Question

On combustion, \(0.2 \mathrm{~g}\) of an organic compound containing carbon, hydrogen and oxygen yields \(0.147 \mathrm{~g}\) carbon dioxide and \(0.12 \mathrm{~g}\) water. The percentage of carbon, hydrogen and oxygen respectively in the compound is: (a) \(22.5,8.7\) and \(68.8\) (b) \(20,6.7\) and \(73.3\) (c) \(18.2,9.5\) and \(72.3\) (d) \(28.9,12.8\) and \(58.8\)

Short answer

(b) 20, 6.7, and 73.3.

Step-by-step solution

Calculate moles of carbon dioxide

To find the number of moles of carbon dioxide formed, use the molar mass of carbon dioxide \(\text{Molar mass of CO}_2 = 44 \ \mathrm{g/mol}\) Now, calculate the moles of carbon dioxide: \[\text{Moles of CO}_2 = \frac{0.147\ \mathrm{g}}{44\ \mathrm{g/mol}} = 0.00334 \ \mathrm{mol}\]

Calculate mass of carbon in carbon dioxide

Each mole of carbon dioxide contains one mole of carbon. Use the atomic mass of carbon, \(12\ \mathrm{g/mol}\), to find the mass of carbon:\[\text{Mass of carbon} = 0.00334 \ \mathrm{mol} \times 12 \ \mathrm{g/mol} = 0.04008 \ \mathrm{g}\]

Calculate moles of water

To calculate the moles of water produced, use the molar mass of water:\(\text{Molar mass of } \mathrm{H}_2\mathrm{O} = 18 \ \mathrm{g/mol}\)Calculate the moles of water:\[\text{Moles of } \mathrm{H}_2\mathrm{O} = \frac{0.12 \ \mathrm{g}}{18 \ \mathrm{g/mol}} = 0.00667 \ \mathrm{mol}\]

Calculate mass of hydrogen in water

Each mole of water contains two moles of hydrogen. Use the atomic mass of hydrogen, \(1 \ \mathrm{g/mol}\). Calculate the mass of hydrogen:\[\text{Mass of } \mathrm{H} = 0.00667 \ \mathrm{mol} \times 2 \ \mathrm{g/mol} = 0.01334 \ \mathrm{g}\]

Calculate mass of oxygen in the compound

The total mass of the compound is \(0.2\ \mathrm{g}\). Use the masses of carbon and hydrogen to find the mass of oxygen:\[\text{Mass of oxygen} = 0.2 \ \mathrm{g} - (0.04008 \ \mathrm{g} + 0.01334 \ \mathrm{g}) = 0.14658 \ \mathrm{g}\]

Calculate percentage composition of each element

Calculate the percentage composition:- Percentage of carbon: \[\frac{0.04008 \ \mathrm{g}}{0.2 \ \mathrm{g}} \times 100 = 20.04\%\]- Percentage of hydrogen: \[\frac{0.01334 \ \mathrm{g}}{0.2 \ \mathrm{g}} \times 100 = 6.67\%\]- Percentage of oxygen: \[\frac{0.14658 \ \mathrm{g}}{0.2 \ \mathrm{g}} \times 100 = 73.29\%\]

Match percentages to options

The calculated percentages are approximately \( 20\% \) for carbon, \( 6.7\% \) for hydrogen, and \( 73.3\% \) for oxygen. These values match option (b): \( 20,6.7\) and \(73.3\).

Key concepts

Combustion Analysis

Combustion analysis is a technique used in chemistry to determine the elemental composition of organic compounds. It is particularly useful for determining the percentage of carbon and hydrogen in a compound. In this process, the organic compound is burned, and the products of the combustion are analyzed. Typically, carbon dioxide ( \( \text{CO}_2 \) ) and water ( \( \text{H}_2\text{O} \) ) are the main products for organic compounds containing carbon and hydrogen.
The idea is simple: burn a known mass of the compound and measure the masses of \( \text{CO}_2 \) and \( \text{H}_2\text{O} \) generated.

• Each mole of \( \text{CO}_2 \) corresponds to one mole of carbon atoms from the original compound.
• Each mole of \( \text{H}_2\text{O} \) corresponds to two moles of hydrogen atoms from the compound.

This helps us calculate the exact masses of carbon and hydrogen that were present in the original sample.

Molar Mass Calculation

Calculating molar mass is an essential step in determining the composition of a compound when performing combustion analysis. The molar mass of a substance helps in converting from grams to moles, which is crucial for finding out the amount of an element present in a compound.
The molar mass is simply the sum of the atomic masses of all the atoms in a molecule. For example:

• The molar mass of carbon dioxide, \( \text{CO}_2 \) , is calculated by adding the atomic masses of one carbon atom (12 g/mol) and two oxygen atoms (16 g/mol each), resulting in 44 g/mol.
• The molar mass of water, \( \text{H}_2\text{O} \) , is calculated by adding the atomic masses of two hydrogen atoms (1 g/mol each) and one oxygen atom (16 g/mol), resulting in 18 g/mol.

Using these molar masses, you can calculate the number of moles of substances produced in a reaction, which directly relates to the amount of each element present in the original compound.

Percentage Composition

Percentage composition provides the ratio of each element's mass to the total mass of the compound, expressed as a percentage. It is a crucial part of analyzing chemical compounds, as it helps to identify the empirical formula.
Here's how we calculate percentage composition for an element:

• First, determine the mass of the element in the compound.
• Then, divide this mass by the total mass of the compound.
• Finally, multiply the result by 100 to get the percentage.

In the exercise provided:

• The mass of carbon, hydrogen, and oxygen in the compound were determined through combustion analysis.
• These values were then converted into percentages based on the initial mass of the organic compound.

This method allows for a straightforward determination of how much each element contributes to the overall makeup of the compound.

Organic Compound Analysis

Analyzing organic compounds involves understanding their structure and elemental composition. Typically, organic compounds consist of carbon, hydrogen, oxygen, and sometimes additional elements such as nitrogen and sulfur.
When analyzing an organic compound:

• Start with determining the elemental composition through methods like combustion analysis.
• Analyze the composition to deduce possible molecular and empirical formulas.
• Estimating the compound's molar mass assists in identifying its formula weight.

Organic compound analysis aims to dissect the mystery of these intricate molecules by breaking them down into their elemental building blocks, thus providing invaluable information required for further chemical synthesis or reaction mechanism studies.