Question

A $0.1$ mole of a carbohydrate with empirical formula $C{H_2}O$ contains $1$ g of hydrogen, what is its molecular formula?
A. \[{C_5}{H_{10}}{O_5}\]
B. \[{C_6}{H_{12}}{O_6}\]
C. \[{C_4}{H_{18}}{O_4}\]
D. \[{C_3}{H_6}{O_3}\]

Answer 1

Hint: As 1 mole of carbohydrate has 2n moles of H, if the molecular formula is \[{\left( {C{H_2}O} \right)_n}\]. By finding the molar mass of hydrogen, the answer can be calculated as it will help in finding the moles which will later help in molecular formula.

Complete step-by-step answer: As given:
  \[ \Rightarrow \]The number of moles of carbohydrate is equal to \[0.1\] moles.
\[ \Rightarrow \]Also, we know that one mole of carbohydrate has \[2\]n moles of H.
\[ \Rightarrow \] Then \[0.1\] mole of carbohydrate = \[2n \times 0.1\] moles.
\[ \Rightarrow \] Molar mass of hydrogen in \[0.1\] moles = \[1\]g as given.
\[ \Rightarrow \] Now, \[2n \times 0.1\] \[ = 1\]
\[ \Rightarrow \] \[2n = 10\]
After solving,
\[ \Rightarrow \] \[n = 5\]
Hence, the molecular formula of the carbohydrate is \[\left( {{C_5}{H_{10}}{0_5}} \right).\]

Additional information:
A carbohydrate is a biomolecule which comprises carbon, hydrogen and oxygen atoms, generally with a hydrogen atom as twice as of oxygen atom, we can say hydrogen-oxygen atom ratio of \[2:1\]. And thereby with the empirical formula of \[{C_m}{\left( {{H_2}O} \right)_n}\;\] (where m may not be the same as n).
Carbohydrates are categorized into four types: which are mono-saccharides, disaccharides, oligosaccharides, and polysaccharides. Mono-saccharides consist of a simple sugar; that is, the chemical formula of mono-saccharides is \[{C_6}{H_{12}}{O_6}\] . Disaccharides are generally two simple sugars. Oligosaccharides are three to six monosaccharide units, and polysaccharides are more than six.
The empirical formula can be stated as the simplest, whole-number ratio of atoms in a compound. Calculate the no. of moles of each type of atom present. Then divide the no. of moles of each element by the smallest number of moles that is calculated in the previous step.

Note: Total number of moles need to be found first, then with the help of these further steps needed to be taken care. Also hint should be checked carefully for better understanding of the complete answer.