A 5.012 -g sample of an iron chloride hydrate was dried in an oven. The mass of the anhydrous compound was \(3.195 \mathrm{~g}\). The compound was dissolved in water and reacted with an excess of \(\mathrm{AgNO}_{3}\). The precipitae of \(\mathrm{AgCl}\) formed weighed \(7.225 \mathrm{~g}\). What is the formula of the original compound?

Short Answer

Expert verified
The empirical formula of the original compound is \(FeCl_2 \cdot 4H_2O\).

Step by step solution

01

Calculate the water mass

First, find the mass of water that was in the hydrate. This is done by subtracting the mass of the anhydrous compound from the mass of the hydrate:\(5.012 \mathrm{~g} - 3.195 \mathrm{~g} = 1.817 \mathrm{~g}\). Therefore, the mass of water in the hydrate is \(1.817 \mathrm{~g}\).
02

Find molar mass of water and convert mass of water to moles

The molar mass of water is \(18.015 \mathrm{~g/mol}\). Therefore, convert the mass of water to moles using the molar mass as a conversion factor: Moles of Water = \(\frac{1.817 \mathrm{~g}}{18.015 \mathrm{~g/mol}} = 0.1009 \mathrm{mol}\).
03

Calculate amount of Cl in the compound

Next, the mass of AgCl formed indicates the amount of Cl in the compound. The molar mass of \(AgCl\) is \(143.32 \mathrm{~g/mol}\), and we know that 1 mole of \(AgCl\) corresponds to 1 mole of Cl. Therefore, Moles of Cl in the compound = \(\frac{7.225 \mathrm{~g}}{143.32 \mathrm{~g/mol}} = 0.05041 \mathrm{mol}\).
04

Calculate mass of Fe in the compound

We must subtract the mass of Cl from the total mass of the anhydrous compound to find the mass of Fe: Mass of \(Fe = 3.195~g - (0.05041~mol \times 35.453~g/mol) = 1.604~g\). Next, convert the mass of Fe to moles. The molar mass of Fe is \(55.845 \mathrm{~g/mol}\). Hence, moles of Fe = \(\frac{1.604 \mathrm{~g}}{55.845 \mathrm{~g/mol}} = 0.02873 \mathrm{mol}\).
05

Calculate the formula of the compound

Now you can determine the empirical formula of the compound. Divide the number of moles of each element by the smallest number of moles calculated: Fe: \(\frac{0.02873}{0.02873} = 1\), Cl: \(\frac{0.05041}{0.02873} = 1.76\approx2\), H2O: \(\frac{0.1009}{0.02873} = 3.51\approx4\). Therefore, the formula of the original compound is \(FeCl_2 \cdot 4H_2O\)

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Most popular questions from this chapter

A \(46.2-\mathrm{mL}, 0.568 M\) calcium nitrate \(\left[\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\right]\) solution is mixed with \(80.5 \mathrm{~mL}\) of \(1.396 \mathrm{M}\) calcium nitrate solution. Calculate the concentration of the final solution.

A \(1.00-\mathrm{g}\) sample of a metal \(\mathrm{X}\) (that is known to form \(\mathrm{X}^{2+}\) ions) was added to a \(0.100 \mathrm{~L}\) of \(0.500 \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{SO}_{4}\). After all the metal had reacted, the remaining acid required \(0.0334 \mathrm{~L}\) of \(0.500 \mathrm{M} \mathrm{NaOH}\) solution for neutralization. Calculate the molar mass of the metal and identify the element.

Describe how you would prepare \(250 \mathrm{~mL}\) of a \(0.707 M \mathrm{NaNO}_{3}\) solution.

Write ionic and net ionic equations for the following reactions: (a) \(\mathrm{AgNO}_{3}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) (b) \(\mathrm{BaCl}_{2}(a q)+\mathrm{ZnSO}_{4}(a q) \longrightarrow\) (c) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}(a q)+\mathrm{CaCl}_{2}(a q) \longrightarrow\)

Magnesium is a valuable, lightweight metal. It is used as a structural metal and in alloys, in batteries, and in chemical synthesis. Although magnesium is plentiful in Earth's crust, it is cheaper to "mine" the metal from seawater. Magnesium forms the second most abundant cation in the sea (after sodium); there are about \(1.3 \mathrm{~g}\) of magnesium in \(1 \mathrm{~kg}\) of seawater. The method of obtaining magnesium from seawater employs all three types of reactions discussed in this chapter: precipitation, acid-base, and redox reactions. In the first stage in the recovery of magnesium, limestone \(\left(\mathrm{CaCO}_{3}\right)\) is heated at high temperatures to produce quicklime, or calcium oxide \((\mathrm{CaO})\) : $$ \mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) $$ When calcium oxide is treated with seawater, it forms calcium hydroxide \(\left[\mathrm{Ca}(\mathrm{OH})_{2}\right]\), which is slightly soluble and ionizes to give \(\mathrm{Ca}^{2+}\) and \(\mathrm{OH}^{-}\) ions: $$ \mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}^{2+}(a q)+2 \mathrm{OH}^{-}(a q) $$ The surplus hydroxide ions cause the much less soluble magnesium hydroxide to precipitate: $$ \mathrm{Mg}^{2+}(a q)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s) $$ The solid magnesium hydroxide is filtered and reacted with hydrochloric acid to form magnesium chloride \(\left(\mathrm{MgCl}_{2}\right)\) \(\mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{HCl}(a q) \longrightarrow\) $$ \mathrm{MgCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ After the water is evaporated, the solid magnesium chloride is melted in a steel cell. The molten magnesium chloride contains both \(\mathrm{Mg}^{2+}\) and \(\mathrm{Cl}^{-}\) ions. In a process called electrolysis, an electric current is passed through the cell to reduce the \(\mathrm{Mg}^{2+}\) ions and oxidize the \(\mathrm{Cl}^{-}\) ions. The halfreactions are $$ \begin{aligned} \mathrm{Mg}^{2+}+2 e^{-} \longrightarrow \mathrm{Mg} \\ 2 \mathrm{Cl}^{-} \longrightarrow \mathrm{Cl}_{2}+2 e^{-} \end{aligned} $$ The overall reaction is $$ \mathrm{MgCl}_{2}(l) \longrightarrow \mathrm{Mg}(s)+\mathrm{Cl}_{2}(g) $$ This is how magnesium metal is produced. The chlorine gas generated can be converted to hydrochloric acid and recycled through the process. (a) Identify the precipitation, acid-base, and redox processes. (b) Instead of calcium oxide, why don't we simply add sodium hydroxide to precipitate magnesium hydroxide? (c) Sometimes a mineral called dolomite (a combination of \(\mathrm{CaCO}_{3}\) and \(\mathrm{MgCO}_{3}\) ) is substituted for limestone \(\left(\mathrm{CaCO}_{3}\right)\) to bring about the precipitation of magnesium hydroxide. What is the advantage of using dolomite? (d) What are the advantages of mining magnesium from the ocean rather than from Earth's crust?

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