Question

What mass of carbon disulphide, \(\mathrm{CS}_{2}\) can be completely oxidized to \(\mathrm{SO}_{2}\) and \(\mathrm{CO}_{2}\) by the oxygen liberated when \(325 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{O}_{2}\) react with water? (a) \(316.67 \mathrm{~g}\) (b) \(52.78 \mathrm{~g}\) (c) \(633.33 \mathrm{~g}\) (d) \(211.11 \mathrm{~g}\)

Short answer

The mass of carbon disulfide that can be completely oxidized by the oxygen liberated is 316.67 g.

Step-by-step solution

Write the balanced chemical equations

First, write the balanced chemical equations for the reactions involved. The reaction of sodium peroxide with water liberates oxygen: 2Na2O2(s) + 2H2O(l) → 4NaOH(aq) + O2(g).Then, write the balanced equation for the oxidation of carbon disulfide by oxygen: CS2(l) + 3O2(g) → CO2(g) + 2SO2(g).

Calculate the moles of Na2O2

Calculate the moles of Na2O2 using its molar mass (77.98 g/mol). Moles of Na2O2 = mass (g) / molar mass (g/mol). For 325 g of Na2O2: Moles of Na2O2 = 325 g / 77.98 g/mol.

Calculate the moles of O2 produced

Using the stoichiometry of the reaction, calculate the moles of O2 produced from Na2O2. From the balanced reaction, 2 moles of Na2O2 produce 1 mole of O2. Use the moles of Na2O2 calculated in Step 2.

Calculate the moles of CS2 oxidized

Using the balanced equation for the oxidation of CS2, determine the moles of CS2 that can be oxidized by the moles of O2 calculated in Step 3. From the equation, 3 moles of O2 oxidize 1 mole of CS2.

Calculate the mass of CS2

Use the molar mass of CS2 (76.14 g/mol) to convert the moles of CS2 to mass. Mass of CS2 = moles of CS2 × molar mass of CS2.

Determine the correct answer

Compare the calculated mass of CS2 with the given options to determine the correct answer.

Key concepts

Oxidation Reactions

Oxidation reactions are chemical processes where a substance gains oxygen or loses electrons, often producing energy in the form of heat or light. They are fundamental to various fields, including industry, environmental science, and our bodies' metabolism. For instance, the rusting of iron and the burning of fuel are both common examples of oxidation reactions.

In the context of the given problem, carbon disulfide is undergoing an oxidation reaction when it reacts with oxygen to form carbon dioxide and sulfur dioxide. Each carbon disulphide molecule gains oxygen to form these products. Writing balanced chemical equations is a critical step in understanding these reactions, as it ensures that the number of each type of atom is conserved in the process. Oxidation reactions, particularly those that are combustion reactions, are usually exothermic, meaning they release energy.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions and serve as a crucial tool in stoichiometry. A well-balanced chemical equation ensures that the Law of Conservation of Mass is followed, indicating that atoms are neither created nor destroyed during a chemical reaction. This is done by adjusting coefficients—the numbers placed in front of compound symbols—to balance the number of atoms of each element on both the reactant and product sides of the equation.

In the exercise example, the chemical equation for the reaction between sodium peroxide and water is balanced to show that two molecules of sodium peroxide yield one molecule of oxygen gas, which is then used to oxidize carbon disulfide. Mastering the skill of balancing chemical equations is fundamental for solving stoichiometry problems because it allows one to correctly use mole ratios to relate reactants and products in a quantitative manner.

Mole Concept

The mole concept is a cornerstone in the study of chemistry, as it allows chemists to count particles by weighing them. A mole is a unit defined as the amount of any substance that contains as many particles (atoms, molecules, ions, or other entities) as there are atoms in 12 grams of pure carbon-12. This number, Avogadro's number, is approximately equal to 6.022 x 10²³. The molar mass, which is the mass of one mole of a substance (measured in grams per mole), serves as the bridge between the macroscopic world we can measure and the microscopic world of atoms and molecules.

In the context of the exercise, to determine the mass of carbon disulfide that can be oxidized, the mole concept is employed to find the relationship between grams of sodium peroxide and the moles of oxygen it can produce, thereafter determining how many moles of carbon disulfide can be oxidized by this amount of oxygen. Using the molar mass of carbon disulfide, these moles can then be converted to grams, providing a clear and quantitative solution to the stoichiometry problem.