91Ó°ÊÓ

A chemical formula is crucial in representing the composition of a compound. In our exercise, the formula given is \( \mathrm{HXO}_3 \), which includes three types of atoms: Hydrogen (H), an unknown element denoted as \( \mathrm{X} \), and Oxygen (O).
This formula indicates:

• One hydrogen atom.
• One unknown atom represented by \( \mathrm{X} \).
• Three oxygen atoms.

Understanding such formulas helps identify the type and number of each atom present. By decoding this formula, we know that finding \( \mathrm{X} \) requires completing the mass balancing based on known atomic masses of hydrogen and oxygen.

The molar mass of a substance is the weight of one mole of that substance. For the acid \( \mathrm{HXO}_3 \) given in the problem, we know that 0.0133 moles weigh 1.123 grams. This information helps us calculate the molar mass \( M \) by dividing the mass by the number of moles:
\[ M = \frac{1.123 \, \text{grams}}{0.0133 \, \text{moles}} \approx 84.51 \, \text{g/mol} \]
This measurement is critical as it helps us determine the contribution each element makes to the total mass. By knowing the molar masses of more common elements (as in our Solution: H = 1 g/mol, O = 16 g/mol), we can work out the unknown component \( \mathrm{X} \). This concept underlies many calculations in chemistry and is essential for identifying unknowns within a formula.

Identifying an unknown element within a chemical compound often relies on understanding its molar mass. Once we calculated the molar mass for the acid \( \mathrm{HXO}_3 \), we subtracted the known contributions from hydrogen and oxygen to isolate the mass of the unknown \( \mathrm{X} \):
\[ \text{Mass of X} = 84.51 - 49 = 35.51 \, \text{g/mol} \]
The calculated atomic mass of \( 35.51 \, \text{g/mol} \) is the key to identifying \( \mathrm{X} \). By matching this against a periodic table, it matches closely with the atomic mass of chlorine, a fundamental step in determining \( \mathrm{X} \) as the element chlorine.

Chlorine is a chemical element that is widely used and recognized by its atomic mass of approximately 35.45 g/mol. In this exercise, through analytical calculations, we determined that the unknown element \( \mathrm{X} \) in \( \mathrm{HXO}_3 \) is chlorine. The slight difference between 35.51 g/mol and 35.45 g/mol can be attributed to rounding in calculations or measurement variability.
Chlorine is typically encountered in compounds such as hydrochloric acid (HCl) and bleach (sodium hypochlorite), highlighting its versatile nature in both industrial and household applications. Its identification within chemical formulas is critical for predicting reactions and understanding compound properties.