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------------------------------------------------ An unknown compound, \( \text{KBrO}_x \), contains 52.92% of Br. Find \( x \).

Given:
- K = 39.1 g/mol
- O = 16 g/mol
- Br = 79.9 g/mol

In the unidentified compound KBrOx, Br makes up 52.92% of the mass. By calculating the mass and then the moles of each type of atom in a 100g sample of the compound, we learn that the empirical formula of the compound is KBrO3. Therefore, x is 3.

Explanation:

The question is a classic example of persentage composition and empirical formula problems in chemistry. In the unknown compound KBrOx, the fact that bromine (Br) comprises 52.92% of the compound implies the remaining 47.08% of the compound's mass is due to potassium (K) and oxygen (O) atoms. Given that the molar masses for K, O, and Br are 39.1 g/mol, 16 g/mol, and 79.9 g/mol respectively, we can determine the value of x, that is the number of oxygen atoms in the compound.

To find x, we can first calculate the mass of each atom type in a 100g sample of the compound, then calculate the moles of each atom type, and finally create the empirical formula of the compound. After these steps, it is found that the empirical formula of the compound is KBrO3, so x = 3.

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