short Answer

Expert verified
The formula of the gold fluoride is \(AuF3\) and its name is Gold(III) fluoride.

Step by step solution

01

Calculate the volume of gold

The volume can be calculated from the given dimensions of the gold foil. It is \(0.25 \mathrm{mm} \times15 \mathrm{mm} \times 15 \mathrm{mm}\) which translates to \(0.25 \mathrm{cm} \times1.5 \mathrm{cm} \times 1.5 \mathrm{cm}\) in cm since 1cm = 10mm. We proceed to multiply these measurements to get the volume of the bar.
02

Calculate the mass of the gold

This requires multiplying the volume of the gold bar calculated in the previous step by the given density of gold, \(19.3 \mathrm{g/cm}^{3}\) to obtain mass.
03

Find the mass of fluorine

The mass of fluorine can be calculated by subtracting the mass of gold derived in Step 2 from the total mass of the gold fluoride, 1.400g.
04

Convert the masses of gold and fluorine into moles

The molar mass of gold is approximately \(197.0 \mathrm{g/mol}\) and that of fluorine is approximately \(19.0 \mathrm{g/mol}\). Divide the mass of each by its molar mass.
05

Calculate the mole ratio

Still assuming that each gold atom reacts with just one fluorine atom, divide each number of moles by the smaller so that the empirical formula has the smallest whole numbers possible. Round off to the nearest whole numbers.
06

Deduce the formula and name of the fluoride

From the outcomes in step 5, construct the formula of the salt and give its name.

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Most popular questions from this chapter

\(\mathrm{XF}_{3}\) consists of \(65 \%\) F by mass. The atomic mass of the element X must be (a) 8 u; (b) 11 u; (c) 31 u; (d) 35 u.

Indicate the oxidation state of \(S\) in \(\left(\text { a) } \mathrm{SO}_{3}^{2-}\right.\) (b) \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-} ;\) (c) \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-} ;\) (d) \(\mathrm{HSO}_{4}^{-} ;\) (e) \(\mathrm{S}_{4} \mathrm{O}_{6}^{2-}\)

The element \(X\) forms the chloride \(X C l_{4}\) containing \(75.0 \% \mathrm{Cl},\) by mass. What is element \(\mathrm{X} ?\)

Without doing detailed calculations, arrange the following in order of increasing \(\% \mathrm{Cr},\) by mass, and explain your reasoning: \(\mathrm{CrO}, \mathrm{Cr}_{2} \mathrm{O}_{3}, \mathrm{CrO}_{2}, \mathrm{CrO}_{3}\)

Explain the important distinctions between each pair of terms: (a) molecular mass and molar mass; (b) empirical and molecular formulas; (c) systematic and trivial, or common, name; (d) hydroxyl and carboxyl functional group.
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