Question

A sample of urea contains 1.121g N, 0.161g of H, 0.480g C and 0.640g O. What is the empirical formula of urea?

Answer 1

Hint: Empirical formula is the simplest formula and for that, you need to divide individual masses of each element by their molar mass to find out moles.

Complete step by step solution:
The empirical formula is the formula which gives the proportions or estimate of the elements present in a compound but does not give the actual arrangement or the numbers of the atoms.
First, we have to find the number of moles for each and every atom present in the molecule. The number of moles is given below:
For N, $1.121g =$ \[\dfrac {1.121}{14} =\text{ }0.0801\]moles
For H, $0.161g =$ \[\dfrac{0.161}{1.008}\text{ }=\text{ }0.1597\]moles
For C, $0.480g =$ \[\dfrac {0.480}{12.01}=0.04\]moles
For O, $0.640g =$ \[\dfrac {0.640}{16.0}=0.04\]moles
As we can see that the minimum number of moles in the case of urea with the given masses of atoms comes out to be 0.04 moles. Now we will divide every mole of an atom with 0.04 and find out the simplest real number. So it comes out to be:
\[N\text{ }:\text{ }H\text{ }:\text{ }C\text{ }:\text{ }O\text{ }=\text{ }2:4:1:1\]
So on simplification, N has 2 atoms, H has 4 atoms, C and O have 1 atom each in the final molecule.

Hence, the empirical formula of the molecule can be written as \[C{{H}_{4}}O{{N}_{2}}\].

Note: You need to remember that in the empirical formula, the number of atoms in each element of a molecule should be a real number, or a whole number(yes it can be 0). It cannot be negative too. Avoid making errors during calculations involving decimals.