Problem 80 - 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 highly concentrated source of energy (9 kcal/g), allowing for efficient energy storage in a smaller space and with less weight. The body can also store fat in adipose tissue without any limit. (b) The percentage of calorie content from fat in the chip snack food is: \( \frac{14 \times 9}{(12 \times 4) + (14 \times 9) + (74 \times 4)}\times 100 \approx 49.66 \% \) (c) The grams of protein equivalent to 25 grams of fat is: \( \frac{25 \times 9}{4} \approx 56.25 \, \text{grams}\)

Step 1: Understanding the role of fats in energy storage

Fats are a highly concentrated source of energy, containing 9 kcal of energy per gram, which is more than double the energy content of protein and carbohydrates (4 kcal per gram). This allows the body to store more energy in a smaller space and with less weight, making fat an efficient energy storage solution. Moreover, the body can store fat in adipose tissue without any limit, unlike carbohydrates storage.

Step 2: Finding the percentage of calorie content that comes from fat

We are given the composition of a chip snack food, containing 12% protein, 14% fat, and the remaining carbohydrate. Since we know the energy content of each macronutrient, we can calculate the calorie content from each and then find the percentage from fat. Calories from protein (per 100 grams) = 12 (percentage) × 4 (kcal/g) Calories from fat (per 100 grams) = 14 (percentage) × 9 (kcal/g) Calories from carbohydrates (per 100 grams) = (100 - 12 - 14) (percentage) × 4 (kcal/g) Now, we can calculate the total calorie content from each macronutrient: Total calories = Calories from protein + Calories from fat + Calories from carbohydrates The percentage of calorie content from fat is: Percentage of calories from fat = (Calories from fat / Total calories) × 100

Step 3: Calculating the grams of protein equivalent to 25 grams of fat

We are given that 25 grams of fat provides a certain fuel value. We need to find out how many grams of protein provide the same fuel value, using the fact that 1 gram of fat provides 9 kcal, and 1 gram of protein provides 4 kcal. Fuel value of 25 grams of fat = 25 (grams) × 9 (kcal/g) To find the grams of protein required to provide the same fuel value: Grams of protein = Fuel value of 25 grams of fat / 4 (kcal/g) Now we can calculate the answers for step 2 and step 3.