Question

An organic compound contains \(69 \%\) carbon and \(4.8 \%\) hydrogen, the remainder being oxygen. Calculate the masses of carbon dioxide and water produced when \(0.20 \mathrm{~g}\) of this substance is subjected to complete combustion.

Short answer

0.506 g of CO2 and 0.0864 g of H2O are produced.

Step-by-step solution

Determine Oxygen Percentage

First, calculate the percentage of oxygen in the compound. Since the total percentage must add up to 100%, we find the oxygen percentage by subtracting the percentages of carbon and hydrogen from 100%.\[ \text{Oxygen ( ext{%})} = 100 ext{ ext{%}} - 69 ext{ ext{%}} - 4.8 ext{ ext{%}} = 26.2 ext{ ext{%}} \]

Calculate Mass of Each Element

Calculate the mass of each element in a 0.20 g sample: \[ \text{Mass of C} = 0.20 \, \mathrm{g} \times \frac{69}{100} = 0.138 \mathrm{~g} \] \[ \text{Mass of H} = 0.20 \, \mathrm{g} \times \frac{4.8}{100} = 0.0096 \mathrm{~g} \] \[ \text{Mass of O} = 0.20 \, \mathrm{g} \times \frac{26.2}{100} = 0.0524 \mathrm{~g} \]

Find Moles of Each Element

Convert the masses of C, H, and O to moles. Use atomic masses: C = 12 g/mol, H = 1 g/mol, O = 16 g/mol.\[ \text{Moles of C} = \frac{0.138}{12} = 0.0115 \text{ mol} \] \[ \text{Moles of H} = \frac{0.0096}{1} = 0.0096 \text{ mol} \] \[ \text{Moles of O} = \frac{0.0524}{16} = 0.003275 \text{ mol} \]

Calculate Mass of Products

When combusted, carbon forms CO2 and hydrogen forms H2O.\[ \text{Moles of } \text{CO}_2: 0.0115 \text{ mol C} \times \frac{1 \text{ mol CO}_2}{1 \text{ mol C}} = 0.0115 \text{ mol CO}_2 \] \[ \text{Moles of } \text{H}_2\text{O}: 0.0096 \text{ mol H} \times \frac{1 \text{ mol H}_2\text{O}}{2 \text{ mol H}} = 0.0048 \text{ mol H}_2\text{O} \] Convert to mass using molar masses: CO2 = 44 g/mol, H2O = 18 g/mol.\[ \text{Mass of CO}_2 = 0.0115 \times 44 = 0.506 \text{ g CO}_2 \] \[ \text{Mass of H}_2\text{O} = 0.0048 \times 18 = 0.0864 \text{ g H}_2\text{O} \]

Final Result

The masses of carbon dioxide and water produced from the complete combustion of 0.20 g of the organic compound are 0.506 g and 0.0864 g, respectively.

Key concepts

Stoichiometry

Stoichiometry is a fascinating part of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It helps predict the amount of products that will be formed in a given reaction, based on the amount of starting materials. In the combustion analysis exercise, stoichiometry is used to find out how much carbon dioxide and water are produced from the complete combustion of the given organic compound.

The process involves converting the percentage composition of the compound into masses, then into moles, which are crucial in stoichiometric calculations. The principle of stoichiometry employs the concept of a balanced chemical equation, ensuring the law of conservation of mass is respected. For instance, by knowing that one mole of carbon produces one mole of carbon dioxide, we can predict that 0.0115 moles of carbon will form the same number of moles of carbon dioxide.

Stoichiometry not only connects the elemental composition of compounds to their reactions, but it also provides a reliable method to calculate unknown quantities. This process is pivotal in industrial applications where resource optimization is essential.

Chemical Composition

Understanding chemical composition is crucial to analyze and synthesize chemical reactions. It refers to the relative amount of each element present in a compound. In the given exercise, chemical composition helps in breaking down the compound into its elemental parts: carbon, hydrogen, and oxygen, and their respective percentages.

To start, the percentage by mass of each element is given, except for oxygen, which requires calculation. In compounds, the sum of the mass percentages is always 100%, allowing the percent mass of oxygen to be derived by subtraction from the total. Following this, the individual masses for a specific sample size can be calculated, which serves as a foundation for finding the moles of each element.

Understanding the chemical composition enables scientists to propose empirical formulas that represent the simplest ratio of elements in a compound. It is indispensable for chemists to ascertain the identity of an unknown compound and to replicate and modify substances in the lab.

Mole Concept

The mole concept is one of the essential ideas in chemistry that relates to the quantity of substance. A mole is defined as the amount of substance containing the same number of discrete entities (such as atoms, molecules, or ions) as there are atoms in 12 grams of pure carbon-12. This number, known as Avogadro's number, is approximately equal to \(6.022 \times 10^{23}\).

In our exercise, converting from the mass of each element to moles allows us to utilize chemical equations effectively. The atomic masses of carbon, hydrogen, and oxygen serve as conversion factors in this step, transforming mass into moles. For example, dividing the mass of carbon by its atomic mass (12 g/mol) translates it to moles.

The mole concept bridges the atomic scale to our macroscopic world, enabling accurate measurements and reactions. By using the mole, chemists can quantify elements and compounds in a standardized way, leading to consistency across scientific disciplines. This concept is a cornerstone, not just for stoichiometry but for all quantitative chemistry.