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A non-stoichiometric metal oxide has the empirical formula M _x O . The metal M exists in the oxide as a mixture of M ²⁺ and M ³⁺ ions. If the ratio of the number of M ²⁺ ions to M ³⁺ ions in the sample is 7:2 , the value of 100x is

Correct answer

90

Step-by-step solution

Let the formula be M _x O . For every 1 mole of O ²⁻ ions, there are x moles of metal M ions. The ratio of M ²⁺ to M ³⁺ is 7:2 . Moles of M ²⁺ = 7 9 x Moles of M ³⁺ = 2 9 x By the principle of electrical neutrality, the total positive charge must equal the total negative charge: 2 ( 7 9 x ) + 3 ( 2 9 x ) = 2 1 14x 9 + 6x 9 = 2 20x 9 = 2 x = 18 20 = 0.90 Therefore, the value of 100x is 100 0.90 = 90 . Answer: 90

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