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Chapter 5: Problem 84

A pound of plain \(\mathrm{M\&M}\) candies contains \(96 \mathrm{~g}\) fat, \(320 \mathrm{~g}\) carbohydrate, and 21 g protein. What is the fuel value in \(\mathrm{kJ}\) in a \(42-\mathrm{g}\) (about 1.5 oz ) serving? How many Calories does it provide?

Short Answer

Expert verified
A 42-g serving of plain M&M's provides approximately \(899.4 \mathrm{~kJ}\) and 215 Calories.

Step by step solution

01

Calculate the energy provided by fat, carbohydrate, and protein in one pound of M&M's

Each macro has a different energy contribution: Fat has 37 kJ/g, carbohydrates have 17 kJ/g, and protein has 17 kJ/g. So, for one pound of M&M's: Energy from fat = \(96 \mathrm{~g}\) x \(37 \mathrm{~kJ/g}\) = \(3552 \mathrm{~kJ}\) Energy from carbohydrates = \(320 \mathrm{~g}\) x \(17 \mathrm{~kJ/g}\) = \(5440 \mathrm{~kJ}\) Energy from protein = \( 21 \mathrm{~g}\) x \(17 \mathrm{~kJ/g}\) = \(357 \mathrm{~kJ}\) Total energy = Energy from fat + Energy from carbohydrates + Energy from protein Total energy = \(3552 + 5440 + 357 \mathrm{~kJ}\) = \(9349 \mathrm{~kJ}\)
02

Calculate the total energy per gram

To find out the energy provided by one gram of plain M&M's, we need to divide the total energy by the weight of the candy. Total energy per gram = Total energy ÷ Total weight Total energy per gram = \(9349 \mathrm{~kJ}\) ÷ \(437 \mathrm{~g}\) = \(21.40 \mathrm{~kJ/g}\)
03

Calculate the energy in a 42-g serving

Now we can calculate the fuel value in a 42-g serving by multiplying the energy per gram by the serving size. Energy in a 42-g serving = Total energy per gram × Serving size Energy in a 42-g serving = \(21.40 \mathrm{~kJ/g}\) × \(42 \mathrm{~g}\) = \(899.4 \mathrm{~kJ}\)
04

Calculate the energy value in Calories

To convert the energy value to Calories (dietary/caloric), we need to know that 1 Calorie is equal to 4.184 kJ. Energy in a 42-g serving (Calories) = Energy in a 42-g serving (kJ) ÷ 4.184 Energy in a 42-g serving (Calories) = \(899.4 \mathrm{~kJ}\) ÷ 4.184 = 215 Calories So, a 42-g serving of plain M&M’s provides approximately 899.4 kJ and 215 Calories.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fuel Value Calculation
Understanding the fuel value of food is akin to assessing the energy that a specific quantity of that food provides when consumed. This concept is crucial for determining caloric intake and managing dietary needs.

Let's begin by considering a real-world example - a serving of M&M candies. The fuel value can be calculated by multiplying the amount of each nutrient (fat, carbohydrates, and protein) in a serving by the energy that each of those nutrients contributes. For instance, fats are generally more energy-dense, with a standard fuel value of approximately 37 kJ/g. Carbohydrates and proteins offer less, about 17 kJ/g each.

To calculate the fuel value for a serving, we would follow these steps:
Energy Content of Nutrients
Fuel values for nutrients are based on the amount of energy they provide, typically measured in kilojoules per gram (kJ/g) or Calories per gram. The three primary macronutrients have standard energy values:
  • Fat: 37 kJ/g (about 9 Calories/g)
  • Carbohydrates: 17 kJ/g (about 4 Calories/g)
  • Protein: 17 kJ/g (also approximately 4 Calories/g)
These values are average estimates and can differ slightly based on the exact composition of a particular food item. In our M&M example, the total energy content is calculated by combining the individual contributions from fats, carbohydrates, and proteins. It is the sum of these components that provides the overall caloric content of the food.
Dietary Calories
In the context of nutrition, Calories (with a capital 'C') refer to kilocalories, which are units used to measure the energy in food. One dietary Calorie is equal to 4.184 kilojoules (kJ). This conversion is vital when reading nutritional information and in calculating energy intake for dietary planning.

When evaluating the calorie content of a serving of M&M's, we convert the measured energy from kilojoules to Calories to align with common dietary standards. This allows individuals to relate the energy content to dietary recommendations and daily calorie allowances.

Remember that counting Calories can help with managing weight and ensuring a balanced diet, but it is also essential to consider the quality and nutritional value of the foods consumed, not just the caloric content.

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Most popular questions from this chapter

The decomposition of slaked lime, \(\mathrm{Ca}(\mathrm{OH})_{2}(s),\) into lime, \(\mathrm{CaO}(s),\) and \(\mathrm{H}_{2} \mathrm{O}(g)\) at constant pressure requires the addition of \(109 \mathrm{~kJ}\) of heat per mole of \(\mathrm{Ca}(\mathrm{OH})_{2}\). (a) Write a balanced thermochemical equation for the reaction. (b) Draw an enthalpy diagram for the reaction.

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing \(0.655 \mathrm{~kJ}\) of heat. It shrinks on cooling, and the atmosphere does \(382 \mathrm{~J}\) of work on the balloon. (b) A 100.0 -g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50{ }^{\circ} \mathrm{C}\) during which it absorbs \(322 \mathrm{~J}\) of heat. Assume the volume of the gold bar remains constant. (c) The surroundings do \(1.44 \mathrm{~kJ}\) of work compressing gas in a perfectly insulated cylinder.

Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not? (c) Can you determine the value of \(\Delta E\) for the process?

You are given \(\Delta H\) for a process that occurs at constant pressure. What additional information do you need to determine \(\Delta E\) for the process?

At the end of 2009 , global population was about 6.8 billion people. What mass of glucose in kg would be needed to provide 1500 Cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) according to the following thermochemical equation: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) \(\Delta H^{\mathrm{o}}=-2803 \mathrm{~kJ}\)
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