Question

Cookie stoichiometry performing a chemical reaction is just like cooking or baking. You combine ingredients in order to make a new thing. We are going to practice our reading recipe skills in hopes that this will help you better understand the concept of stoichiometry (using relationships between compounds involved in a chemical reaction). Below you will find a recipe for baking sugar cookies. Answer the questions that follow about the recipe.

a) If you have 5.5 cups flour, 2 cups butter, 3 cups sugar, 2 eggs, and an unlimited supply of baking soda and powder, how many cookies can you make?
b) If you want to make 120 cookies, how much of each ingredient will you need?
c) If you have 9 cups flour, 5 cups butter, 4.5 cups sugar, 8 eggs, and an excess of baking soda and powder, how many cookies can you make? Besides baking soda and powder, how much of each ingredient will be left over?

Answer 1

To calculate the number of cookies made and the leftover ingredients, you need to identify the limiting reactant. In this case, the limiting reactant differs for each scenario, and the calculations are based on the ratios provided in the recipe. For question (a), the limiting reactant is butter, resulting in 32 cookies. For question (b), the recipe needs to be scaled up to make 120 cookies. And for question (c), the limiting reactant is flour, resulting in 72 cookies. The leftover amounts of each ingredient can also be calculated.

Step-by-step explanation:

To calculate the number of cookies you can make, you need to determine the limiting reactant. This is the ingredient that will run out first and limit the number of cookies you can produce. In this case, let's consider the limiting reactant to be the ingredient that requires the smallest amount to make a single cookie. From the recipe, we can see that 1 cup of flour, 1/2 cup of butter, 1/2 cup of sugar, and 1/4 egg are needed for 8 cookies. Using these ratios, we can determine the number of cookies that can be made with the given amounts:

a) For 5.5 cups of flour, you can make (5.5/1) x 8 = 44 cookies. For 2 cups of butter, you can make (2/0.5) x 8 = 32 cookies. For 3 cups of sugar, you can make (3/0.5) x 8 = 48 cookies. And for 2 eggs, you can make (2/0.25) x 8 = 64 cookies. Since you can only make the smallest number of cookies (32), the limiting reactant is butter and you can make 32 cookies.

b) To make 120 cookies, you need to scale up the recipe. Using the ratio of 8 cookies to the amounts of each ingredient, you can calculate the new amounts needed:

- Flour: (120/8) x 1 = 15 cups

- Butter: (120/8) x 0.5 = 7.5 cups

- Sugar: (120/8) x 0.5 = 7.5 cups

- Eggs: (120/8) x 0.25 = 3.75 eggs (rounded to 4 eggs)

c) For 9 cups of flour, you can make (9/1) x 8 = 72 cookies. For 5 cups of butter, you can make (5/0.5) x 8 = 80 cookies. For 4.5 cups of sugar, you can make (4.5/0.5) x 8 = 72 cookies. And for 8 eggs, you can make (8/0.25) x 8 = 256 cookies. Since you can only make the smallest number of cookies (72), the limiting reactant is flour and you can make 72 cookies.

For the leftover ingredients:

- For question a), you will have 5.5 - (1 x 32/8) = 2.5 cups of flour, 2 - (0.5 x 32/8) = 0 cups of butter, 3 - (0.5 x 32/8) = 1.5 cups of sugar, and 2 - (0.25 x 32/8) = 1 egg.

- For question c), you will have 9 - (1 x 72/8) = 1 cup of flour, 5 - (0.5 x 72/8) = 1 cup of butter, 4.5 - (0.5 x 72/8) = 1 cup of sugar, and 8 - (0.25 x 72/8) = 5 eggs.