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In a sample of a metal-deficient oxide with the formula MxY2O4 (where M and Y are metals), the metal M exists in both +2 and +3 oxidation states, while Y is in the +3 oxidation state. If one-third of the M ions are in the +2 state, determine the value of X.

1. 0.25
2. 0.33
3. 0.67
4. 0.75

Correct answer: 0.75

Solution

In M_x Y2 O4 the cations must total +8 (4 O at -2). Y2 contributes +6, so M contributes +2 total. With one-third of M as +2 and two-thirds as +3, average charge per M = (1/3)(2)+(2/3)(3) = 8/3, giving x = 2/(8/3) = 0.75 (index 3). The stored value 0.33 (index 1) is wrong.

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