The empirical formula of the compound is:
[tex]\boxed{\boxed{\huge\text{$\rm C_{10}H_{14}O$}}}[/tex]
The empirical formula is the simplest whole number ratio of the elements present in the compound based on its relative molar proportions.
To determine the empirical formula of the unknown compound in the question, we need to find the simplest whole number ratio of the elements present. We'll start by converting the given masses (m) of each element to moles (n) using their respective molar masses (M).
[tex]\hrulefill[/tex]
[tex]\displaystyle\large \text{$\rm n(C)=\frac{mass\ of\ C}{Molar\ mass\ of\ C}=\frac{32.60}{12.01}= 2.714\,moles$}[/tex]
[tex]\displaystyle\large \text{$\rm n(H)=\frac{mass\ of\ H}{Molar\ mass\ of\ H}=\frac{4.04}{1.008}= 4.007\,moles$}[/tex]
[tex]\displaystyle\large \text{$\rm n(O)=\frac{mass\ of\ O}{Molar\ mass\ of\ O}=\frac{4.57}{16.00}= 0.2856\,moles$}[/tex]
[tex]\hrulefill[/tex]
The molar ratio of the compound, is the ratio of:
[tex]\large\text{Moles of Carbon : Moles of Hydrogen : Moles of Oxygen}\\\\\large\text{$\implies 2.714 : 4.007 : 0.2856$}[/tex]
Simplifying this by dividing each element by the smallest number of moles (0.2856), the molar ratio is then:
[tex]\large\text{$\implies 10 : 14 : 1$}[/tex]
[tex]\hrulefill[/tex]
Therefore, the empirical formula of the compound is:
[tex]\boxed{\boxed{\huge\text{$\rm C_{10}H_{14}O$}}}[/tex]
[tex]\hrulefill[/tex]
