Question

Silver sulfadiazine burn-treating cream creates a barrier against bacterial invasion and releases antimicrobial agents directly into the wound. If \(25.0 \mathrm{~g} \mathrm{Ag}_{2} \mathrm{O}\) is reacted with \(50.0 \mathrm{~g} \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{SO}_{2}\), what mass of silver sulfadiazine, \(\mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{~N}_{4} \mathrm{SO}_{2}\), can be produced, assuming \(100 \%\) yield? $$ \mathrm{Ag}_{2} \mathrm{O}(s)+2 \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{SO}_{2}(s) \longrightarrow 2 \mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{~N}_{4} \mathrm{SO}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

The mass of silver sulfadiazine produced, assuming 100% yield, is \(77.00 \mathrm{~g}\).

Step-by-step solution

Calculate the moles of reactants involved

To convert the given mass of reactants to moles, we will first find their respective molar masses. We will then divide the given mass by the molar mass of the respective reactants. Molar mass of Ag₂O = (2 * 107.87) + 16 = 231.74 g/mol Molar mass of C₁₀H₁₀N₄SO₂ = (10 * 12.01) + (10 * 1.01) + (4 * 14.01) + 32.06 + (2 * 16) = 250.28 g/mol Moles of Ag₂O = mass / molar mass = 25.0 g / 231.74 g/mol = 0.1078 mol Moles of C₁₀H₁₀N₄SO₂ = mass / molar mass = 50.0 g / 250.28 g/mol = 0.1998 mol

Identify the limiting reactant

According to the balanced equation, 1 mole of Ag₂O reacts with 2 moles of C₁₀H₁₀N₄SO₂. We need to compare the mole ratio of both reactants to determine the limiting reactant. Mole ratio of Ag₂O to C₁₀H₁₀N₄SO₂ = (0.1078 mol) / (0.1998 mol) = 0.5396 Since the mole ratio is less than 1 (the required ratio as per the balanced equation), we can conclude that Ag₂O is the limiting reactant.

Calculate the moles of AgC₁₀H₉N₄SO₂ produced

According to the balanced equation, 1 mole of Ag₂O reacts with 2 moles of C₁₀H₁₀N₄SO₂ to produce 2 moles of AgC₁₀H₉N₄SO₂. Therefore, the moles of AgC₁₀H₉N₄SO₂ produced would be: Moles of AgC₁₀H₉N₄SO₂ produced = 2 * moles of limiting reactant (Ag₂O) = 2 * 0.1078 mol = 0.2156 mol

Calculate the mass of AgC₁₀H₉N₄SO₂ produced

To convert the moles of AgC₁₀H₉N₄SO₂ produced to mass, we need to find its molar mass first. Molar mass of AgC₁₀H₉N₄SO₂ = 107.87 + (10 * 12.01) + (9 * 1.01) + (4 * 14.01) + 32.06 + (2 * 16) = 357.14 g/mol Mass of AgC₁₀H₉N₄SO₂ produced = moles * molar mass = 0.2156 mol * 357.14 g/mol = 77.00 g So, the mass of silver sulfadiazine produced, assuming 100% yield, is 77.00 g.

Key concepts

Molar Mass

Understanding molar mass is crucial in stoichiometry, as it helps you convert between mass and moles, which are essential units in chemistry. The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It combines the atomic masses of all atoms in a chemical formula. For instance, consider the compound silver oxide (Ag₂O). To find its molar mass, sum up the atomic masses of two silver (Ag) atoms and one oxygen (O) atom:

• Atomic mass of silver (Ag) = 107.87 g/mol, therefore: 2 * 107.87 = 215.74 g/mol for silver.
• Atomic mass of oxygen (O) = 16 g/mol.

Adding these values together gives a molar mass of 231.74 g/mol for Ag₂O. Calculating the molar mass of a compound like C₁₀H₁₀N₄SO₂ follows the same principle, considering the atomic masses for carbon, hydrogen, nitrogen, sulfur, and oxygen. This methodology enables precise conversions required for mass-to-mole calculations.

Limiting Reactant

In any chemical reaction, the limiting reactant is the substance that gets completely consumed first. It limits the extent of the reaction and thus determines the maximum amount of product that can be formed. Identifying the limiting reactant is critical in calculations involving mass and yield.
In our example reaction between Ag₂O and C₁₀H₁₀N₄SO₂, the stoichiometric coefficients indicate that 1 mole of Ag₂O should react with 2 moles of C₁₀H₁₀N₄SO₂. We start by calculating the moles of each reactant, as shown previously:

• Moles of Ag₂O = 0.1078 mol
• Moles of C₁₀H₁₀N₄SO₂ = 0.1998 mol

The ratio 0.1078/0.1998 being less than 0.5 means that Ag₂O is insufficient compared to the required amount to fully react with all C₁₀H₁₀N₄SO₂. Hence, Ag₂O is the limiting reactant, controlling the amount of AgC₁₀H₉N₄SO₂ formed.

Chemical Reaction Equation

A balanced chemical equation is fundamental for understanding stoichiometric relationships in a reaction. It uses reactant and product ratios to provide insights into the conversion process and product formation.
In the equation: \[\mathrm{Ag}_{2} \mathrm{O}(s) + 2 \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{SO}_{2}(s) \longrightarrow 2 \mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{N}_{4} \mathrm{SO}_{2}(s) + \mathrm{H}_{2} \mathrm{O}(l)\]Each term in the equation must be balanced to follow the law of conservation of mass. This means the number of each type of atom on both sides of the equation is equal. In our case:

• One mole of Ag₂O reacts with two moles of C₁₀H₁₀N₄SO₂.
• This forms two moles of AgC₁₀H₉N₄SO₂ and one mole of water (H₂O).

Balancing equations is critical for identifying limiting reactants and related stoichiometric calculations.

Mass Calculation

Calculating the mass of products formed in a chemical reaction entails using stoichiometry to connect moles and mass via molar mass. After identifying the limiting reactant, which defines the reaction scale, you can determine the amount of each product produced.
For the reaction in question, once the limiting reactant Ag₂O is identified, calculate the theoretical yield of AgC₁₀H₉N₄SO₂:

• Start with the moles of limiting reactant: 0.1078 mol.
• According to the balanced equation, 1 mole of Ag₂O produces 2 moles of AgC₁₀H₉N₄SO₂. Thus, you have 0.1078 mol * 2 = 0.2156 mol of desired product.
• The molar mass of AgC₁₀H₉N₄SO₂ is 357.14 g/mol.

Multiply the product moles by its molar mass to get the mass: 0.2156 mol * 357.14 g/mol equals 77.00 g. This mass reflects the theoretical amount of product expected given complete reaction of the limiting reactant.