Problem 84 - Chemistry The Central Science

Question

A pound of plain \(\mathrm{M\&M}\) candies contains \(96 \mathrm{~g}\) fat, \(320 \mathrm{~g}\) carbohydrate, and 21 g protein. What is the fuel value in \(\mathrm{kJ}\) in a \(42-\mathrm{g}\) (about 1.5 oz ) serving? How many Calories does it provide?

Step-by-Step Solution

Answer

A 42-g serving of plain M&M's provides approximately \(899.4 \mathrm{~kJ}\) and 215 Calories.

Step 1: Calculate the energy provided by fat, carbohydrate, and protein in one pound of M&M's

Each macro has a different energy contribution: Fat has 37 kJ/g, carbohydrates have 17 kJ/g, and protein has 17 kJ/g. So, for one pound of M&M's: Energy from fat = \(96 \mathrm{~g}\) x \(37 \mathrm{~kJ/g}\) = \(3552 \mathrm{~kJ}\) Energy from carbohydrates = \(320 \mathrm{~g}\) x \(17 \mathrm{~kJ/g}\) = \(5440 \mathrm{~kJ}\) Energy from protein = \( 21 \mathrm{~g}\) x \(17 \mathrm{~kJ/g}\) = \(357 \mathrm{~kJ}\) Total energy = Energy from fat + Energy from carbohydrates + Energy from protein Total energy = \(3552 + 5440 + 357 \mathrm{~kJ}\) = \(9349 \mathrm{~kJ}\)

Step 2: Calculate the total energy per gram

To find out the energy provided by one gram of plain M&M's, we need to divide the total energy by the weight of the candy. Total energy per gram = Total energy ÷ Total weight Total energy per gram = \(9349 \mathrm{~kJ}\) ÷ \(437 \mathrm{~g}\) = \(21.40 \mathrm{~kJ/g}\)

Step 3: Calculate the energy in a 42-g serving

Now we can calculate the fuel value in a 42-g serving by multiplying the energy per gram by the serving size. Energy in a 42-g serving = Total energy per gram × Serving size Energy in a 42-g serving = \(21.40 \mathrm{~kJ/g}\) × \(42 \mathrm{~g}\) = \(899.4 \mathrm{~kJ}\)

Step 4: Calculate the energy value in Calories

To convert the energy value to Calories (dietary/caloric), we need to know that 1 Calorie is equal to 4.184 kJ. Energy in a 42-g serving (Calories) = Energy in a 42-g serving (kJ) ÷ 4.184 Energy in a 42-g serving (Calories) = \(899.4 \mathrm{~kJ}\) ÷ 4.184 = 215 Calories So, a 42-g serving of plain M&M’s provides approximately 899.4 kJ and 215 Calories.

Key Concepts

Fuel Value Calculation

Understanding the fuel value of food is akin to assessing the energy that a specific quantity of that food provides when consumed. This concept is crucial for determining caloric intake and managing dietary needs.

Let's begin by considering a real-world example - a serving of M&M candies. The fuel value can be calculated by multiplying the amount of each nutrient (fat, carbohydrates, and protein) in a serving by the energy that each of those nutrients contributes. For instance, fats are generally more energy-dense, with a standard fuel value of approximately 37 kJ/g. Carbohydrates and proteins offer less, about 17 kJ/g each.

To calculate the fuel value for a serving, we would follow these steps:

Energy Content of Nutrients

Fuel values for nutrients are based on the amount of energy they provide, typically measured in kilojoules per gram (kJ/g) or Calories per gram. The three primary macronutrients have standard energy values:

• Fat: 37 kJ/g (about 9 Calories/g)
• Carbohydrates: 17 kJ/g (about 4 Calories/g)
• Protein: 17 kJ/g (also approximately 4 Calories/g)

These values are average estimates and can differ slightly based on the exact composition of a particular food item. In our M&M example, the total energy content is calculated by combining the individual contributions from fats, carbohydrates, and proteins. It is the sum of these components that provides the overall caloric content of the food.

Dietary Calories

In the context of nutrition, Calories (with a capital 'C') refer to kilocalories, which are units used to measure the energy in food. One dietary Calorie is equal to 4.184 kilojoules (kJ). This conversion is vital when reading nutritional information and in calculating energy intake for dietary planning.

When evaluating the calorie content of a serving of M&M's, we convert the measured energy from kilojoules to Calories to align with common dietary standards. This allows individuals to relate the energy content to dietary recommendations and daily calorie allowances.

Remember that counting Calories can help with managing weight and ensuring a balanced diet, but it is also essential to consider the quality and nutritional value of the foods consumed, not just the caloric content.