Dimensional Analysis
Elephant toothpaste Recipe
Consider the following recipe for elephant toothpaste. Use it to help answer the question.
How many milliliters of 3% hydrogen peroxide are needed to make 7 liters of elephant toothpaste solution?
350 mL of 3% hydrogen peroxide
100 milliliters
15 g of dry yeast
15 g of dish soap
236 mL of water
Yields: 2 L elephant toothpaste solution
A. 1,225 milliliters
B. 1,523 milliliters
C. 503 milliliters
Answer (2)
Determine the ratio between the desired volume (7 liters) and the recipe's volume (2 liters): r a t i o = 2 7 = 3.5
Multiply the amount of 3% hydrogen peroxide in the original recipe (350 mL) by the scaling ratio (3.5): 350 m L × 3.5 = 1225 m L
Conclude that 1225 mL of 3% hydrogen peroxide is needed to make 7 liters of elephant toothpaste solution.
The final answer is: 1225 mi ll i l i t ers
Explanation
Understanding the Problem We are given a recipe for elephant toothpaste that yields 2 liters of solution and requires 350 mL of 3% hydrogen peroxide. We need to determine how many milliliters of 3% hydrogen peroxide are needed to make 7 liters of elephant toothpaste solution.
Calculating the Scaling Ratio First, we need to find the ratio between the desired volume (7 liters) and the recipe's volume (2 liters). This ratio will tell us how much to scale up the recipe. The ratio is calculated as: r a t i o = rec i p e v o l u m e d es i re d v o l u m e = 2 l i t ers 7 l i t ers = 3.5 This means we need to scale the recipe by a factor of 3.5 to get 7 liters of elephant toothpaste.
Determining the Required Amount of Hydrogen Peroxide Now, we multiply the amount of 3% hydrogen peroxide in the original recipe (350 mL) by the scaling ratio (3.5) to find the amount of 3% hydrogen peroxide needed for 7 liters of solution: re q u i re d h y d ro g e n p ero x i d e = r a t i o × 350 m L = 3.5 × 350 m L = 1225 m L Therefore, we need 1225 mL of 3% hydrogen peroxide to make 7 liters of elephant toothpaste solution.
Final Answer Therefore, to make 7 liters of elephant toothpaste solution, you will need 1225 mL of 3% hydrogen peroxide.
Examples
This type of problem, involving scaling recipes or mixtures, is commonly used in cooking, chemistry, and manufacturing. For example, if you are baking a cake and want to make a larger cake than the recipe allows, you need to scale up all the ingredients proportionally. Similarly, in chemistry, when preparing solutions of a specific concentration, you may need to adjust the amounts of different chemicals based on the desired volume. In manufacturing, scaling recipes is essential for producing consistent products in different quantities.
To make 7 liters of elephant toothpaste solution, you need 1225 mL of 3% hydrogen peroxide. This is calculated by scaling the original recipe (which uses 350 mL for 2 liters) by a factor of 3.5. Therefore, the answer is 1225 mL.
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