Question

The organic solvent thiophene is a carbon-hydrogensulfur compound that yields \(\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{O},\) and \(\mathrm{SO}_{2}\) when burned in an excess of oxygen. When subjected to combustion analysis, a \(1.3020 \mathrm{g}\) sample of thiophene produces \(2.7224 \mathrm{g} \mathrm{CO}_{2}, 0.5575 \mathrm{g} \mathrm{H}_{2} \mathrm{O},\) and \(0.9915 \mathrm{g} \mathrm{SO}_{2} .\) What is the empirical formula of thiophene?

Short answer

The empirical formula of thiophene is \(\mathrm{C}_4\mathrm{H}_4\mathrm{S}\).

Step-by-step solution

Determine the Masses of C, H and S

From the combustion, 2.7224g of \(\mathrm{CO}_2\) gives the mass of C as: \((12.01 / 44.01) \times 2.7224 \mathrm{g}\) \(\mathrm{CO}_2\). H from 0.5575g \(\mathrm{H}_2\mathrm{O}\) is: \((2.016 / 18.015) \times 0.5575 \mathrm{g}\) \(\mathrm{H}_2\mathrm{O}\). And S from 0.9915g \(\mathrm{SO}_2\) is: \((32.065 / 64.066) \times 0.9915 \mathrm{g}\) \(\mathrm{SO}_2\).

Calculate the Number of Moles

The number of moles is given by the mass divided by the molar mass. Calculate the number of moles for C, H, and S using their respective molar masses of 12.01 g/mol, 1.008 g/mol, and 32.065 g/mol.

Determine the Empirical Formula

To determine the empirical formula, divide each of the number of moles calculated by the smallest number obtained. Then, round to the nearest whole number to get the ratio and therefore the formula.

Key concepts

Combustion Analysis

Combustion analysis is a crucial technique used to determine the composition of organic compounds. When a compound is burned in oxygen, it produces different gases that correspond to its constituent elements. For example, carbon becomes carbon dioxide \(\mathrm{CO}_2\), hydrogen forms water \(\mathrm{H}_2\mathrm{O}\), and sulfur generates sulfur dioxide \(\mathrm{SO}_2\). By analyzing these product gases, we can determine the mass of each element present in the original compound.
In this process, the original sample is placed in a combustion chamber where it is combusted completely. The resultant gases are then collected and weighed. To illustrate, the combustion of thiophene produces \(2.7224 \, \text{g}\) of \(\mathrm{CO}_2\), \(0.5575 \, \text{g}\) of \(\mathrm{H}_2\mathrm{O}\), and \(0.9915 \, \text{g}\) of \(\mathrm{SO}_2\). By using their respective molar masses and combining these weights, we determine the mass of carbon, hydrogen, and sulfur in the compound, leading us to calculate the empirical formula.

Organic Compounds

Organic compounds are primarily made of carbon atoms bonded with hydrogen, oxygen, nitrogen, or other elements. These compounds form the basis of life and involve a range of chemical substances, from simple molecules to complex macromolecules.
Thiophene is an organic compound containing carbon, hydrogen, and sulfur. Since organic compounds can be vast in number and diverse in structure, finding their empirical formulas helps scientists understand their basic structural composition. Using combustion analysis, we can break down the elements in thiophene to determine its overall composition. This process aids in understanding the fundamental makeup of organic molecules, crucial for applications in chemistry, biology, and industry.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It involves calculations based on the balanced chemical equation and the conservation of mass principle. This provides a coherent method to calculate the amounts of substances involved in the reactions.
To find the empirical formula through combustion analysis, stoichiometry links the masses of the produced gases to the amount of original substance. Using stoichiometry, the mass of each element in a compound like thiophene can be calculated from the mass of \(\mathrm{CO}_2\), \(\mathrm{H}_2\mathrm{O}\), and \(\mathrm{SO}_2\) produced. This ensures that we understand how many atoms of each element are in the simplest repeating unit of the compound, providing its empirical formula.

Moles Calculation

Moles calculation is fundamental in chemistry for converting between the mass of a substance and the number of particles or atoms. The mole is a unit of measurement that conveys the amount of a chemical substance that contains as many entities as there are atoms in 12 grams of pure carbon-12.
In determining the empirical formula from combustion analysis, we calculate the moles of carbon, hydrogen, and sulfur from the given quantities of \(\mathrm{CO}_2\), \(\mathrm{H}_2\mathrm{O}\), and \(\mathrm{SO}_2\).

• The moles of carbon are derived using the mass of \(\mathrm{CO}_2\): the mass of \(\mathrm{CO}_2\) produced is divided by its molar mass to find the corresponding moles.
• Similarly, we find moles of hydrogen from the mass of \(\mathrm{H}_2\mathrm{O}\), and moles of sulfur from \(\mathrm{SO}_2\).

After calculating the moles, we simplify these values to the smallest possible whole number ratio to deduce the empirical formula. This calculation is central to translating mass data received from experiments into meaningful chemical information.