# The elemental centesimal analysis

## Definition

We call elemental centesimal analysis the determination of the percentages of elements present in the substance.

## Method

By various methods the sample is made to react in order to produce simple substances such as
$CO_2$, $CO$, $H_2O$, $NH_3$ or $ N_2$.
These substances are collected and their numbers of moles are determined and so it can be concluded on the number of moles of elements that could only come from the sample.

## Example

To perform the elemental analysis of an organic compound containing the elements $C$, $H$ and $O$, a sample of $230\;mg$ is taken. It is heated in the presence of an excess of copper oxide $CuO$ .
Under these conditions, there is obtained carbon dioxide, water and metallic copper. After the chemical processing is completed, one obtains $440\;mg$ of carbon dioxide and $270\;mg$ of water.
Find the percentages of the three elements in this substance!

1.
Number of moles of carbon dioxide =
$n$ =
$\frac{m}{M}$ $=$ $\frac{0.440}{44}$ $=$ $0.010$
One mole $CO_2$ contains one mole of carbon. The carbon can only come from the sample:
Mass of carbon in the sample =
$m$ $=$ $n\cdot M$ $=$ $0.010\cdot 12$ $=$ $0.120\; g $
2.
Number of moles of water =
$n=$ $\frac{m}{M}$ $=$ $\frac{0.270}{18}$ $=$ $0.015$
One mole $H_2O$ contains two moles of hydrogen. The hydrogen can only come from the sample:
Mass of hydrogen in the sample =
$m $ $= $ $n\cdot M$ $ =$ $ 2\cdot 0.015\cdot 1 $ $= $ $0.030\; g $
3.
Mass of oxygen =
$0.230-0.120-0.030$ $=$ $0.080 \;g$
4.
Percentage of carbon =
$\%_C$ $=$ $\frac{0.120\cdot 100}{0.23}$ $=$ $52.2$
Percentage of hydrogen =
$\%_H$ $=$ $\frac{0.03\cdot 100}{0.23}$ $=$ $13.0$
Percentage of oxygen =
$\%_O$ $=$ $\frac{0.08\cdot 100}{0.23}$ $=$ $34.8$