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Sagot :
ANSWER
The actual yield is 125.646 grams
STEP-BY-STEP EXPLANATION
Given information
The mass of sodium in grams = 57.50 grams
The percentage yield = 86%
The next step is to write the balanced equation of the reaction
[tex]2Na_{(s)}+Cl_{2(g)}\text{ }\rightarrow2NaCl_{(aq)}[/tex]From the above reaction, we can see that 2 moles of sodium react with 1 mole of chloride too give moles of sodium chloride
The next step is to find the number of moles sodium using the below formula
[tex]\text{mole = }\frac{\text{ mass}}{\text{ molar mass}}[/tex]According to the periodic table, the molar mass of sodium is 23 g/mol
[tex]\begin{gathered} \text{mole = }\frac{57.50}{23} \\ \text{mole = }2.5\text{ moles} \end{gathered}[/tex]The next step is to find the number of moles of sodium chloride using a stoichiometry ratio
From the above reaction, you can see that 2 moles of sodium react to give 2 moles of sodium chloride
Let x represents the number of moles of sodium chloride
[tex]\begin{gathered} 2\text{ moles }\rightarrow\text{ 2 moles} \\ 2.5\text{ moles }\rightarrow\text{ x moles} \\ \text{cross multiply} \\ 2\text{ }\times\text{ x = 2 }\times\text{ 2.5} \\ 2x\text{ = 5} \\ \text{Divide both sides by 2} \\ \frac{\cancel{2}x}{\cancel{2}}\text{ = }\frac{5}{2} \\ x\text{ = 2.5 moles} \end{gathered}[/tex]Therefore, the number of moles of NaCl is 2.5 moles
The next step is to find the theoretical yield using the below formula
[tex]\text{mole = }\frac{\text{ mass}}{\text{ molar mass}}[/tex]According to the periodic table, the molar mass of NaCl is 58.44 g/mol
[tex]\begin{gathered} 2.5\text{ = }\frac{mass}{58.44} \\ \text{cross multiply} \\ \text{mass = 2.5 }\times\text{ 58.44} \\ \text{mass = 146.1 grams} \end{gathered}[/tex]Since the theoretical yield is 146.1 grams, then we can now find the actual yield using the below formula
[tex]\begin{gathered} \text{Percentage yield =}\frac{actual\text{ yield}}{\text{theoretical yield}} \\ \end{gathered}[/tex]Recall that, the percentage yield is86%
[tex]\begin{gathered} \frac{86}{100}\text{ = }\frac{actual\text{ yield}}{146.1} \\ 0.86\text{ = }\frac{actual\text{ yield}}{146.1} \\ \text{cross multiply} \\ \text{actual yield = 0.86 }\times\text{ 146.1} \\ \text{actual yield = 125.646 grams} \end{gathered}[/tex]Therefore, the actual yield is 125.646 grams
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