Question

A quantity of \(0.2 \mathrm{~g}\) of an organic compound containing, \(\mathrm{C}, \mathrm{H}\) and \(\mathrm{O}\), on combustion yielded \(0.147 \mathrm{~g} \mathrm{CO}_{2}\) and \(0.12 \mathrm{~g}\) water. The percentage of oxygen in it is (a) \(73.29 \%\) (b) \(78.45 \%\) (c) \(83.23 \%\) (d) \(89.50 \%\)

Short answer

The percentage of oxygen in the compound is 73.29%.

Step-by-step solution

Calculate the number of moles of CO2 and H2O produced

First, calculate the moles of carbon dioxide (CO2) using its molar mass (44.01 g/mol), and similarly for water (H2O) using its molar mass (18.02 g/mol). For CO2: moles = mass / molar mass = 0.147 g / 44.01 g/mol. For H2O: moles = mass / molar mass = 0.12 g / 18.02 g/mol.

Calculate the mass of carbon and hydrogen in the compound

From the moles of CO2 and H2O, calculate the mass of carbon and hydrogen. Each mole of CO2 contains 1 mole of carbon, so mass of carbon = moles of CO2 * atomic mass of C (12.01 g/mol). Each mole of H2O contains 2 moles of hydrogen, so mass of hydrogen = moles of H2O * 2 * atomic mass of H (1.008 g/mol).

Calculate the mass of oxygen in the compound

Knowing the total mass of the compound and the mass of carbon and hydrogen, the mass of oxygen can be found by subtracting the mass of carbon and hydrogen from the total mass of the compound. Mass of oxygen = total mass - (mass of carbon + mass of hydrogen).

Calculate the percentage of oxygen in the compound

Finally, calculate the percentage of oxygen by dividing the mass of oxygen by the total mass of the compound and multiplying by 100. Percentage of oxygen = (mass of oxygen / total mass of the compound) * 100.

Key concepts

Stoichiometry

where each carbon (C) atom in the compound contributes to the formation of one molecule of CO2, and every two hydrogen (H) atoms contribute to the formation of one molecule of H2O. By applying stoichiometry, we can determine the amount of carbon and hydrogen in the original compound from the mass of CO2 and H2O produced.

Mole Concept

The mole concept is fundamental in chemistry for quantifying atoms, molecules, or ions. In the context of the problem, we use the mole as a bridge between the mass of a substance and the number of particles it contains.

Each mole corresponds to Avogadro's number of particles, roughly 6.022 × 10^23, which is the number of atoms in exactly 12 grams of carbon-12. This concept allows us to convert between mass and moles using molar mass, which is the mass per mole of a substance.

To illustrate, for carbon dioxide (CO2) with a molar mass of 44.01 grams per mole, the moles produced from a mass of just 0.147 grams of CO2 can be calculated. Similarly, this relation is used to determine moles of H2O from its mass. Once the moles of CO2 and H2O are determined, these values can guide us in finding the moles of carbon and hydrogen atoms originally present in the compound.

Empirical Formula Calculation

The determination of an empirical formula is an integral part of empirical formula calculation. It represents the simplest whole-number ratio of atoms in a compound. In a combustion analysis, empirical formula calculation starts with identifying the mass of each element in the compound.

From the given exercise, the masses of carbon and hydrogen are derived from the moles of CO2 and H2O produced during combustion. The next step is to convert these masses to moles and find the simplest ratio of carbon to hydrogen to oxygen atoms. This ratio builds the empirical formula of the original compound, which gives us insight into the actual molecular structure of the substance.

Part of the challenge lies in recognizing that the mass of oxygen is not directly measured during combustion but can be inferred. This is done by subtracting the sum of the masses of carbon and hydrogen from the total mass of the organic compound, thereby leading us toward determining the compound's empirical formula.

Elemental Composition Analysis

Elemental composition analysis is the detailed breakdown of the elemental constituents within a chemical substance. Utilizing the previous concepts of stoichiometry and mole calculations, we can ascertain the percentage composition of each element within a compound.

The process begins by determining the masses of individual elements obtained either directly from experimental measurements like in combustion analysis or indirectly through stoichiometric relationships. With these masses, we calculate what fraction of the total mass of the compound they represent.

Completion of the analysis involves converting these mass fractions into percentages, leading to the empirical formula. In the problem at hand, after obtaining the masses of carbon and hydrogen, we apply this process to oxygen. By isolating the mass of oxygen, we can ultimately express the percentage of oxygen in the original organic compound, demonstrating a clear application of elemental composition analysis.