Question

Carbon combines with hydrogen to form three hydrocarbons A, B, and C. The percentage of hydrogen in A, B, and C is 25, 14.3, and 7.7 respectively.

1. Find the empirical formula of these hydrocarbons
2. Which law of chemical combination does this example illustrate.

Answer 1

1. Empirical formula

• The empirical formula can be defined as a chemical formula of the compound showing the simplest ratio of elements in a compound rather than representing the total number of atoms in the molecule.

Empirical formula of A

• The percentage of hydrogen = 25%
• Let the formula be ${\mathrm{CH}}_{\mathrm{x}}$
• Hence the empirical formula can be calculated as:
• $$\begin{gathered} \frac{x}{x+12}x100=25 \\ \frac{x}{x+12}=\frac{25}{100}=\frac{1}{4}\Rightarrow x=4 \end{gathered}$$

Hence the empirical formula is ${\mathrm{CH}}_4$

Empirical formula of B

• The percentage of hydrogen = 14.3%
• Let the formula be ${\mathrm{CH}}_y$
• Hence the empirical formula can be calculated as:
• $$\begin{gathered} \frac{y}{y+12}x100=14.3 \\ \frac{y}{y+12}=\frac{14.3}{100} \\ 100y=14.3y+12x14.3 \\ 100y-14.3y=12x14.3 \\ y=\frac{12x14.3}{100-14.3}=2 \end{gathered}$$

Hence the empirical formula is ${\mathrm{CH}}_2$

Empirical formula of C

• The percentage of hydrogen = 7.7%
• Let the formula be ${\mathrm{CH}}_z$
• Hence the empirical formula can be calculated as:
• $$\begin{gathered} \frac{z}{z+12}x100=7.7 \\ \frac{z}{z+12}=\frac{7.7}{100} \\ 100z=7.7z+12x7.7 \\ 100z-7.7z=12x7.7 \\ y=\frac{12x7.7}{100-7.7}=1 \end{gathered}$$

Hence the empirical formula is $\mathrm{CH}$

2. Proust's law

1. Proust's law states that ‘A chemical compound always contains the same elements combined together in the same proportion by mass’
2. It is also known as Proust's law of constant proportion or law of definite proportion.
3. The law was published in 1794.
4. For example, pure water obtained from different sources such as a river, a well, a spring, the sea, etc., always contains hydrogen and oxygen together in the ratio of 1:8 by mass.
5. Similarly, carbon dioxide ${\mathrm{CO}}_2$can be obtained by different methods such as,

• Burning of carbon
• Heating of limestone
• Applying dilute $\mathrm{HCl}$ to marble pieces

Each sample of${\mathrm{CO}}_2$ contains carbon and oxygen in a 3:8 ratio.