Problem 136 - Chemistry and Chemical Reactivity

Question

Stibnite, \(\mathrm{Sb}_{2} \mathrm{S}_{3},\) is a dark gray mineral from which antimony metal is obtained. What is the mass percent of antimony in the sulfide? If you have \(1.00 \mathrm{kg}\) of an ore that contains \(10.6 \%\) antimony, what mass of \(\mathrm{Sb}_{2} \mathrm{S}_{3}\) (in grams) is in the ore?

Step-by-Step Solution

Answer

The mass of \(\mathrm{Sb}_{2} \mathrm{S}_{3}\) in the ore is approximately 148 grams.

Step 1: Calculate the Molar Masses

First, determine the molar masses of antimony (Sb) and sulfur (S) using the periodic table. Antimony (Sb) has a molar mass of approximately 121.76 grams per mole, and sulfur (S) has a molar mass of 32.07 grams per mole.

Step 2: Calculate Molar Mass of Stibnite

The chemical formula for stibnite is \(\mathrm{Sb}_{2} \mathrm{S}_{3}\). This compound contains two Sb atoms and three S atoms. Calculate the molar mass: \[\text{Molar mass of } \mathrm{Sb}_2\mathrm{S}_3 = 2(121.76) + 3(32.07) = 339.68 \text{ g/mol}\]

Step 3: Calculate Mass Percent of Antimony

To find the mass percent of antimony in stibnite, use the formula:\[\text{Mass percent of Sb} = \left(\frac{\text{Mass of Sb in } \mathrm{Sb}_2\mathrm{S}_3}{\text{Molar mass of } \mathrm{Sb}_2\mathrm{S}_3}\right) \times 100\]The mass of Sb in \(\mathrm{Sb}_{2} \mathrm{S}_{3}\) is \(2 \times 121.76 = 243.52\) g. Therefore, the mass percent is: \[\left(\frac{243.52}{339.68}\right) \times 100 \approx 71.69\%\]

Step 4: Calculate Mass of Stibnite in the Ore

Given that the ore contains 10.6% antimony, and the total mass of the ore is 1.00 kg, the mass of antimony in the ore is: \[10.6\% \times 1000 \text{ g (or } 1 \text{ kg) } = 106 \text{ g}\]Knowing that stibnite contains approximately 71.69% antimony, we set up the equation:\[\frac{243.52}{339.68} = \frac{106}{\text{mass of } \mathrm{Sb}_{2} \mathrm{S}_{3}} \]Solving this gives:\[\text{mass of } \mathrm{Sb}_{2} \mathrm{S}_{3} \approx 148 \text{ g}\]

Key Concepts

Stibnite

Stibnite is a mineral composed primarily of the compound antimony trisulfide, with the chemical formula \( \mathrm{Sb}_{2} \mathrm{S}_{3} \). This mineral is known for its dark gray color and metallic luster. It is the primary source of the metal antimony, which is utilized in a range of applications including flame retardants, lead-acid batteries, and alloys.
Stibnite's significance extends beyond its industrial applications, also captivating geologists and mineralogists due to its unique crystalline structure. To better understand its composition, chemists analyze the molar mass of its components, antimony and sulfur, a crucial step in calculating its mass percent of antimony.

• Color: Dark gray
• Uses: Source of antimony, flame retardants, batteries
• Key feature: Metallic luster

Antimony

Antimony (Sb) is a metallic element found in group 15 of the periodic table. It is known for its brittle texture and silvery appearance. While antimony itself is not used extensively in its pure form, its compounds such as \( \mathrm{Sb}_2 \mathrm{S}_3 \), found in stibnite, are invaluable.
Antimony's main applications are in the manufacturing of flame retardants and as an alloying material where it enhances the hardness and strength of lead, notably in the construction of lead-acid batteries.
Understanding the chemical behavior of antimony is important and begins with its atomic properties, such as its molar mass, which is approximately 121.76 grams per mole. This forms a basis for further calculations, including determining its proportion in compounds like stibnite.

Molar Mass

Molar mass is an essential concept in chemistry, representing the mass of one mole of a chemical element or compound. It is calculated by summing the atomic masses of all atoms in a molecule, as found on the periodic table.
In the case of stibnite, the formula \( \mathrm{Sb}_{2} \mathrm{S}_{3} \) indicates there are two antimony atoms and three sulfur atoms. Hence, its molar mass is determined as follows:

• Antimony (Sb): 2 atoms \( \times \) 121.76 g/mol = 243.52 g/mol
• Sulfur (S): 3 atoms \( \times \) 32.07 g/mol = 96.21 g/mol

Adding these values gives the molar mass of stibnite: \( 243.52 + 96.21 = 339.68 \) g/mol.
Understanding how to calculate molar mass is crucial, aiding in quantitatively analyzing chemical reactions and compositions.

Mass Percent Formula

The mass percent formula is used to determine the composition of a component within a compound, expressed as a percentage. This value reveals how much, by mass, a particular element contributes to the overall compound.
To calculate the mass percent of antimony in stibnite \( (\mathrm{Sb}_2 \mathrm{S}_3) \), the formula used is:\[\text{Mass percent of Sb} = \left( \frac{\text{Mass of Sb in } \mathrm{Sb}_2 \mathrm{S}_3} {\text{Molar mass of } \mathrm{Sb}_2 \mathrm{S}_3}\right) \times 100\]Inserting the calculated weights:\[\left(\frac{243.52}{339.68}\right) \times 100 \approx 71.69\%\]This shows that approximately 71.69% of stibnite's mass is attributed to antimony.
Mass percent calculations are vital in chemistry for formulating mixtures, understanding reactive proportions, and quantifying material purity.