A metal oxide has the formula Z₂O₃. It can be reduced by hydrogen to give a free metal and water. 0.1596 gm of the metal oxide requires 6mg of hydrogen for complete reduction. The atomic mass of the metal is

${\mathrm{Z}}_2{\mathrm{O}}_3+3{\mathrm{H}}_2\to 2\mathrm{Z}+3{\mathrm{H}}_2\mathrm{O}$

1 mole of the metal requires 3 moles of H_2​ for complete reduction.

Moles of H₂​ consumed =$\frac{6 \mathrm{mg}}{2 \mathrm{g}}=3\times {10}^{-3}\mathrm{mole}$

Moles of metal oxide reduced = $\frac{3\times {10}^{-3}}{3}\mathrm{mole}={10}^{-3}\mathrm{mole}$

∴ molecular mass of Z₂​O₃​= $\frac{0.1596 \mathrm{g}}{{10}^{-3}}=159.6 \mathrm{g}$

⇒2×M_Z​+3×M_O​=159.6

⇒2×M_Z​+3×16=159.6 

⇒M_Z​= $\frac{(159.6-48)}{2}=55.8$