Question

measurements show that unknown compound x has the following composition:
write the empirical chemical formula of x.

Explanation:

Step1: Assume 100g of the compound

If we assume we have 100g of compound \(X\), then the mass of iron (\(Fe\)) is \(m_{Fe}=69.9g\) and the mass of oxygen (\(O\)) is \(m_{O} = 30.0g\).

Step2: Calculate the number of moles of each element

The molar mass of \(Fe\) is \(M_{Fe}=55.85g/mol\), and the molar mass of \(O\) is \(M_{O}=16.00g/mol\).
The number of moles of \(Fe\), \(n_{Fe}=\frac{m_{Fe}}{M_{Fe}}=\frac{69.9g}{55.85g/mol}\approx1.25mol\)
The number of moles of \(O\), \(n_{O}=\frac{m_{O}}{M_{O}}=\frac{30.0g}{16.00g/mol}=1.875mol\)

Step3: Find the mole - ratio

Divide each number of moles by the smaller number of moles. Here, \(n = 1.25mol\) (for \(Fe\))
For \(Fe\): \(\frac{n_{Fe}}{n}=\frac{1.25mol}{1.25mol}=1\)
For \(O\): \(\frac{n_{O}}{n}=\frac{1.875mol}{1.25mol}=1.5\)
Multiply each ratio by 2 to get whole - numbers.
For \(Fe\): \(1\times2 = 2\)
For \(O\): \(1.5\times2=3\)

Answer:

\(Fe_2O_3\)