# A student tried to recover all the gold metal from a 1.738 M solution of gold (III) sulfate by...

## Question:

A student tried to recover all the gold metal from a 1.738 M solution of gold (III) sulfate by adding magnesium metal. They started with 450 gal of solution and added 65 lbs of magnesium metal. When the reaction was complete, they recovered 150 lbs gold metal. What was their percent yield?

## Percent yield:

Percent yield is a measure of how efficient a certain chemical process is with regards to product formation. It is mathematically defined as the ratio of the actual yield and the theoretical yield.

{eq}\rm \%\ yield=\dfrac{actual \ yield}{theoretical\ yield} \times 100\%{/eq}

Theoretical yield is the maximum amount of the product a reaction can give based on the given limiting reactant. This value can be stoichiometrically derived using the amount of the limiting reactant. On the other hand, the actual yield is the actual quantity of product obtained when the reaction is conducted and is lesser compared to the theoretical yield.

Percent yield is the percent ratio between the actual and theoretical yield of the process.

{eq}\rm \%\ yield=\dfrac{actual\ yield}{theoretical\ yield} \times 100\%{/eq}

The actual yield of the recovery is 150 pounds of gold (Au).

The theoretical yield is the maximum amount of gold that can be recovered. For this case, we have a 450 gallons of the gold solution which is equivalent to 1703.44 liters. Using the concentration, the theoretical yield is (molar of Au is 196.97 g/mol):

{eq}\rm theoretical\ yield=(Volume\ of\ solution)\times (Concentration\ of\ solution)\times (Molar\ mass\ of\ Au)\times (Conversion\ factor)\\ \rm theoretical\ yield=1703.44\ L\ \times \left( \dfrac{1.738\ mol\ Au}{L} \right) \times \left( \dfrac{196.97\ g\ Au}{mol\ Au}\right) \times \left( \dfrac{1\ lb}{453.59\ g} \right)\\ \rm theoretical\ yield= 1286\ lb\ Au{/eq}

The percent yield is:

{eq}\rm \%\ yield=\dfrac{actual\ yield}{theoretical\ yield} \times 100\%\\ \rm \%\ yield=\dfrac{150\ lb\ Au}{1286\ lb\ Au} \times 100\%\\ \boxed{\rm \%\ yield=11.7\%}{/eq}