How do I do this chemistry quick lab on limiting reactants?

An original cookie recipe with the following ingredients yields 24 cookies:

  • 1/2 cup sugar
  • 1/2 cup brown sugar
  • 1 1/3 stick margarine (at room temperature)
  • 1 egg
  • 1/2 tsp. salt
  • 1 tsp. vanilla
  • 1/2 tsp. baking soda
  • 1 1/2 cup flour
  • 1 1/3 cup chocolate chips

Suppose you are given the following amounts of ingredients:

  • 1 dozen eggs
  • 24 tsp. of vanilla
  • 1 lb. (82 tsp.) of salt
  • 1 lb. (84 tsp.) of baking soda
  • 3 cups of chocolate chips
  • 5 lb. (11 cups) of sugar
  • 2 lb. (4 cups) of brown sugar
  • 1 lb. (4 sticks) of margarine

a. For each ingredient, calculate how many cookies could be prepared if all of that ingredient were consumed. (For example, the recipe shows that using 1 egg—with the right amounts of the other ingredients—yields 24 cookies. How many cookies can you make if the recipe is increased proportionately for 12 eggs?)

b. To determine the limiting reactant for the new ingredients list, identify which ingredient will result in the fewest number of cookies.

c. What is the maximum number of cookies that can be produced from the new amounts of ingredients?

1 Answer
Jun 10, 2018

Answer:

Here's what I get.

Explanation:

a. Cookies from proportional increase

What is the "theoretical yield" of cookies from each of the "reactants?"

  • #"Theor. yield from eggs" = 12 color(red)(cancel(color(black)("eggs"))) × "24 cookies"/(1 color(red)(cancel(color(black)("egg")))) = "288 cookies"#
  • #"Theor. yield from vanilla" = 24 color(red)(cancel(color(black)("tsp vanilla"))) × "24 cookies"/(1 color(red)(cancel(color(black)("tsp vanilla")))) = "576 cookies"#
  • #"Theor. yield from salt" = 82 color(red)(cancel(color(black)("tsp salt"))) × "24 cookies"/(0.5 color(red)(cancel(color(black)("tsp salt")))) = "3936 cookies"#
  • #"Theor. yield from baking soda"#

#= 84 color(red)(cancel(color(black)("tsp baking soda"))) × "24 cookies"/(0.5 color(red)(cancel(color(black)("tsp baking soda")))) = "4032 cookies"#

  • #"Theor. yield from chocolate chips"#

#= 3 color(red)(cancel(color(black)("cups chocolate chips"))) × "24 cookies"/(1.333 color(red)(cancel(color(black)("cups chocolate chips")))) = "54 cookies"#

  • #"Theor. yield from sugar" = 11 color(red)(cancel(color(black)("cups sugar"))) × "24 cookies"/(0.5 color(red)(cancel(color(black)("cup sugar")))) = "528 cookies"#
  • #"Theor. yield from brown sugar"#

#= 4 color(red)(cancel(color(black)("cups brown sugar"))) × "24 cookies"/(0.5 color(red)(cancel(color(black)("cup brown sugar")))) = "192 cookies"#

Finally, "we leave it as an exercise for the student" to calculate that

  • #"Theor. yield from margarine = 72 cookies"#

b. Identify the limiting reactant

The limiting reactant is the amount of chocolate chips because they can produce the smallest amount of cookies.

c. Determine the theoretical yield

The theoretical yield is 54 cookies, because that is all you can get from the chocolate chips provided.

Here's a video that uses a more straightforward example of making grilled cheese sandwiches.