Problem 26 - Chemistry in 30 days

Question

If \(0.2 \mathrm{~g}\) of an organic compound containing carbon, hydrogen and oxygen on combustion, yielded \(0.147 \mathrm{~g}\) of carbon dioxide and \(0.12 \mathrm{~g}\) of water, what will be the content of oxygen in the substance? (a) \(73.29 \%\) (b) \(78.45 \%\) (c) \(83.23 \%\) (d) \(89.50 \%\)

Step-by-Step Solution

Answer

The percentage of oxygen in the compound is closest to 73.29%.

Step 1: Determine Carbon Content

First, calculate the amount of carbon in the compound. Carbon is present in carbon dioxide (CO₂). Since the molar mass of CO₂ is 44 g/mol and the carbon part is 12 g/mol, the mass fraction of carbon in CO₂ is \( \frac{12}{44} \). Multiply the mass of CO₂ produced by this fraction to find the mass of carbon: \( 0.147 \times \frac{12}{44} = 0.04 \text{ g} \).

Step 2: Determine Hydrogen Content

Next, calculate the amount of hydrogen in the compound. Hydrogen is present in water (H₂O). Since the molar mass of H₂O is 18 g/mol and the hydrogen part is 2 g/mol, the mass fraction of hydrogen in H₂O is \( \frac{2}{18} \). Multiply the mass of H₂O produced by this fraction to find the mass of hydrogen: \( 0.12 \times \frac{2}{18} = 0.0133 \text{ g} \).

Step 3: Calculate Mass of Oxygen in Compound

To find the oxygen content in the original compound, subtract the masses of carbon and hydrogen from the total mass of the compound. This is because the compound only contains carbon, hydrogen, and oxygen. Thus, the mass of oxygen = Total mass - Mass of carbon - Mass of hydrogen: \( 0.2 - 0.04 - 0.0133 = 0.1467 \text{ g} \).

Step 4: Calculate Percentage of Oxygen

Finally, calculate the percentage of oxygen in the compound using the formula: \( \text{Percentage of oxygen} = \left( \frac{\text{Mass of oxygen}}{\text{Total mass of compound}} \right) \times 100 \). Substituting the values, \( \left( \frac{0.1467}{0.2} \right) \times 100 = 73.35 \% \).

Key Concepts

Molecular Composition Determination

Understanding how to determine the molecular composition of a compound through combustion analysis is crucial in chemistry. Combustion analysis involves burning a sample to break it down into its elemental components. For organic compounds, this often results in carbon turning into carbon dioxide (CO₂) and hydrogen forming water (H₂O).

When you know the amounts of CO₂ and H₂O produced, you can use them to find out how much carbon and hydrogen were present in the original compound. From there, you can calculate the mass of any other elements (like oxygen) by subtraction. This is done by knowing the total initial mass of the compound and subtracting the calculated masses of carbon and hydrogen.

The key to solving these problems is understanding molar masses and using them to calculate mass fractions. For example, the carbon content in CO₂ is calculated by the mass fraction \( \frac{12}{44} \), because the molar mass of carbon is 12 g/mol and that of CO₂ is 44 g/mol.

Elemental Analysis in Chemistry

Elemental analysis is a technique used to determine the elemental composition of a chemical substance. In the context of combustion analysis, it involves the precise calculation of the amounts of elements such as carbon, hydrogen, and oxygen present in an organic compound.

The process typically involves:

• Measurement of the mass of CO₂ and H₂O generated from combustion.
• Calculation of the mass of carbon and hydrogen using their respective mass fractions in these compounds.
• Subtraction of the mass of these elements from the total mass of the compound to determine the oxygen content.

Each of these steps requires careful calculation and an understanding of chemical equations. This helps in piecing together the amounts of carbon, hydrogen, and oxygen originally present in the compound, a skill that is vital in organic chemistry.

This method illuminates the broader concept of elemental analysis, serving not only in analytical labs but also in industries where knowing the exact composition of a material is crucial.

Organic Compound Combustion

In chemistry, organic compound combustion is a process by which carbon-containing substances react with oxygen to release energy. This typically results in the production of CO₂ and H₂O. The analysis of these products allows us to determine the composition of the original compound.

The steps for analyzing organic compound combustion include:

• Combusting the sample in the presence of excess oxygen.
• Capturing and weighing the resulting CO₂ and H₂O.
• Using stoichiometry to ascertain the quantities of carbon and hydrogen in the sample.
• Inferring the oxygen content by subtracting the mass of carbon and hydrogen from the total mass.

Each molecule of CO₂ and H₂O provides a snapshot of the carbon and hydrogen atoms within the compound. This makes combustion a powerful tool for determining the molecular composition of organic compounds, offering insights into their structural and functional attributes.