Problem 83 - Chemistry: The Central Science

Question

(a) A serving of a particular ready-to-serve chicken noodle soup contains \(2.5 \mathrm{~g}\) fat, \(14 \mathrm{~g}\) carbohydrate, and \(7 \mathrm{~g}\) protein. Estimate the number of Calories in a serving. (b) According to its nutrition label, the same soup also contains \(690 \mathrm{mg}\) of sodium. Do you think the sodium contributes to the caloric content of the soup?

Step-by-Step Solution

Answer

A serving of the ready-to-serve chicken noodle soup contains approximately 106.5 Calories, calculated by considering the caloric values of fats (9 Calories/gram), carbohydrates (4 Calories/gram), and proteins (4 Calories/gram) present in the soup. The sodium content in the soup does not contribute to the caloric content as sodium is a mineral without caloric value.

Step 1: Identify caloric values of fat, carbohydrate, and protein

We can estimate the total calories in a serving of the soup by knowing the caloric values of each macronutrient. Fat, carbohydrate, and protein have the following caloric values per gram (rounded to whole numbers for simplicity): 1. Fat: 9 calories per gram 2. Carbohydrate: 4 calories per gram 3. Protein: 4 calories per gram

Step 2: Calculate the caloric contribution of fat, carbohydrate, and protein

Using the caloric values per gram established in Step 1, we will multiply the grams of each macronutrient in the soup by their corresponding caloric values to find the caloric contribution of each. 1. Fat: \(2.5 \mathrm{~g} \times 9\ \dfrac{\mathrm{calories}}{\mathrm{gram}} = 22.5 \ \mathrm{calories}\) 2. Carbohydrate: \(14 \mathrm{~g} \times 4\ \dfrac{\mathrm{calories}}{\mathrm{gram}} = 56 \ \mathrm{calories}\) 3. Protein: \(7 \mathrm{~g} \times 4\ \dfrac{\mathrm{calories}}{\mathrm{gram}} = 28 \ \mathrm{calories}\)

Step 3: Calculate total calories in a serving of soup

Add the caloric contribution of fat, carbohydrate, and protein to find the total calories in a serving of the soup. Total Calories = Fat Calories + Carbohydrate Calories + Protein Calories Total Calories = \(22.5 \ \mathrm{calories} + 56 \ \mathrm{calories} + 28 \ \mathrm{calories} = 106.5 \ \mathrm{calories}\) The estimated total calories in a serving of chicken noodle soup are approximately 106.5 Calories.

Step 4: Determine if sodium contributes to the caloric content of the soup

Sodium is a mineral and does not provide calories. Therefore, the sodium content in the soup does not contribute to the caloric content. In conclusion, a serving of the ready-to-serve chicken noodle soup contains approximately 106.5 Calories. The sodium content in the soup does not contribute to the caloric content.