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 more than twice the amount of energy per gram compared to proteins and carbohydrates (9 Calories/gram for fats vs. 4 Calories/gram for proteins and carbohydrates). This allows the body to store more energy in a smaller amount of space. (b) 26.81% of the calorie content in the chip snack food is from fat. (c) 56.25 grams of protein provide the same fuel value as 25 grams of fat.

Step 1: (a) Explanation for energy storage suitability for fats in the human body

Fats are well suited for energy storage in the human body because they provide more than twice the amount of energy per gram compared to proteins and carbohydrates. With 9 Calories per gram of fat, the human body can store more energy in a smaller amount of space, which is essential for maintaining body functions, warmth, and activity levels when food is scarce.

Step 2: (b) The percentage of calorie content from fat

We know that the chip snack food is composed of 12% protein, 14% fat, and the rest carbohydrate, which implies the carbohydrate content is 100% - 12% - 14% = 74%. The calorie content for each component per gram is as follows: - Protein: 4 Calories per gram - Carbohydrate: 4 Calories per gram - Fat: 9 Calories per gram To find the percentage of overall calorie content from fat, we follow these steps: 1. Calculate Calories from each gram of protein, carbohydrate, and fat. 2. Calculate the total Calories. 3. Calculate the percentage of Calories from fat. To maintain uniformity, let's assume the chip snack food weighs 100 grams. Therefore, the amounts are: - Protein: 12 grams - Carbohydrate: 74 grams - Fat: 14 grams

Step 3: Calculate Calories from each component

Protein: \(12\text{ g} \times 4\text{ Calories/g} = 48\text{ Calories}\) Carbohydrate: \(74\text{ g} \times 4\text{ Calories/g} = 296\text{ Calories}\) Fat: \(14\text{ g} \times 9\text{ Calories/g} = 126\text{ Calories}\)

Step 4: Calculate total Calories

Total Calories: \(48\text{ Calories (protein)} + 296\text{ Calories (carbohydrate)} + 126\text{ Calories (fat)} = 470\text{ Calories}\)

Step 5: Calculate percentage of Calories from fat

Percentage of Calories from fat: \(\frac{126\text{ Calories (fat)}}{470\text{ Calories (total)}} \times 100\% = 26.81\% \) Thus, 26.81% of the calorie content in this chip snack food is from fat.

Step 6: (c) Grams of protein providing the same fuel value as 25g of fat

We are given that 25 grams of fat provide a certain amount of energy, and we need to find how many grams of protein would provide the same amount of energy. First, we'll find the energy provided by 25 grams of fat.

Step 7: Calculate energy from 25 grams of fat

Energy from 25 grams of fat: \(25\text{ g} \times 9\text{ Calories/g} = 225\text{ Calories}\) Now we'll find the amount of protein (in grams) needed to provide this amount of energy.

Step 8: Calculate grams of protein for the same energy

Let's denote the grams of protein as \(x\): \(x\text{ g (protein)} \times 4\text{ Calories/g}\ = 225\text{ Calories}\) Now, we'll solve for \(x\): \(x = \frac{225\text{ Calories}}{4\text{ Calories/g}} = 56.25\text{ g}\) Therefore, 56.25 grams of protein provide the same fuel value as 25 grams of fat.