If salicylic acid costs $21 per kilogram, how much would it cost to purchase enough salicylic acid (formula mass= 138.1) to make 1.0 kilogram of aspirin (formula mass= 180.2), assuming your percent yield was obtained in the reaction? (Note 1 to 1 mole ration in equation).
Hint: This is a two step process. First use the % yield relationship to calculate theoretical amount of aspirin needed to get an actual amount of 1.0 Kg of aspirin. Then use the stoichiometric relation from the chemical equation to calculate how much salicylic acid would be needed to make that much aspirin.
The hint really lays it out for you. Do you have questions on that?
Yes, really didn't know how to set it up.
To calculate the cost of purchasing enough salicylic acid to make 1.0 kilogram of aspirin, you need to follow a two-step process.
Step 1: Calculate the theoretical amount of aspirin needed
First, you need to calculate the theoretical amount of aspirin needed to obtain 1.0 kilogram of aspirin, taking into account the percent yield.
Percent yield is the ratio of the actual yield to the theoretical yield, expressed as a percentage. In this case, the percent yield is already assumed to be obtained in the reaction.
To find the theoretical amount of aspirin needed, you can reverse this equation:
Actual yield = Percent yield × Theoretical yield
Since the actual yield is given as 1.0 kilogram, you can rearrange the formula to solve for the theoretical yield:
Theoretical yield = Actual yield / Percent yield
Now, you need to plug in the given values. The actual yield is 1.0 kilogram, and the percent yield is not provided in the question. You would need to have that information to proceed further with the calculation.
Step 2: Calculate the amount of salicylic acid needed
Once you have calculated the theoretical amount of aspirin needed in step 1, you can then use the stoichiometric relation from the balanced chemical equation to calculate how much salicylic acid would be needed to make that amount of aspirin.
The balanced chemical equation provides the mole ratio between salicylic acid and aspirin. Since the equation states a 1:1 mole ratio, it means that for every 1 mole of salicylic acid, you produce 1 mole of aspirin.
To convert from moles of aspirin to moles of salicylic acid, you multiply by the mole ratio:
moles of salicylic acid = moles of aspirin × mole ratio
Finally, you can convert moles of salicylic acid to grams using the molar mass of salicylic acid:
grams of salicylic acid = moles of salicylic acid × molar mass of salicylic acid
Since you know the cost of salicylic acid per kilogram ($21), you can calculate the cost to purchase the required amount of salicylic acid by converting grams to kilograms and multiplying by the cost per kilogram.