Question

How many grams of sulfur (S) are needed to react completely with \(246 \mathrm{~g}\) of mercury \((\mathrm{Hg})\) to form \(\mathrm{HgS}\) ?

Short answer

Approximately 39.35 grams of sulfur are needed.

Step-by-step solution

Write the Balanced Chemical Equation

The chemical reaction between sulfur and mercury to form mercuric sulfide (HgS) is given by the balanced equation: \[ \text{Hg} + \text{S} \rightarrow \text{HgS} \] This shows that one mole of mercury reacts with one mole of sulfur to form one mole of mercuric sulfide.

Calculate Moles of Mercury

The molar mass of mercury (Hg) is approximately \(200.59 \text{ g/mol}\). To find the number of moles of mercury, use the formula: \[ \text{Moles of Hg} = \frac{\text{Mass of Hg}}{\text{Molar Mass of Hg}} = \frac{246 \text{ g}}{200.59 \text{ g/mol}} \approx 1.227 \text{ moles} \]

Determine Moles of Sulfur Needed

According to the balanced equation, 1 mole of mercury reacts with 1 mole of sulfur. Therefore, 1.227 moles of mercury will react with 1.227 moles of sulfur.

Convert Moles of Sulfur to Grams

The molar mass of sulfur (S) is approximately \(32.07 \text{ g/mol}\). Thus, the mass of sulfur needed is: \[ \text{Mass of S} = \text{Moles of S} \times \text{Molar Mass of S} = 1.227 \text{ moles} \times 32.07 \text{ g/mol} \approx 39.35 \text{ g} \]

Key concepts

Balanced Chemical Equation

In chemistry, a balanced chemical equation is like a recipe that describes how molecules interact during a reaction. To understand this exercise, we start with the process between mercury and sulfur transforming into mercuric sulfide. The balanced chemical equation for this reaction is:
Hg + S → HgS.
This equation is balanced, meaning the number of atoms for each element is the same on both sides. One mercury atom reacts with one sulfur atom to form one molecule of mercuric sulfide. Balanced equations ensure the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction, is followed. This balance allows us to calculate the amount of substances needed or produced accurately.

Moles

The concept of moles is fundamental in chemistry as it allows chemists to count particles by weighing them. A mole, like a dozen, is a counting unit. Specifically, one mole equals approximately 6.022 x 10²³ particles of a substance. The mole concept bridges the gap between the microscopic world of atoms and molecules and the macroscopic scales we measure in labs.
Knowing the number of moles helps us understand how substances react in set proportions. In this exercise, calculating the moles of mercury is crucial. By determining the moles, we find out how many atoms are really taking part in the reaction with sulfur. One useful formula to remember is:
\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]This calculation aligns with the balanced equation to find the exact moles of each component involved.

Molar Mass

Molar mass is another essential concept, representing the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol) and combines the atomic masses of the elements in a compound as listed on the periodic table. For example, the molar mass of mercury (Hg) is around 200.59 g/mol, while sulfur (S) is approximately 32.07 g/mol.

• Molar mass allows chemists to convert between the mass of a substance and the number of moles.
• It's crucial in calculating how much of one material will react with another.

In the exercise provided, using the molar masses of both mercury and sulfur helps us convert grams into moles, allowing a comparison based on the balanced chemical reaction. This computation reveals the stoichiometric relationship between the substances.

Mercuric Sulfide

Mercuric sulfide (HgS), also known as cinnabar in its natural mineral form, is the compound formed when mercury and sulfur react. It appears as a deep red or sometimes black, depending on the crystal structure. In the chemical equation Hg + S → HgS, one mole of mercury combines with one mole of sulfur to form one mole of mercuric sulfide.
Mercuric sulfide is noteworthy in various applications:

• Used historically as a pigment known for its vibrant red color.
• It's a more stable, nontoxic form of mercury, prevalent in traditional medicine and alchemy.

Understanding the properties and reactions leading to compounds like HgS is important in both chemistry studies and practical applications.