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Chapter 3: Problem 118

Analysis of a metal chloride \(\mathrm{XCl}_{3}\) show that it contains 67.2 percent \(\mathrm{Cl}\) by mass. Calculate the molar mass of \(\mathrm{X}\) and identify the element.

Short Answer

Expert verified
The element X in the molecule \(XCl_3\) is Chromium (Cr) with a calculated molar mass of approximately 52.687 g/mol.

Step by step solution

01

Calculate the mass fraction of Chlorine and the unknown element in the compound

Given that the compound \(XCl_3\) contains 67.2 percent Chlorine by mass, it means the rest is the unknown element. Therefore the mass percent of X (the unknown element) is \(100\% - 67.2\% = 32.8\%\)
02

Calculate the molar mass of Chlorine

The atomic mass of Chlorine (Cl) is 35.453 g/mol. In the molecule \(XCl_{3}\), we have 3 atoms of Chlorine, so the total mass contributed by Chlorine in this molecule is \(3 \times 35.453g/mol = 106.359 g/mol\)
03

Calculate the molar mass of the unknown element

Given that the mass ratio is 32.8:67.2, the mass of X (unknown element) can be calculated from the mass of Cl derived in the step before in the following way: \((32.8/67.2) \times 106.359 g/mol = 52.687 g/mol\) This is the molar mass of the unknown element X.
04

Identify the unknown element

Now, comparing this molar mass with the periodic table or a list of atomic masses, we find that the element with this molar mass closest to 52.687 g/mol is Chromium (Cr) - its atomic weight is 52.00 g/mol. So, the unknown element X in \(XCl_3\) is Chromium (Cr).

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Most popular questions from this chapter

Balance the following equations using the method outlined in Section 3.7 : (a) \(\mathrm{C}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}\) (b) \(\mathrm{CO}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}\) (c) \(\mathrm{H}_{2}+\mathrm{Br}_{2} \longrightarrow \mathrm{HBr}\) (d) \(\mathrm{K}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{KOH}+\mathrm{H}_{2}\) (e) \(\mathrm{Mg}+\mathrm{O}_{2} \longrightarrow \mathrm{MgO}\) (f) \(\mathrm{O}_{3} \longrightarrow \mathrm{O}_{2}\) (g) \(\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\) (h) \(\mathrm{N}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{NH}_{3}\) (i) \(\mathrm{Zn}+\mathrm{AgCl} \longrightarrow \mathrm{ZnCl}_{2}+\mathrm{Ag}\) (j) \(\mathrm{S}_{8}+\mathrm{O}_{2} \longrightarrow \mathrm{SO}_{2}\) (k) \(\mathrm{NaOH}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}+\mathrm{H}_{2} \mathrm{O}\) (l) \(\mathrm{Cl}_{2}+\mathrm{NaI} \longrightarrow \mathrm{NaCl}+\mathrm{I}_{2}\) \((\mathrm{m}) \mathrm{KOH}+\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow \mathrm{K}_{3} \mathrm{PO}_{4}+\mathrm{H}_{2} \mathrm{O}\) (n) \(\mathrm{CH}_{4}+\mathrm{Br}_{2} \longrightarrow \mathrm{CBr}_{4}+\mathrm{HBr}\)

Describe the steps involved in the mole method.

Nitric oxide (NO) reacts with oxygen gas to form nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\), a dark-brown gas: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ In one experiment 0.886 mole of NO is mixed with 0.503 mole of \(\mathrm{O}_{2}\). Calculate which of the two reactants is the limiting reactant. Calculate also the number of moles of \(\mathrm{NO}_{2}\) produced.

A mixture of methane \(\left(\mathrm{CH}_{4}\right)\) and ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) of mass \(13.43 \mathrm{~g}\) is completely burned in oxygen. If the total mass of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) produced is \(64.84 \mathrm{~g},\) calculate the fraction of \(\mathrm{CH}_{4}\) in the mixture.

A sample containing \(\mathrm{NaCl}, \mathrm{Na}_{2} \mathrm{SO}_{4},\) and \(\mathrm{NaNO}_{3}\) gives the following elemental analysis: Na: 32.08 percent; O: 36.01 percent; Cl: 19.51 percent. Calculate the mass percent of each compound in the sample.
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