Problem 28 - General Chemistry: Principles and Modern Applications

Question

Without doing detailed calculations, explain which of the following has the greatest mass percent of sulfur. \(\mathrm{SO}_{2}, \mathrm{S}_{2} \mathrm{Cl}_{2}, \mathrm{Na}_{2} \mathrm{S}, \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}, \mathrm{or} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{SH}\)

Step-by-Step Solution

Answer

The compound with the greatest mass percent of sulfur is Na2S (sodium sulfide).

Step 1: Estimating molar masses

To decide on the greatest percent of sulfur, let's begin by roughly estimating the molar masses of the key elements: Sulfur (S) about 32, Oxygen (O) about 16, Chlorine (Cl) about 35.5, Sodium (Na) about 23, Carbon (C) about 12, and Hydrogen (H) about 1.

Step 2: Evaluating each compound

We can now evaluate each compound for its mass percent of Sulfur. In \(\mathrm{SO}_{2}\), S is about 32 and the rest of \(2 \times \mathrm{O}\) is around 32, which makes S about 50%. In \(\mathrm{S}_{2} \mathrm{Cl}_{2}\), \(2 \times \mathrm{S}\) = 64 and the rest about \(2 \times 35.5\), which keeps S less than 50%. For \(\mathrm{Na}_{2} \mathrm{S}\), S is about 32 and the rest about \(2 \times 23\), keeping S over 50%. For \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\), \(2 \times \mathrm{S}\) = 64 and the rest far more, hence, we quickly see that S is less than 50%. Finally, in \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{SH}\), S is about 32, but the rest is far less. So S is definitely less than 50% here too.

Step 3: Identify the compound with the greatest mass percent of Sulfur

From the analysis of each compound, we can tell that the compound with the highest mass percent of Sulfur is Na2S (sodium sulfide).

Key Concepts

Molar Mass

Understanding molar mass is crucial when comparing the mass percent of elements in a compound. Molar mass is the mass of one mole of a substance and is usually expressed in grams per mole (g/mol). It combines the atomic masses of all atoms present in a molecule.
For instance, sulfur has an atomic mass of approximately 32 g/mol. To find the molar mass of a compound like sulfur dioxide (\(\text{SO}_2\)), you add up the mass of one sulfur atom (32 g/mol) and two oxygen atoms (each about 16 g/mol). This makes the molar mass of \(\text{SO}_2\) around 64 g/mol.
Recognizing differences in molar masses helps us estimate elements' percentages in compounds without detailed calculations. Notably, a higher amount of sulfur in a compound's molar mass indicates a more prominent presence of sulfur, as seen in sodium sulfide (\(\text{Na}_2\text{S}\)).

Chemical Compounds

Chemical compounds consist of two or more elements chemically combined in fixed proportions. These compounds exhibit properties differing from their individual elements.
Every compound, whether it's simple or complex, has a distinct chemical formula representing its elemental composition. For example, \(\text{SO}_2\) (sulfur dioxide), \(\text{S}_2\text{Cl}_2\) (disulfur dichloride), and \(\text{Na}_2\text{S}\) (sodium sulfide) are compounds containing sulfur, each with varying proportions of sulfur to other elements.
Understanding how to read and interpret the formula of a compound allows us to determine the number of atoms and the total molar mass of the compound, which is essential for calculating the mass percent of any specific element, such as sulfur.

Sulfide

Sulfides are a group of chemical compounds containing sulfur combined with a more electropositive element. They are significant in various industrial processes and naturally occurring minerals.
A classic example of sulfide is \(\text{Na}_2\text{S}\), sodium sulfide. In this compound, sulfur is bonded with sodium, showcasing a typical sulfide bond. The key feature of sulfides is the presence of sulfur and its ability to bond in these configurations.
Sulfides can be simple, such as \(\text{Na}_2\text{S}\), or more complex, but what remains consistent is the chemical behavior patterns they exhibit due to sulfur's properties. By recognizing these patterns, such as their molar mass contributions, one can easily determine sulfur's prominence in a chemical formula, aiding in the calculation of mass percent.