Respuesta :
ANSWER
The mass of NaOH that reacted is 219.58 grams
EXPLANATION
Given that
The mass of Fe(OH)3 is 196 grams
Follow the steps below to find the mass of NaOH
Step 1; Write the balanced equation of the reaction
[tex]\text{ Fe\lparen NO}_3)_3\text{ + 3NaOH }\rightarrow\text{ Fe\lparen OH\rparen}_3\text{ + 3NaNO}_3[/tex]Step 2; Find the moles of Fe(OH)3 using the below formula
[tex]\text{ mole = }\frac{\text{ mass}}{\text{ molar mass}}[/tex]Recall, that the molar mass of Fe(OH)3 is 106.87 g/mol
[tex]\begin{gathered} \text{ mole = }\frac{\text{ 196}}{\text{ 106.87}} \\ \text{ mole = 1.83 moles} \end{gathered}[/tex]The number of moles of Fe(OH)3 is 1.83 moles
Step 3; Find the number of moles of NaOH using a stoichiometry ratio
In the equation above, 1 mole of Fe(OH)3 gives 3 moles of NaOH
Let x represents the number of moles of Fe(OH)3
[tex]\begin{gathered} \text{ 1 mole Fe\lparen OH\rparen}_3\text{ }\rightarrow\text{ 3 moles NaOH} \\ \text{ 1.83 moles Fe\lparen OH\rparen}_3\text{ }\rightarrow\text{ x moles NaOH} \\ \text{ Cross multiply} \\ \text{ 1 mole Fe\lparen OH\rparen}_3\text{ }\times\text{ x moles NaOH = 1.83 moles Fe\lparen OH\rparen}_3\times3\text{ moles NaOH} \\ \text{ Isolate x moles NaOH} \\ \text{ x moles NaOH = }\frac{1.83moles\cancel{Fe(OH)\placeholder{⬚}_3}\times\text{ 3 moles NaOH}}{1mole\cancel{Fe(OH)\placeholder{⬚}_3}} \\ \text{ x moles NaOH = 1.83 }\times\text{ 3} \\ \text{ x moles NaOH = 5.49 moles} \end{gathered}[/tex]The number of moles of NaOH is 5.49 moles
Step 4; Find the mass of NaOH using the below formula
[tex]\begin{gathered} \text{ mole = }\frac{\text{ mass}}{\text{ molar mass}} \\ \text{ cross multiply} \\ \text{ mass = mole }\times\text{ molar mass} \end{gathered}[/tex]Recall, that the molar mass of NaOH is 39.997 g/mol
[tex]\begin{gathered} \text{ mass = 5.49 }\times\text{ 39.997} \\ \text{ mass = 219.58 grams} \end{gathered}[/tex]Therefore, the mass of NaOH that reacted is 219.58 grams
