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 2 of 3: Apply the mole ratio

n(\ce{Ga2O3}) = \tfrac{1}{2} n(\ce{GaN}) = 0.5974\ \text{mol}

Analysis

The balanced equation $\ce{Ga2O3 + 2NH3 -> 2GaN + 3H2O}$ gives $n(\ce{Ga2O3}):n(\ce{GaN}) = 1:2$ , so $n(\ce{Ga2O3}) = 1.195/2 = 0.5974$ mol.