Problem 82 - Chemistry Matter and Change

Question

Popcorn The average mass of a kernel of popcorn is 0.125 g. If 1 pound \(=16\) ounces, and 1 ounce \(=28.3 \mathrm{g},\) then how many kernels of popcorn are there in 0.500 pounds of popcorn?

Step-by-Step Solution

Answer

There are 1,808 kernels of popcorn in 0.500 pounds of popcorn, given 1 pound = 16 ounces, 1 ounce = 28.3 g, and the average mass of a kernel of popcorn is 0.125 g.

Step 1: Convert pounds to grams

First, convert the mass of popcorn from pounds to grams, using the given conversion factors. \[0.500\,\mathrm{pounds} \times \frac{16\,\mathrm{ounces}}{1\,\mathrm{pound}} \times \frac{28.3\,\mathrm{g}}{1\,\mathrm{ounce}}\]

Step 2: Calculate the mass in grams

Now, calculate the value. \[0.500 \times 16 \times 28.3 = 226\,\mathrm{g}\] So, the mass of popcorn is 226 g.

Step 3: Calculate the number of kernels

Finally, divide the total mass of popcorn by the average mass of one kernel to find out the number of kernels. \[\frac{226\,\mathrm{g}}{0.125\,\mathrm{g / kernel}}\]

Step 4: Find the result

Calculate the value. \[\frac{226}{0.125} = 1,808\] Hence, there are 1,808 kernels of popcorn in 0.500 pounds of popcorn.

Key Concepts

Understanding Mass Calculations

Mass calculations in chemistry often involve converting units to solve problems related to weight and mass. In the popcorn problem, we begin with a mass given in pounds, a unit commonly used in the U.S., and need to convert it into grams, a standard metric unit. To perform these calculations correctly, we need to understand the concept of mass and how different units of mass relate to each other.

In this problem, it is essential to recognize the given relationship: 1 pound is equal to 16 ounces, and 1 ounce is equal to 28.3 grams. Using these relationships, we can convert our starting mass from pounds to grams by multiplying successively by each conversion factor. This ensures that we maintain the correct dimensionality, ultimately arriving at a result in grams, which is more convenient for calculations involving smaller masses, like that of popcorn kernels.

When dividing the total mass of popcorn in grams by the mass of one kernel in grams, we find the number of kernels. This is a standard method in mass calculations: find the total mass and divide by the unit mass for one object.

Approach to Problem-Solving in Chemistry

Problem-solving in chemistry often requires breaking down a problem into smaller, manageable steps. The popcorn exercise demonstrates this beautifully by using tiered conversions to solve the problem.

The initial step is to clearly understand what the problem asks: finding the number of popcorn kernels in a given mass. With this in mind, the next step is to identify the necessary conversions and calculations to perform.

• First, convert the given mass quantity into a more usable form (pounds to grams).
• Then calculate the value given by these conversions.
• Finally, use a simple division to find the desired quantity, which is the number of kernels.

By solving chemistry problems methodically, students learn to grasp complex concepts through simpler individual operations. Each step not only progresses the solution but also helps cement the understanding of the scientific method and logical reasoning used in chemistry.

The Role of Mathematical Conversions

Mathematical conversions are crucial for problem-solving in chemistry because they allow scientists and students to express measurements in different units, facilitating easier comparisons and calculations.

In the context of the popcorn problem, mathematical conversions transformed the mass from one set of units (pounds) to another (grams). Here’s how this works:

• Identify the starting unit (pounds in this case) and determine the chain of conversions needed to reach the desired unit.
• Apply the conversion factors one at a time, ensuring units cancel out correctly, leaving the desired unit for the mass.
• Perform arithmetic operations carefully, as precision in calculations is essential in chemistry.

These conversions help in translating the real-world measurements into a form that can be used in scientific analysis. This skill is indispensable for students as it builds their ability to approach a wide range of chemistry problems, ensuring they can find solutions regardless of the units in which data is presented.