Answer: After analyzing all the cases, it seems that there is no way to adjust the quantities of water, sugar, and lemon juice to avoid leftover ingredients while still maintaining the original ratio given in the recipe.
Step-by-step explanation:
To reduce the amount of leftover ingredients in the Just Lemons Lemonade recipe, we can adjust the amounts of water, sugar, and lemon juice. Let's calculate the new quantities based on the given information and stoichiometry.
Given:
Water = 946.36 g
Sugar = 196.86 g
Lemon Juice = 193.37 g
Lemonade = 719.84 g
The original recipe equation is:
2 water + sugar + lemon juice = 4 lemonade
To calculate the mole ratios, we need to convert the masses of each ingredient to moles.
Molar mass of water (H2O) = 18.015 g/mol
Molar mass of sugar (C12H22O11) = 342.30 g/mol
Molar mass of lemon juice (C6H8O7) = 192.13 g/mol
Molar mass of lemonade = 719.84 g/mol
Number of moles:
Moles of water = 946.36 g / 18.015 g/mol = 52.55 mol
Moles of sugar = 196.86 g / 342.30 g/mol = 0.575 mol
Moles of lemon juice = 193.37 g / 192.13 g/mol = 1.006 mol
Moles of lemonade = 719.84 g / 719.84 g/mol = 1 mol
Now, let's adjust the quantities to reduce the leftover ingredients. We'll start by keeping the amount of lemonade constant (1 mole or 719.84 g) and adjusting the other ingredients.
Case 1: Adjusting water
Assume x moles of water.
From the equation, we have:
2 water + sugar + lemon juice = 4 lemonade
Substituting the known quantities:
2x + 0.575 mol + 1.006 mol = 1 mol
Rearranging the equation:
2x = 1 mol - 0.575 mol - 1.006 mol
2x = -0.581 mol
This equation has a negative value, which is not physically possible. Therefore, adjusting only the amount of water won't work.
Case 2: Adjusting sugar
Assume y moles of sugar.
Using the equation:
2 water + sugar + lemon juice = 4 lemonade
Substituting the known quantities:
2(52.55 mol) + y mol + 1.006 mol = 1 mol
Rearranging the equation:
y = 1 mol - 2(52.55 mol) - 1.006 mol
y = -106.1 mol
Again, we obtain a negative value, which is not possible. Adjusting only the amount of sugar won't work either.
Case 3: Adjusting lemon juice
Assume z moles of lemon juice.
Using the equation:
2 water + sugar + lemon juice = 4 lemonade
Substituting the known quantities:
2(52.55 mol) + 0.575 mol + z mol = 1 mol
Rearranging the equation:
z = 1 mol - 2(52.55 mol) - 0.575 mol
z = -101.1 mol
Once again, we obtain a negative value, which is not possible. Adjusting only the amount of lemon juice won't work.