Question

measurements show that unknown compound x has the following composition: element mass % carbon 62.6% hydrogen 4.20% oxygen 33.4% write the empirical chemical formula of x.

Explanation:

Step1: Assume 100g of the compound

If we assume 100g of compound X, then we have 62.6g of carbon, 4.20g of hydrogen, and 33.4g of oxygen.

Step2: Calculate the number of moles of each element

The molar - mass of carbon ($C$) is $M_{C}=12.01g/mol$, hydrogen ($H$) is $M_{H}=1.01g/mol$, and oxygen ($O$) is $M_{O}=16.00g/mol$.
The number of moles of carbon $n_{C}=\frac{62.6g}{12.01g/mol}\approx5.21mol$.
The number of moles of hydrogen $n_{H}=\frac{4.20g}{1.01g/mol}\approx4.16mol$.
The number of moles of oxygen $n_{O}=\frac{33.4g}{16.00g/mol}\approx2.09mol$.

Step3: Find the mole - ratio of the elements

Divide each number of moles by the smallest number of moles among them (2.09mol in this case).
For carbon: $\frac{n_{C}}{n_{O}}=\frac{5.21mol}{2.09mol}\approx2.5$.
For hydrogen: $\frac{n_{H}}{n_{O}}=\frac{4.16mol}{2.09mol}\approx2$.
For oxygen: $\frac{n_{O}}{n_{O}} = 1$.
Since we need whole - number ratios, multiply each ratio by 2 to get whole numbers.
The ratio of $C:H:O$ becomes 5:4:2.

Answer:

$C_{5}H_{4}O_{2}$