Two metallic oxides contain 27.6% and 30% oxygen respectively. If the formula of the first oxide is X₃O₄, that of the second will be:

• A. XO
• B. X₂O₂
• C. X₂O₅
• D. X₂O₃

To determine the formula of the second metallic oxide, we first need to analyze the information given about the two oxides.

Understanding the First Oxide

The first oxide has a formula of X₃O₄ and contains 27.6% oxygen. We can calculate the molar mass of this oxide:

• Molar mass of O = 16 g/mol
• Molar mass of X = Molar mass of X₃O₄ - (4 × 16)

Let’s find the total mass of the compound:

• Mass of O in X₃O₄ = 4 × 16 = 64 g
• Let the molar mass of X₃O₄ be M. Then, 27.6% of M = 64 g.

From this, we can find M:

M = 64 g / 0.276 ≈ 231.16 g/mol.

Analyzing the Second Oxide

The second oxide contains 30% oxygen. Let’s denote its formula as XₙOₘ. Using the same approach:

• Mass of O in the second oxide = 30% of its molar mass.

Let’s denote the molar mass of the second oxide as M₂:

• 0.30 × M₂ = Mass of O

Since we know the mass of oxygen in the second oxide is 30% of its total mass, we can set up the equation:

Mass of O = 0.30 × M₂ = 16 × m (where m is the number of oxygen atoms in the formula).

Finding the Correct Formula

To find the ratio of X to O, we can compare the two oxides:

• For X₃O₄: Ratio of X to O = 3:4
• For the second oxide with 30% oxygen, we can test the options:

Testing the Options

• A. XO: Ratio = 1:1 (not possible)
• B. X₂O₂: Ratio = 1:1 (not possible)
• C. X₂O₅: Ratio = 2:5 (not matching)
• D. X₂O₃: Ratio = 2:3 (matches closely with 30% oxygen)

Thus, the formula of the second oxide is likely X₂O₃.