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Chapter 3: Problem 120

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

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

Step by step solution

01

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
02

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.
03

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
04

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.

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Most popular questions from this chapter

One of the components that make up common table sugar is fructose, a compound that contains only carbon, hydrogen, and oxygen. Complete combustion of \(1.50 \mathrm{~g}\) of fructose produced \(2.20 \mathrm{~g}\) of carbon dioxide and \(0.900 \mathrm{~g}\) of water. What is the empirical formula of fructose?

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A substance \(\mathrm{X}_{2} \mathrm{Z}\) has the composition (by mass) of \(40.0 \% \mathrm{X}\) and \(60.0 \% \mathrm{Z}\). What is the composition (by mass) of the compound \(\mathrm{XZ}_{2}\).

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