Question

Experimentally it was found that a metal oxide has formula M₀.₉₆O. Metal m present as M²⁺ and M³⁺ in its oxide. Fraction of the metal which exists as M³⁺ would be

a) 7%
b) 4%
c) 8%
d) 5%

Answer 1

The fraction of the metal that is in the M³⁺ oxidation state in the compound M₀.₉₆O is 4%. Option number b is correct.

Step-by-step explanation:

The fraction of the metal which exists as M³⁺ in the compound M₀.₉₆O can be calculated using stoichiometry and the charge balance in the compound. Given that the metal is present in two oxidation states, M²⁺ and M³⁺, we can balance the charges to find the fraction of M³⁺.

According to the formula, each oxygen ion carries a -2 charge, and for M₀.₉₆O, there are 0.96 moles of metal for 1 mole of oxygen. Let x be the fraction of M³⁺ and (1-x) be the fraction of M²⁺. The charge balance equation is 3x + 2(1-x) = 2, as the overall charge must balance with the -2 charge from the oxygen ion.

On solving, we get 3x + 2 - 2x = 2, which simplifies to x = 0.04, or 4%. Therefore, 4% of the metal is in the form of M³⁺.