Question

The empirical formula of sucrose is:
(A) $C{{H}_{2}}O$
(B) $CHO$
(C) ${{C}_{12}}{{H}_{22}}{{O}_{11}}$
(D) $C{{({{H}_{2}}O)}_{2}}$

Answer 1

Hint: Start by writing the molecular formula of sucrose. Try dividing the molecular formula by some whole numbers like 1, 2, 3, etc. to get integer value only for subscripts of all components. Once the division is complete and the molecular formula can’t be further reduced, then you get the empirical formula.

Complete step by step solution:
-Empirical formula is the formula that shows the smallest ratio (in whole integers) of the number of atoms of each element present in a molecule of the compound.
-Sucrose is also known as Cane sugar and has the molecular formula, ${{C}_{12}}{{H}_{22}}{{O}_{11}}$.
- Sucrose is the common table sugar (white sugar) which we use in our kitchen.
- Sucrose on hydrolysis gives glucose and fructose.
- Now, we need to find the empirical formula of sucrose.
-We know the molecular formula and from the empirical formula concept we have the relation, $\text{Molecular}\,\text{formula = n }\!\!\times\!\!\text{ Empirical}\,\text{formula}$
-Therefore, $\text{Empirical formula = }\dfrac{\text{Molecular formula}}{\text{n}}$ where n is the whole integer.
-Let’s start by dividing the molecular formula by the smallest integer.
-When we divide by 1, we get the empirical formula is equal to the molecular formula.
-When we divide by 2, we get the empirical formula as ${{C}_{6}}{{H}_{11}}{{O}_{5.5}}$ which is invalid because all subscripts should be whole integers.
-We know that 11 is a prime number and doesn’t have any divisors.
-Therefore, for sucrose, the empirical formula is equal to the molecular formula, ${{C}_{12}}{{H}_{22}}{{O}_{11}}$.

Therefore, the correct answer is option (C).


Note: Remember that if the molecular formula contains any prime numbers then the empirical formula will always be equal to the molecular formula because prime numbers do not have any divisors and the molecular formula cannot be further reduced to the smallest ratio.