Problem 2

Resistive gas sensors using semiconducting metal oxides (SMOX) detect tiny amounts of impurities. The mixed oxide X, which has the normal spinel structure

\mathrm{A^{2+}B^{3+}_2O^{2-}_4}

, is obtained by decomposing in air the crystalline hydrated metal oxalate

\ce{ZC2O4*\mathit{k}H2O}

of metal Z. When heated to 140 °C the hydrate loses 19.7 % of its mass; further heating in air at 500 °C yields 2.407 g of black X together with 3.8 dm

^3

\ce{CO2}

(at 101325 Pa, 500 °C). (a) Determine the formula of X and the value of

k

. (b) In the spinel structure the

\ce{O^{2-}}

ions form a face-centred cubic lattice;

\mathrm{A^{2+}}

cations occupy part of the tetrahedral voids and

\mathrm{B^{3+}}

cations part of the octahedral voids. Calculate the percentage of tetrahedral sites occupied in a normal spinel

\mathrm{AB_2O_4}

Step 2 of 4: Molar mass of the spinel

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3\,\ce{ZC2O4} + 2\,\ce{O2} \rightarrow \ce{Z3O4} + 6\,\ce{CO2};\quad M(\ce{Z3O4}) = \dfrac{2.407}{0.010} = 240.7 \Rightarrow M(\mathrm{Z}) = 58.9\ (\mathrm{Co})

Analysis

A spinel $\mathrm{Z_3O_4}$ needs 3 oxalate units and releases 6 CO2, so $n(\ce{Z3O4}) = n(\ce{CO2})/6 = 0.010$ mol and $M(\ce{Z3O4}) = 2.407/0.010 = 240.7$ g mol $^{-1}$ . Then $M(\mathrm{Z}) = (240.7 - 4\times 16.0)/3 = 58.9$ g mol $^{-1}$ : the metal is cobalt and X is $\ce{Co3O4}$ .