Problem 82 - Chemistry The Central Science

Question

(a) Why are fats well suited for energy storage in the human body? (b) A particular chip snack food is composed of \(12 \%\) protein, \(14 \%\) fat, and the rest carbohydrate. What percentage of the calorie content of this food is fat? (c) How many grams of protein provide the same fuel value as \(25 \mathrm{~g}\) of fat?

Step-by-Step Solution

Answer

(a) Fats are well-suited for energy storage in the human body because they provide a concentrated and efficient form of energy (9 kcal/g), do not retain water weight, and can be used during fasting or extended physical activity. (b) The chip snack's calorie percentage from fat is approximately \(26.81\%\). (c) \(56.25\, \text{g}\) of protein provides the same fuel value as \(25\, \text{g}\) of fat.

Step 1: (a) Fats as energy storage in the human body

Fats are well suited for energy storage in the human body because they provide a concentrated and efficient form of energy. For each gram of fat, the body can extract 9 kcal of energy, which is more than double the energy provided by the same quantity of protein or carbohydrate. Additionally, fats don't retain water weight, allowing them to store more energy in less space compared to carbohydrates or proteins. This makes fats an efficient energy store that can be used when the body requires additional energy, such as during periods of fasting or extended physical activity.

Step 2: (b) Finding the calorie percentage from fat

Start by identifying the percentage composition of the chip snack: - Protein: \(12\%\) - Fat: \(14\%\) - Carbohydrate: \(100\% - (12\% + 14\%) = 74\%\) Given the calorie values for protein, fat, and carbohydrate, calculate the calorie contribution from each component: - Calories from protein: \(12\% * 4 \, \text{kcal} = 48\, \text{kcal}\) - Calories from fat: \(14\% * 9 \, \text{kcal} = 126\, \text{kcal}\) - Calories from carbohydrate: \(74\% * 4 \, \text{kcal} = 296\, \text{kcal}\) Determine the total calorie count: - Total calories: \(48\, \text{kcal} + 126\, \text{kcal} + 296\, \text{kcal} = 470\, \text{kcal}\) Calculate the calorie percentage from fat: - Calorie percentage from fat: \(\frac{126\, \text{kcal}}{470\, \text{kcal}} * 100\% \approx 26.81\%\) So, about \(26.81\%\) of the calorie content of this food is from fat.

Step 3: (c) Finding the grams of protein with the same fuel value as given grams of fat

We are given that there are \(25 \, \text{g}\) of fat. Calculate the fuel value (calories) of this amount of fat: - Fuel value of fat: \(25\, \text{g} * 9 \, \text{kcal/g} = 225\, \text{kcal}\) Now, calculate the amount of protein that provides the same fuel value (calories): - Grams of protein: \(\frac{225\, \text{kcal}}{4\, \text{kcal/g}} = 56.25\, \text{g}\) Therefore, \(56.25\, \text{g}\) of protein provides the same fuel value as \(25\, \text{g}\) of fat.

Key Concepts

Energy Storage in Fats

Fats play a crucial role in the human body, acting as a dense form of energy storage. The reason why they excel in this function is due to their chemical structure, which is rich in long chains of hydrocarbons that store a large amount of energy. Unlike carbohydrates and proteins, which store only about 4 kilocalories (kcal) of energy per gram, fats can store more than double that amount, with approximately 9 kcal per gram.

This high energy density means that fat reserves can serve as a long-term energy source, ideal for times when food intake is not sufficient to meet the body's energy needs, such as during fasting or sustained exercise. Additionally, because fats do not bind water, they are even more efficient at packing energy into smaller volumes, making them the body's preferred choice for energy storage for these reasons.

Caloric Content of Macronutrients

Understanding the caloric content of macronutrients—proteins, fats, and carbohydrates—is fundamental for comprehending human nutrition. Our bodies break down these macronutrients to meet energy requirements, and each provides a different calorie yield. Specifically, proteins and carbohydrates each provide about 4 kcal per gram, while fats offer 9 kcal per gram, making them the most calorically dense macronutrient.

Given the composition of a chip snack with 12% protein, 14% fat, and 74% carbohydrate, calculating the total calorie content involves multiplying these percentages by their respective caloric values. For instance, the caloric contribution from fats is higher relative to their mass because of their higher kcal per gram value, which results in a calorie percentage of approximately 26.81% from fat in that particular snack.

Comparing Fuel Values of Fats and Proteins

When comparing the fuel values of fats and proteins, it's evident that fats are a more potent source of energy. This is because for every gram consumed, fats yield more than twice the calories of proteins. To illustrate, if we take 25 grams of fat, we get 225 kcal of energy. To achieve the same energy output from proteins, which provide only 4 kcal per gram, a person would need to consume 56.25 grams of protein.

This comparison underscores the efficiency of fat as an energy source and also provides insight into dietary considerations where individuals may be focused on either weight loss or endurance sports. Understanding the differences in fuel values among macronutrients can guide dietary choices aimed at achieving specific health or performance goals.