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? $$ \mathrm{Ag}_{2} \mathrm{O}(s)+2 \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{SO}_{2}(s) \longrightarrow 2 \mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{N}_{4} \mathrm{SO}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$

First, we need to find the molar mass of each compound involved in the reaction. Look up the atomic masses of the individual elements and multiply them by the number of atoms in the formula. Then add all of the results together to get the molar mass for each compound. Ag₂O: (2 * 107.868) + (1 * 16.00) = 231.736 g/mol C₁₀H₁₀N₄SO₂: (10 * 12.01) + (10 * 1.008) + (4 * 14.007) + (1 * 32.07) + (2 * 16.00) = 250.293 g/mol AgC₁₀H₉N₄SO₂: (1 * 107.868) + (10 * 12.01) + (9 * 1.008) + (4 * 14.007) + (1 * 32.07) + (1 * 16.00) = 357.144 g/mol

Using the molar mass, we can convert the mass of each reactant to moles. For Ag₂O: \( moles = \frac{mass}{molar \thinspace mass} = \frac{25.0 \thinspace g}{231.736 \thinspace g/mol} = 0.1079 \thinspace mol \) For C₁₀H₁₀N₄SO₂: \( moles = \frac{50.0 \thinspace g}{250.293 \thinspace g/mol} = 0.1997 \thinspace mol \)

Use stoichiometry to calculate the theoretical yield for both reactants. Divide the number of moles of each reactant by the stoichiometric coefficient (the numbers that balance the chemical equation). For Ag₂O (using stoichiometric coefficient of 1): \(0.1079 \thinspace mol\) For C₁₀H₁₀N₄SO₂ (using stoichiometric coefficient of 2): \( \frac{0.1997 \thinspace mol}{2} = 0.09985 \thinspace mol \) The limiting reactant is the one that produces the least amount of product, so in this case, it's C₁₀H₁₀N₄SO₂.

Since we found that C₁₀H₁₀N₄SO₂ is the limiting reactant, we will use it to calculate the mass of silver sulfadiazine that can be produced. From the balanced equation, we see that 2 moles of C₁₀H₁₀N₄SO₂ react to produce 2 moles of AgC₁₀H₉N₄SO₂. So the moles of product will be the same as the moles of the limiting reactant: \( 0.09985 \thinspace mol \). Now, we will convert the moles of product to mass: \( mass \thinspace of \thinspace product = moles \thinspace of \thinspace product \times molar \thinspace mass \) \( mass \thinspace of \thinspace AgC_{10}H_{9}N_{4}SO_{2} = 0.09985 \thinspace mol \times 357.144 \thinspace g/mol = 35.67 \thinspace g \) The mass of silver sulfadiazine that can be produced, assuming a 100% yield, is 35.67 g.