Problem 64 - Chemistry: An Atoms-Focused Approach

Question

Why is the quantity of \(\mathrm{CO}_{2}\) obtained in a combustion analysis not a direct measure of the oxygen content of the starting compound?

Step-by-Step Solution

Answer

Answer: The quantity of \(\mathrm{CO}_{2}\) obtained in a combustion analysis is not a direct measure of the oxygen content of the starting compound because it only quantitatively provides information about the carbon content. The oxygen content must be calculated indirectly after determining the carbon and hydrogen content by subtracting their mass from the total mass of the starting compound.

Step 1: Understanding combustion analysis

Combustion analysis is a technique used to determine the elemental composition of a compound, specifically the carbon, hydrogen, and oxygen content. In this process, the compound is burned in an excess of oxygen, and the \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\) produced are measured. Combustion analysis is often used when empirical formulas of unknown compounds need to be determined.

Step 2: Combustion reaction

In a combustion analysis, the starting compound (containing carbon, hydrogen, and possibly oxygen) reacts with an excess of oxygen gas, and the products are \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\). The balanced combustion reaction can be represented as: $$ \mathrm{C}_x\mathrm{H}_y\mathrm{O}_z + \left(\frac{x+z}{2}\right)\mathrm{O}_{2} \to x\mathrm{CO}_{2} + \frac{y}{2}\mathrm{H}_{2}\mathrm{O} $$ Here, \(x\), \(y\), and \(z\) represent the number of carbon, hydrogen, and oxygen atoms in the starting compound, respectively.

Step 3: Amount of \(\mathrm{CO}_{2}\) produced

From the balanced combustion reaction, it is clear that for each carbon atom in the starting compound, one molecule of \(\mathrm{CO}_{2}\) is produced. Since we can measure the mass of \(\mathrm{CO}_{2}\) produced during combustion, we can also determine the amount of carbon in the starting compound using the stoichiometry of the reaction.

Step 4: Indirect measure of oxygen content

Although the oxygen atoms present in the starting compound also react with the excess of oxygen gas, they do not quantitatively contribute to the production of \(\mathrm{CO}_{2}\). While the \(\mathrm{CO}_{2}\) amount can help determine the carbon content, it cannot provide information about the oxygen content specifically.

Step 5: Explaining the indirect measure of oxygen content

To determine the oxygen content in the starting compound, first, the carbon and hydrogen content needs to be calculated using the measurements of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\), respectively. Once the carbon and hydrogen content are known, the oxygen content can be indirectly calculated by subtracting the mass of carbon and hydrogen from the total mass of the starting compound. Therefore, the quantity of \(\mathrm{CO}_{2}\) obtained in a combustion analysis is not a direct measure of the oxygen content of the starting compound because it only quantitatively provides information about the carbon content. The oxygen content has to be calculated indirectly after determining the carbon and hydrogen content.