Animated Solution for Chemistry - Basic Concepts in Chemistry: A gaseous hydrocarbon gives upon combustion, $0.72\text{ g}$ of water and $3.08\text{ g}$ of ${\text{CO}}_2$. The empirical formula of the hydrocarbon is

Imagine you have a mystery gas, a hydrocarbon, and you want to know exactly what it's made of. You can't just look at it under a microscope and count the atoms. Instead, chemists use a brilliant technique called Combustion Analysis.

By burning the hydrocarbon completely in the presence of excess oxygen, we force a chemical transformation. Every single carbon atom in the original molecule is converted into carbon dioxide (${\text{CO}}_2$), and every single hydrogen atom is converted into water (${\text{H}}_2\text{O}$). This means the mass of carbon in the ${\text{CO}}_2$ produced is exactly equal to the mass of carbon in the original sample. The same logic applies to the hydrogen in the water.

Let's start by analyzing the carbon dioxide. We are given that $3.08\text{ g}$ of ${\text{CO}}_2$ is produced. We know from the periodic table that the molar mass of ${\text{CO}}_2$ is $44\text{ g/mol}$ (since Carbon is $12$ and two Oxygens are $32$). Out of these $44\text{ g}$, exactly $12\text{ g}$ come from carbon.

Using a simple unitary method, we can find the mass of carbon in our specific sample:

Calculating this gives us exactly $0.84\text{ g}$ of Carbon.

Next, we turn our attention to the water produced, which is $0.72\text{ g}$. The molar mass of ${\text{H}}_2\text{O}$ is $18\text{ g/mol}$ (two Hydrogens are $2$, and one Oxygen is $16$). Out of these $18\text{ g}$, exactly $2\text{ g}$ come from hydrogen.

Again, applying the unitary method:

This calculation yields exactly $0.08\text{ g}$ of Hydrogen.

Now that we have the masses of both elements, we need to find their molar ratio to determine the empirical formula. The empirical formula represents the simplest whole-number ratio of atoms in a compound.

We convert the masses into moles by dividing by their respective atomic masses:

Notice how clean these numbers are? That is always a great sign in chemistry problems! The molar ratio of Carbon to Hydrogen is $0.07:0.08$.

To convert this into a whole-number ratio, we simply multiply both sides by $100$, giving us $7:8$.

Therefore, the simplest formula that fits this ratio is ${\text{C}}_7{\text{H}}_8$. This is our empirical formula, and it perfectly matches option (d).