Question

Calcium is used to reduce vanadium (V) oxide to elemental vanadium in a sealed steel vessel. Vanadium is used in vanadium steel alloys for jet engines, high quality knives, and tools. Write a balanced chemical equation for this process. What mass of calcium is needed, in theory, to produce 20.0kgof vanadium from vanadium oxide?

Short answer

The mass of calcium needed to produce 20kg of is $39.3\mathrm{kg}$.

Step-by-step solution

The chemical equation involved in this process

The unbalanced reaction is $\mathit{C}\mathit{a}\mathbf{+}{\mathbf{V}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{5}}\mathbf{\to }\mathbf{V}\mathbf{+}\mathit{C}\mathit{a}\mathit{O}$$\mathrm{Ca}+{\mathrm{V}}_2{\mathrm{O}}_5\to \mathrm{V}+\mathrm{CaO}$

The balanced reaction is $\mathbf{5}\mathit{C}\mathit{a}\mathbf{+}{\mathbf{V}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{5}}\mathbf{\to }\mathbf{2}\mathbf{}\mathbf{V}\mathbf{+}\mathbf{5}\mathit{C}\mathit{a}\mathit{O}$

Calculating the mass of calcium needed to produce Vanadium from Vanadium oxide

$\begin{array}{l}\mathrm{Mr}\left(\mathrm{Ca}\right)=40.08\mathrm{g}/\mathrm{mol}\\ \mathrm{Mr}\left(\mathrm{V}\right)=50.94\mathrm{g}/\mathrm{mol}\end{array}$

5 moles of Calcium produce 2 moles of .

$\begin{array}{l}m\left(\mathrm{Ca}\right)=\left(20.0\mathrm{kgV}\times \frac{{10}^3\mathrm{g}}{1\mathrm{kg}}\times \frac{1\mathrm{molV}}{50.94\mathrm{gV}}\right)\times \left(\frac{5\mathrm{molCa}}{2\mathrm{molV}}\times \frac{40.08\mathrm{gCa}}{1\mathrm{molCa}}\right)\\ m\left(\mathrm{Ca}\right)=39.3\times {10}^3\mathrm{g}=39.3\mathrm{kg}\end{array}$

Thus, the mass of Calcium needed to produce of is $39.3\mathrm{kg}$.