Question

Lanthanum was reacted with hydrogen in a given experiment to produce the nonstoichiometric compound.${\mathbf{\text{LaH}}}_{\mathbf{\text{2.90}}}$Assuming that the compound contains${\mathbf{\text{H}}}^{\mathbf{\text{-}}}{\mathbf{\text{,La}}}^{\mathbf{\text{2+}}}{\mathbf{\text{,and\hspace{0.17em}La}}}^{\mathbf{\text{3+}}}\mathbf{\text{,}}$ calculate the fraction of ${\mathbf{\text{La}}}^{\mathbf{\text{2+}}}{\mathbf{\text{\hspace{0.17em}and\hspace{0.17em}La}}}^{\mathbf{\text{3+}}}$present

Short answer

The fraction of ${\text{La}}^{\text{2+}}$is$10\%$

The fraction of ${\text{La}}^{\text{3+}}$is $90\%$

Step-by-step solution

Calculation for the fraction ofLa2+ and La3+

$\begin{array}{l}L{a}_{2.90}H\to L{a}^{2+}L{a}^{3+}H\\ x=L{a}^{2+}\\ y=L{a}^{3+}\\ x+y=-1\left(H\right)\to x\\ =1-y\\ 2x+3y=2.90\\ 2(1-y)+3y=2.90\end{array}$

Calculating the percentage ofLa3+ and La2+

$\begin{array}{l}y=0.90\to x\\ 1-y=0.10\\ x=0.10\\ y=0.90\end{array}$

Here,$90\%$ of ${\text{La}}^{\text{3+}}$and $10\%$of${\text{La}}^{\text{2+}}$ is present