Question

How would you determine the molecular formula of \[{C_4}{H_9}\]?

Answer 1

Hint: Empirical formula is defined as the smallest ratios of the elements which constitutes the molecular formula of a compound. The molecular formula is derived from the empirical formula by multiplying the empirical formula using a whole number integer.

Complete step by step answer:
The given empirical formula is \[{C_4}{H_9}\]. The formula indicates that it is a hydrocarbon. The hydrocarbons are simplest organic compounds composed of hydrogen and carbon atoms.
Empirical formulae are distinct from molecular formula as it is the simplest representation of the number of atoms in a molecule. In this case four carbon atoms are present and a ration of nine hydrogen atoms.
When the empirical formula is multiplied by a whole number integer like n gives the molecular formula of the compound. Thus \[\left[ {EF} \right] \times n = MF\].
Let us assume that the compound is an alkane. Alkanes are composed of carbon and hydrogen atoms and satisfy the general formula \[C{}_n{H_{2n + 2}}\].
The given formula \[{C_4}{H_9}\] does not satisfies the formula \[C{}_n{H_{2n + 2}}\] as if \[n = 4\], the formula becomes \[{C_4}{H_{10}}\]. So the empirical formula should be multiplied by a factor which is \[2\]. Thus on multiplying with \[{C_4}{H_9}\], The molecular formula is = $2 \times ({C_4}{H_9}) = {C_8}{H_{18}}.$
Now the molecular formula satisfies the general formula \[C{}_n{H_{2n + 2}}\]. Hence the molecular formula of \[{C_4}{H_9}\] is \[{C_8}{H_{18}}\] and the compound is octane.

Note: The molar formula is also calculated from the molar mass of a compound. In that case the percent composition of each element is determined first followed by the multiplication by a whole number integer. The empirical formula is also calculated from the molecular formula. The sum of the masses of the elements in the empirical formula is called empirical formula mass. The molar mass is different from the empirical formula mass as it is the sum of masses of the elements in one mole of a compound.