Question

Although we tend to make less use of mercury these days because of the cnvironmental problems created by its improper disposal, mercury is still an important metal because of its unusual property of existing as a liquid at room temperature. One process by which mercury is produced industrially is through the heating of its common ore cinnabar (mercuric sulfide, \(\mathrm{HgS}\) ) with lime (calcium oxide, \(\mathrm{CaO}\) ). $$ 4 \mathrm{HgS}(s)+4 \mathrm{CaO}(s) \rightarrow 4 \mathrm{Hg}(l)+3 \mathrm{CaS}(s)+\mathrm{CaSO}_{4}(s) $$ What mass of mercury would be produced by complete reaction of \(10.0 \mathrm{~kg}\) of \(\mathrm{HgS}\) ?

Short answer

The mass of mercury produced by the complete reaction of 10.0 kg of HgS is 8.63 kg.

Step-by-step solution

Find the Molar Mass of HgS and Hg

First, we need to find the molar masses of Mercuric Sulfide (HgS) and Mercury (Hg) using the periodic table. For HgS, the molar mass is the sum of the molar masses of Hg and S: Molar mass of Hg = 200.59 g/mol Molar mass of S = 32.07 g/mol Molar mass of HgS = 200.59 + 32.07 = 232.66 g/mol For Hg, the molar mass is given directly from the periodic table: Molar mass of Hg = 200.59 g/mol

Convert Mass of HgS to Moles

Now we'll convert the given mass of HgS (10.0 kg) to moles. Make sure to convert the mass to grams first: Mass of HgS = 10.0 kg × (1000 g / 1 kg) = 10000 g Moles of HgS = (10000 g) / (232.66 g/mol) = 42.99 mol

Find Moles of Hg using the Balanced Equation

In the balanced chemical equation, we have: 4 HgS(s) + 4 CaO(s) -> 4 Hg(l) + 3 CaS(s) + CaSO4(s) From the stoichiometry, we see that the reaction produces 4 moles of Hg for every 4 moles of HgS consumed. So, we can directly relate the moles of HgS to moles of Hg: Moles of Hg = (Moles of HgS) × (4 moles Hg / 4 moles HgS) = 42.99 mol

Convert Moles of Hg to Mass

Now that we have the moles of Hg, we can convert that back to mass using the molar mass of Hg: Mass of Hg = (Moles of Hg) × (Molar mass of Hg) = (42.99 mol) × (200.59 g/mol) = 8627.25 g Since the mass is quite large, we can also express it in kilograms: Mass of Hg = 8627.25 g × (1 kg / 1000 g) = 8.63 kg So, the mass of mercury produced by the complete reaction of 10.0 kg of HgS is 8.63 kg.

Key concepts

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance, typically expressed in grams per mole (g/mol). A mole is a unit of measurement used in chemistry that represents a specific number of particles, usually atoms or molecules, and is constant for any substance. That number, known as Avogadro's number, is approximately \(6.022 \times 10^{23}\) particles.

The molar mass is calculated by summing the atomic masses of all atoms in a molecule of the substance. For example, to find the molar mass of mercuric sulfide (\(\mathrm{HgS}\)), we add together the atomic masses of mercury (Hg) and sulfur (S). With the atomic mass of Hg being 200.59 g/mol and that of S being 32.07 g/mol, the molar mass of \(\mathrm{HgS}\) is \(200.59 \mathrm{g/mol} + 32.07 \mathrm{g/mol} = 232.66 \mathrm{g/mol}\).

This concept of molar mass is also crucial when converting between mass and moles of a substance, as it is used in mole-to-mass or mass-to-mole conversions. During stoichiometry calculations, we often use the molar mass to understand how much of each reactant is needed, or how much of a product is generated from a given amount of reagents.

The Role of Chemical Reactions in Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It requires a balanced chemical equation, where the number of atoms for each element is equal on both reactant and product sides, to ensure the law of conservation of mass is followed.

In our mercury example, the chemical reaction entails heating mercuric sulfide with lime to produce mercury, calcium sulfide, and calcium sulfate: \(4 \mathrm{HgS}(s) + 4 \mathrm{CaO}(s) \rightarrow 4 \mathrm{Hg}(l) + 3 \mathrm{CaS}(s) + \mathrm{CaSO}_{4}(s)\). The stoichiometry tells us that for every four moles of \(\mathrm{HgS}\) heated, we get four moles of mercury \((\mathrm{Hg})\). By understanding this mole ratio, we can predict the quantity of mercury produced from a certain amount of cinnabar ore.

Understanding chemical reactions and their stoichiometry is essential because it allows chemists to calculate the quantities of substances needed or produced in a reaction. It ensures that all reactants are used efficiently, and helps in predicting the outcomes of reactions for practical purposes like industrial production or laboratory experiments.

Mole-to-Mass Conversion in Stoichiometry

After determining the stoichiometric ratios from the balanced chemical equation, chemists often need to convert these mole ratios into masses, since mass is a more practical measurement for laboratory work and industry processes. This is because moles describe the number of particles, but mass relates to the amount of matter we can physically measure and handle.

For the conversion, we use the molar mass as a conversion factor. In our example, we convert the mass of \(\mathrm{HgS}\) to moles using its molar mass and then use the stoichiometric ratio to find the equivalent moles of mercury. This process includes converting the initial mass from kilograms to grams, which is more aligned with the molar mass unit (g/mol).

The formula for mole-to-mass conversion looks like this: \[ \text{Mass (g)} = \text{Moles} \times \text{Molar Mass (g/mol)} \]
Once you have moles, the above formula helps you find the mass of a product or reactant. In our mercury production example, after finding the moles of mercury, we multiply it by the molar mass of mercury to get the final mass in grams, which we can then convert back to kilograms if needed. The concepts of molar mass, chemical reactions, and stoichiometric calculations are tightly intertwined and mastering these conversions is key to succeeding in chemistry.