A compound, KBrO𝑥, where x is unknown, is analyzed and found to contain 52.92% Br. What is the value of x?

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Start by assuming you have 100 grams of the compound KBrO_x. This means you have 52.92 grams of Br in the compound.

Calculate the moles of Br using its molar mass (approximately 79.90 g/mol). Use the formula: \( \text{moles of Br} = \frac{\text{mass of Br}}{\text{molar mass of Br}} \).

Determine the mass of K and O in the compound. Since the total mass is 100 grams, the mass of K and O together is 100 - 52.92 grams.

Assume the compound is KBrO_x, where x is the number of oxygen atoms. Calculate the moles of K using its molar mass (approximately 39.10 g/mol).

Use the remaining mass to find the moles of O, and then determine the value of x by dividing the moles of O by the moles of Br to find the ratio of O to Br.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Mass and Percent Composition

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. Percent composition refers to the percentage by mass of each element in a compound. To find the unknown 'x' in KBrO𝑥, we need to relate the given percent composition of bromine (Br) to the total molar mass of the compound, which includes contributions from potassium (K), bromine (Br), and oxygen (O).

Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements present. In this case, determining the value of 'x' involves finding the ratio of the moles of Br to the moles of O in KBrO𝑥. By using the percent composition data, we can derive the empirical formula, which will help identify the value of 'x' in the compound.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the conservation of mass. In this problem, stoichiometry allows us to convert the percent composition of Br into moles and relate it to the moles of O in KBrO𝑥. This relationship is crucial for determining the unknown 'x' by ensuring that the total mass of the compound aligns with the given percentage.

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