I am very confused with this problem, i tried using the percent yeild but i got stuck. Can u help?
The O'Keefe's have 75 gallons of cucumbers for pickling. The 1.5 M KOH
solution costs $3.50 per liter, 9 M H2SO4 solution costs $8 per liter, and ethanol
costs $20 per liter. A 50 g jar of alum from the grocery store costs $5.79. Do you
think it’s worth the time and trouble for Richard and Diane to make their own
alum from discarded aluminum cans? Explain your answer showing all
calculations.
This info was attached as well
O’Keefe’s Farm Fresh Pickles
Take 2 gallons washed/chunked pickling cucumbers. Place in a crock or other
large non-aluminum container. Measure enough water to cover the cucumbers, then add 1
pint of pickling salt to water, then bring the water to a boil. Finally, pour boiling brine
(salt water) over the cucumbers. Then weigh cucumbers down with a plate so that they
stay submerged under the brine. Allow this to stand for 1 week.
After 1 week, drain the pickles and discard the brine. Cover pickles with fresh
boiling water and let stand for 24 hours.
Drain, but save the liquid. Add a walnut sized piece of alum (6 grams) to the
liquid. Bring to a boil and then pour over the pickles. Let stand for 24 hours. Note: you
can omit the alum if you wish, but alum does help to keep the pickles crisp.
After 24 hours, drain the liquid and discard it. Boil together 6 pints of vinegar, 2
pints water, 2oz of mustard seed, 4 cups of sugar, 5 oz of cinnamon sticks, 1 oz whole
allspice. Add to pickles through a strainer. Let stand 24 hours.
Bring to boiling point, but do not boil. Wash jars clean and keep hot until needed.
Prepare lids as manufacturer directs. Pack pickles into hot clean jar leaving 1/2 inch of
headspace. Wipe rim with clean damp cloth and seal. Continue until all jars are sealed.
Process in a boiling bath for 10 min.
To determine if it's worth it for Richard and Diane to make their own alum from discarded aluminum cans, we need to compare the cost of making alum to the cost of buying it directly from the store.
To make alum, we would need some specific chemicals: 1.5 M KOH solution, 9 M H2SO4 solution, and ethanol.
Let's break down the process step by step:
1. Calculate the cost of the chemicals needed to make 1 mole of alum.
- The molar mass of alum (AlK(SO4)2) is approximately 474.39 g/mol.
- From the formula, we can see that we need 2 moles of KOH and 1 mole of H2SO4 to make 1 mole of alum.
- The cost of 1 mole of KOH can be calculated by multiplying the cost per liter (given as $3.50) by the molarity (1.5 mol/L) and dividing the result by the molar mass of KOH.
- Similarly, calculate the cost of 1 mole of H2SO4 using the given price ($8 per liter) and molarity (9 mol/L) divided by the molar mass of H2SO4.
- Add the cost of the KOH and H2SO4 to get the total cost of the chemicals needed.
2. Calculate the amount of chemicals needed to make alum from the given amount of cucumbers.
- Assume that 75 gallons of cucumbers are converted into 75 x (3.78541 L/gal) = X liters.
- Use the balanced chemical equation for alum synthesis to determine the stoichiometry between cucumbers and the required chemicals.
- From the equation, we can see that we need 6 moles of KOH and 1 mole of H2SO4 per mole of cucumbers.
- Multiply the moles of KOH and H2SO4 per mole of cucumbers by the amount of cucumbers (in moles) to get the total amount of each chemical needed.
3. Calculate the cost of the chemicals needed based on the amount required.
- Multiply the cost computed in step 1 by the respective moles of KOH and H2SO4 calculated in step 2.
4. Add the cost of the chemicals required to make the alum from discarded aluminum cans.
- In addition to KOH and H2SO4, we also need ethanol, which costs $20 per liter.
- Calculate the cost of ethanol based on the amount required to make the alum, similar to step 3.
5. Compare the total cost of chemicals needed to make the alum with the cost of buying a jar of alum from the store ($5.79).
- If the cost of making the alum is higher, it may not be worth the time and effort.
- If the cost is lower, it might be worth considering making the alum from discarded aluminum cans.
By following these steps and performing the calculations, you can determine whether it is worth it for Richard and Diane to make their own alum or buy it from the store.