Problem 1

The element gallium (Ga,

Z=31

) is recovered as a by-product of aluminium production. Gallium nitride is made by heating

\ce{Ga2O3}

with ammonia:

\ce{Ga2O3 + 2NH3 -> 2GaN + 3H2O}

. Calculate the mass of

\ce{Ga2O3}

needed to prepare 100 g of GaN. (

M(\ce{Ga2O3}) = 187.4

g mol

^{-1}

M(\ce{GaN}) = 83.7

g mol

^{-1}

)

Step 3 of 3: Convert back to mass

m(\ce{Ga2O3}) = 0.5974 \times 187.4 = 111.9\ \text{g} \approx 112\ \text{g}

Analysis

$m = n \times M = 0.5974 \times 187.4 = 111.9$ g ≈ 112 g of $\ce{Ga2O3}$ .

Common pitfall. Do not use the 1:2 ratio the wrong way round: 1 mole of

\ce{Ga2O3}

gives 2 moles of GaN, not the reverse.