Question

0.0833 mol of carbohydrate of empirical formula \[C{{H}_{2}}O\] contains 1 g of hydrogen.
The molecular formula of carbohydrate is:
a.) \[{{C}_{5}}{{H}_{10}}{{O}_{5}}\]
b.) \[{{C}_{6}}{{H}_{12}}{{O}_{6}}\]
c.) \[{{C}_{12}}{{H}_{22}}{{O}_{11}}\]
d.) \[{{C}_{3}}{{H}_{4}}{{O}_{3}}\]

Answer 1

Hint: The general molecular formula of carbohydrates is \[{{(C{{H}_{2}}O)}_{n}}\] or \[{{C}_{n}}{{H}_{2n}}{{O}_{n}}\]. Means if carbohydrates contains n number of carbons and n number of oxygen atoms, then the carbohydrate contains 2n number of hydrogen atoms.

Complete step by step answer:
Molecular formulas are the multiples of empirical formulas.
In the question it is given that the number of given moles of the carbohydrate is 0.0833 mol.
One mole of carbohydrate contains 2n grams of hydrogens as per molecular formula of carbohydrates.
Therefore the number of hydrogen present in the given amount of carbohydrate = \[2n\times 0.0833g\]
In the question it is given that \[2n\times 0.0833g\] of carbohydrate contains one gram of hydrogen.
We can write the above data into a mathematical equation as follows.
 \[2n\times 0.0833g = 1g\]
By solving the above mathematical expression we will get n = 6.
\[\begin{align}
 & 2n\times 0.0833g=1g \\
 & n=\dfrac{1}{2\times 0.0833} \\
 & n=\dfrac{1}{0.166} \\
 & n=6 \\
\end{align}\]

Therefore the molecular formula of given carbohydrate can be written as \[{{(C{{H}_{2}}O)}_{n}}\] = \[{{(C{{H}_{2}}O)}_{6}}\]=\[{{C}_{6}}{{H}_{12}}{{O}_{6}}\].
Thus the molecular formula of carbohydrate is \[{{C}_{6}}{{H}_{12}}{{O}_{6}}\].
So, the correct answer is “Option B”.

Note: Carbohydrates come under biomolecules containing Carbon, Hydrogen and Oxygen in their structures. Generally carbohydrates contain 1: 2 : 1 ratio of C : H : O. Means 1 mole of carbon, 2 moles of hydrogen and 1 mole of oxygen. There are four primary functions of carbohydrates in the human body. They generate energy, store the energy in the human body, prepare macromolecules, and additional protein and fat.