To find the empirical formula of a compound of silicon and oxygen given that it contains 47% by mass of silicon, and knowing the atomic masses of silicon (Si) and oxygen (O) are 28 g/mol and 16 g/mol respectively, we can follow these steps:
### Step 1: Calculate the mass percentage of oxygen
Since the compound is 100% composed of silicon and oxygen, we can find the mass percentage of oxygen by subtracting the mass percentage of silicon from 100%.
[tex]\[ \text{Percentage of Oxygen} = 100\% - 47\% = 53\% \][/tex]
### Step 2: Calculate the moles of silicon and oxygen in 100 grams of the compound
Assuming we have 100 grams of the compound, we can calculate the moles of each element.
For silicon:
[tex]\[ \text{Mass of Silicon} = 47 \, \text{grams} \][/tex]
[tex]\[ \text{Moles of Silicon} = \frac{\text{Mass of Silicon}}{\text{Atomic Mass of Silicon}} = \frac{47 \, \text{grams}}{28 \, \text{g/mol}} \approx 1.67857 \, \text{moles} \][/tex]
For oxygen:
[tex]\[ \text{Mass of Oxygen} = 53 \, \text{grams} \][/tex]
[tex]\[ \text{Moles of Oxygen} = \frac{\text{Mass of Oxygen}}{\text{Atomic Mass of Oxygen}} = \frac{53 \, \text{grams}}{16 \, \text{g/mol}} \approx 3.3125 \, \text{moles} \][/tex]
### Step 3: Determine the simplest mole ratio
To find the simplest whole number ratio, we divide the moles of each element by the smallest number of moles calculated.
[tex]\[ \text{Silicon ratio} = \frac{\text{Moles of Silicon}}{\text{Smallest number of moles}} = \frac{1.67857}{1.67857} \approx 1 \][/tex]
[tex]\[ \text{Oxygen ratio} = \frac{\text{Moles of Oxygen}}{\text{Smallest number of moles}} = \frac{3.3125}{1.67857} \approx 2 \][/tex]
### Step 4: Write the empirical formula
Using the whole number ratios obtained, the empirical formula of the compound can be written. For every one silicon atom, there are approximately two oxygen atoms.
Thus, the empirical formula of the compound is [tex]\(\text{SiO}_2\)[/tex].
