Question

If \(0.2\) gram of an organic compound containing carbon, hydrogen and oxygen, on combustion, yielded \(0.147\) gram carbon dioxide and \(0.12\) gram water. What will be the content of oxygen in the substance? (a) \(73.29 \%\) (b) \(68.45 \%\) (c) \(85.23 \%\) (d) \(89.50 \%\)

Short answer

The content of oxygen in the substance is 68.45% (option b).

Step-by-step solution

Convert the Mass of CO2 to Mass of Carbon

To find the mass of carbon in the compound, we use the mass of carbon dioxide. The molecular weight of CO2 is 44 g/mol, and each molecule of CO2 contains one carbon atom with a molecular weight of 12 g/mol. Thus, the mass of carbon in the CO2 produced is \( \left( \frac{12}{44} \right) \times 0.147 \) grams.

Calculate Mass of Hydrogen from Water

Water (H2O) has a molar mass of 18 g/mol. Each molecule of water contains 2 hydrogen atoms, giving a total hydrogen mass of 2 g/mol in water. Therefore, the mass of hydrogen in the water produced is \( \left( \frac{2}{18} \right) \times 0.12 \) grams.

Determine Total Mass of Carbon and Hydrogen

Add the masses of carbon and hydrogen calculated in Steps 1 and 2 to obtain the total mass of carbon and hydrogen in the compound.

Find Mass of Oxygen

Subtract the total mass of carbon and hydrogen from the original mass of the organic compound (0.2 grams) to find the mass of oxygen in the compound.

Calculate the Percentage of Oxygen

The percentage of oxygen is calculated by dividing the mass of oxygen (from Step 4) by the total mass of the compound (0.2 grams) and multiplying by 100 to convert it to a percentage.

Key concepts

Mass-to-Mass Conversion

Mass-to-mass conversion is a key concept in chemistry, particularly for organic compounds. This process involves using the mass of a compound to determine the mass of a specific element within it. For instance, in the combustion analysis, we start with the mass of carbon dioxide (CO2) to determine the mass of carbon.

Here's how it works: We know the molecular weight of CO2 is 44 g/mol, with carbon contributing 12 g/mol. By using the formula, mass of carbon = \( \left( \frac{12}{44} \right) \times \text{mass of } CO_2 \), we can convert from the mass of CO2 to the mass of carbon.

Similarly, for water (H2O), which has a molar mass of 18 g/mol, to find the mass of hydrogen, we use hydrogen's mass contribution of 2 g/mol. The conversion uses the formula, mass of hydrogen = \( \left( \frac{2}{18} \right) \times \text{mass of } H_2O \).

Thus, mass-to-mass conversion is an essential step in combustion analysis to quantify each component after a chemical reaction.

Percent Composition Calculation

Calculating the percent composition tells us the proportion of each element in a compound, expressed as a percentage. In the given exercise, after identifying the masses of carbon and hydrogen, and ultimately oxygen, we need to find out how much each contributes to the whole.

First, add the masses of carbon and hydrogen to determine how much of the compound they constitute. The mass of oxygen is then found by subtracting this total from the initial mass of the compound.

To calculate the percentage of oxygen, use this formula:

• Percent oxygen = \( \left( \frac{\text{mass of oxygen}}{\text{total mass of compound}} \right) \times 100 \)

This calculation gives insight into the purity and empirical composition of unknown substances, making it a critical part of analytical chemistry.

Empirical Formula Determination

The empirical formula represents the simplest whole-number ratio of elements in a compound. Determining this formula helps chemists understand the basic composition of a compound, specifically useful in analyzing unknown substances.

Using the mass of each element derived from mass-to-mass conversions, the next step involves calculating the moles of each element. This is done by dividing the mass of each element by its atomic mass.

• Moles of Carbon = \( \frac{\text{mass of carbon}}{12} \)
• Moles of Hydrogen = \( \frac{\text{mass of hydrogen}}{1} \)
• Moles of Oxygen = \( \frac{\text{mass of oxygen}}{16} \)

Next, divide each mole value by the smallest number of moles calculated to find a ratio. Often these are adjusted to the nearest whole numbers to create the simplest form.

By converting experimental data into an empirical formula, chemists gain foundational insights needed for further research, synthesis, and applications.