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Chapter 3: Problem 128

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
When 25.0g of Ag2O reacts with 50.0g of C10H10N4SO2, assuming a 100% yield, \(71.33 \ g\) of silver sulfadiazine (AgC10H9N4SO2) can be produced.

Step by step solution

01

Convert Masses to Moles

To convert the masses of the reactants to moles, we first need to determine the molar mass of each reactant: Molar mass of Ag2O = \(2 * Ag + O = 2 * 107.87 + 16.00 = 231.74 \ g/mol\) Molar mass of C10H10N4SO2 = \(10 * C + 10 * H + 4 * N + S + 2 * O = 10 * 12.01 + 10 * 1.01 + 4 * 14.01 + 32.07 + 2 * 16.00 = 250.30 \ g/mol\) Now, we can convert the masses to moles using the molar mass for each reactant: Moles of Ag2O = \(25.0g \div 231.74g/mol = 0.1078 \ mol\) Moles of C10H10N4SO2 = \(50.0g \div 250.30g/mol = 0.1997 \ mol\)
02

Determine the Limiting Reactant

Using the balanced chemical equation, we can determine the mole ratio between the reactants: Mole ratio (Ag2O:C10H10N4SO2) = 1:2 By dividing the moles of each reactant by their respective mole ratio, we can determine which reactant is the limiting reactant: For Ag2O: \(0.1078 \ mol ÷ 1 = 0.1078\) For C10H10N4SO2: \(0.1997 \ mol ÷ 2 = 0.09985\) Since 0.09985 is smaller than 0.1078, C10H10N4SO2 is the limiting reactant.
03

Calculate Moles of Silver Sulfadiazine Produced

Using the stoichiometry from the balanced chemical equation, we can calculate the moles of silver sulfadiazine (AgC10H9N4SO2) produced: Mole ratio (AgC10H9N4SO2:C10H10N4SO2) = 2:2 Moles of AgC10H9N4SO2 produced = \(0.1997 \ mol \times \frac{2 \ mol \ AgC10H9N4SO2}{2 \ mol \ C10H10N4SO2} = 0.1997\ mol\)
04

Convert Moles of Silver Sulfadiazine to Mass

Now, we need to determine the molar mass of AgC10H9N4SO2: Molar mass of AgC10H9N4SO2 = \(Ag + 10 * C + 9 * H + 4 * N + S + 2 * O = 107.87 + 10 * 12.01 + 9 * 1.01 + 4 * 14.01 + 32.07 + 2 * 16.00 = 357.14 \ g/mol\) Using the molar mass, we can convert the moles of silver sulfadiazine produced into mass: Mass of AgC10H9N4SO2 = \(0.1997 \ mol \times 357.14 \ g/mol = 71.33 \ g\) Therefore, when 25.0g of Ag2O reacts with 50.0g of C10H10N4SO2, assuming a 100% yield, 71.33g of silver sulfadiazine (AgC10H9N4SO2) can be produced.

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