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?

Short answer

(a) Fats are well suited for energy storage in the human body because they provide a concentrated source of energy (9 kcal/gm) and can be efficiently stored without adding excessive weight and volume. They also serve as insulation and protection for internal organs. (b) The percentage of calorie content from fat in the snack food is approximately \(26.81\%\). (c) 56.25 grams of protein provide the same fuel value as 25 grams of fat.

Step-by-step solution

(a) Importance of Fats for Energy Storage in the Human Body

Fats are essential for energy storage in the human body because they provide a concentrated source of energy. They contain more than twice the amount of energy per gram than proteins and carbohydrates, at approximately 9 kcal/gm for fats, while 4 kcal/gm for both proteins and carbohydrates. This high-energy density makes fats an efficient way to store energy without adding excessive weight and volume to our bodies. Additionally, our body can store fat in specialized cells called adipocytes, which help to serve as insulation and protection for our internal organs.

(b) Calculating the Caloric Content from Fat in a Snack Food

The percentage composition of the snack food is given as: Protein: \(12\%\) Fat: \(14\%\) Carbohydrate: \(100\% - (12\% + 14\%) = 74\%\) Now let's assume the total weight of the snack is 100g. Then, we have: Protein weight: \(12g\) Fat weight: \(14g\) Carbohydrate weight: \(74g\) We will convert these weights to calories using kcals per gram: Protein: \(12g * 4 kcal/g = 48 kcal\) Fat: \(14g * 9 kcal/g = 126 kcal\) Carbohydrate: \(74g * 4 kcal/g = 296 kcal\) Total caloric content: \(48 kcal + 126 kcal + 296 kcal = 470 kcal\) Now, we can find the percentage of calorie content from fat: \[\% \text{ of Calorie Content from Fat} = (\frac{\text{Calorie Content from Fat}}{\text{Total Caloric Content}})*100\%\] \[\% \text{ of Calorie Content from Fat} = (\frac{126 kcal}{470 kcal}) * 100\% \approx 26.81\%\]

(c) Finding the Equivalent Fuel Value in Protein for 25g of Fat

We are given that 25g of fat has a certain fuel value, and we need to find the amount of protein that provides the same fuel value. Fat fuel value: \(25g * 9 kcal/g = 225 kcal\) To find the equivalent fuel value in protein, we will use the kcal per gram of protein (4 kcal/g) and solve for the protein mass: \( Protein Mass (g) * 4 kcal/g = 225 kcal \) \( Protein Mass (g) = \frac{225 kcal}{4 kcal/g} = 56.25g \) Thus, 56.25 grams of protein provide the same fuel value as 25 grams of fat.