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A chromium containing compound has a formula FexCryO4 and is 28.59% oxygen by mass Find x and y

Question

A chromium containing compound has a formula FexCryO4 and is 28.59% oxygen by mass 

Find x and y

check_circleAnswer
Step 1

Given, mass percentage of O in FexCryO4 = 28.59%

Molar mass of 4 O in FexCryO4 = 4 × 16 g/mol = 64 g/mol

Mass percentage is expressed as:

Mass of a component
Mass % of a component
100 %
Total mass
Molar mass of O
of O in Fe2Cr,O4 = Molar mass of FexCry04
Mass
x 100%
64 g/mol
Molar mass of FexCryO4
x 100%
28.59 %
Molar mass of FexCryO4 223.85 g/mol
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Mass of a component Mass % of a component 100 % Total mass Molar mass of O of O in Fe2Cr,O4 = Molar mass of FexCry04 Mass x 100% 64 g/mol Molar mass of FexCryO4 x 100% 28.59 % Molar mass of FexCryO4 223.85 g/mol

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Step 2

The molar mass of FexCryO4 can be expressed as:

Molar mass of FexCryO4 x(molar mass of Fe)
y(molar mass of Cr) 4(molar mass of O)
223.85 g/mol x(55.85 g/mol) y(52 g/mol) 64 g/mol
223.85 g/mol 64 g/mol x(55.85 g/mol)y(52 g/mol)
=
159.85 g/mol x(55.85 g/mol) y(52 g/mol)
(1)
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Image Transcriptionclose

Molar mass of FexCryO4 x(molar mass of Fe) y(molar mass of Cr) 4(molar mass of O) 223.85 g/mol x(55.85 g/mol) y(52 g/mol) 64 g/mol 223.85 g/mol 64 g/mol x(55.85 g/mol)y(52 g/mol) = 159.85 g/mol x(55.85 g/mol) y(52 g/mol) (1)

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Step 3

So, the sum of [x(55.85 g/mol) + y(52 g/mol)] must not exceed 159.85 g/mol. And there must be at least one Fe and one Cr in FexCryO4. Now, from equation (1) we ...

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