Wüstite, a non-stoichiometric iron(II)…

Wüstite, a non-stoichiometric iron(II) oxide with the formula Fe0.93O, has a rock-salt structure with cubic unit-cell edge 431 pm (four formula units…

Numerical answer

Wüstite, a non-stoichiometric iron(II) oxide with the formula

\mathrm{Fe_{0.93}O}

, has a rock-salt structure with cubic unit-cell edge

431\ \mathrm{pm}

(four formula units per cell). The iron deficiency is compensated by

\mathrm{Fe^{3+}}

ions so that the crystal is electrically neutral. Taking atomic masses

\mathrm{Fe}=55.85

\mathrm{O}=16.00\ \mathrm{g\,mol^{-1}}

and

N_A=6.022\times10^{23}\ \mathrm{mol^{-1}}

, the mass of

\mathrm{Fe^{3+}}

present in

1\ \mathrm{cm^3}

of the crystal, in grams, is ______. Give the answer correct to two decimal places.

Show answer and solution

Answer: 0.65

Let

y

be the number of

\mathrm{Fe^{3+}}

ions per formula unit. Charge neutrality for

\mathrm{Fe_{0.93}O}

2(0.93-y)+3y=2

, so

y=2-1.86=0.14

(about 15% of the iron is Fe(III)). Molar mass of the formula unit is

0.93\times55.85+16.00=67.94\ \mathrm{g\,mol^{-1}}

. Unit-cell volume is

a^3=(431\times10^{-10}\ \mathrm{cm})^3=8.007\times10^{-23}\ \mathrm{cm^3}

, so the density is

d=\dfrac{4\times67.94}{6.022\times10^{23}\times8.007\times10^{-23}}=5.637\ \mathrm{g\,cm^{-3}}

. The mass fraction of

\mathrm{Fe^{3+}}

\dfrac{0.14\times55.85}{67.94}=0.1151

. The mass of

\mathrm{Fe^{3+}}

per

\mathrm{cm^3}

5.637\times0.1151=0.649\ \mathrm{g}\approx0.65\ \mathrm{g}

. The key point is that the density uses the actual non-stoichiometric formula mass, with 4 formula units per face-centred cell.

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