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Try to reduce the amount of leftover ingredients by changing the amount of one, two, or all three starting ingredients. Show your stoichiometric calculations below.

Just Lemons Lemonade Recipe Equation:


2 water + sugar + lemon juice = 4 lemonade




Mole conversion factors:


1 mole of water = 1 cup = 236. 59 g


1 mole of sugar = 1 cup = 198 g


1 mole of lemon juice = 1 cup = 229. 96 g


1 mole of lemonade = 1 cup = 225. 285 g



Water = 946. 36 g


Sugar = 196. 86 g


Lemon Juice = 193. 37 g


Lemonade = 719. 84 g

User Krojew
by
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1 Answer

5 votes

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.

User Sumskyi
by
9.0k points