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Chapter 6: Problem 5

One food product has an energy content of 170 kcal per serving and another has \(280 \mathrm{kJ}\) per serving. Which food has a greater energy content per serving?

Short Answer

Expert verified
The first food product (170 kcal per serving) has a greater energy content.

Step by step solution

01

Understand the Problem

We need to compare the energy content in calories (kcal) of two food products, one with 170 kcal per serving and the other with 280 kJ per serving.
02

Convert Kilojoules to Kilocalories

To compare the energy content directly, we first need to convert the energy content given in kilojoules (kJ) into kilocalories (kcal). Use the conversion factor: 1 kcal = 4.184 kJ. Divide the kilojoules by 4.184 to get kilocalories.\[ \text{Energy in kcal} = \frac{280 \text{ kJ}}{4.184} \approx 66.92 \text{ kcal} \]
03

Compare the Energy Contents

Now, compare the two energy contents: 170 kcal and approximately 66.92 kcal. The food product with 170 kcal clearly has a higher energy content than the one with approximately 66.92 kcal.

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Key Concepts

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

Energy Content Comparison
In the world of nutrition, understanding the energy content of food is crucial. It helps you make informed choices based on your dietary needs. Energy content measures how much energy your body can gain from consuming a particular food. Typically, it's expressed in kilocalories (kcal) or kilojoules (kJ). Here's why comparing energy content is essential:
  • If you're watching your weight, you might opt for lower energy foods to help manage your intake.
  • For athletes or active individuals, choosing higher energy foods ensures they have enough fuel for activity.
So, when comparing two foods, like in our example with 170 kcal and 280 kJ per serving, converting the units into the same measurement is crucial. Only then can you accurately determine which has the higher energy content.
Kilojoules to Kilocalories Conversion
Understanding how to convert kilojoules to kilocalories is a handy skill. Different countries and products might use one unit over the other, so knowing the conversion can help you better understand food labels. The conversion factor you need is:
  • 1 kilocalorie (kcal) equals 4.184 kilojoules (kJ).
To perform the conversion, divide the kilojoule number by 4.184. For instance, if a food item provides 280 kJ per serving, you calculate:\[\text{Energy in kcal} = \frac{280 \text{ kJ}}{4.184} \approx 66.92 \text{ kcal}\]This converted value allows you to easily compare it to another product listed in kilocalories. This step is vital for understanding energy content from different food products.
Calorimetry in Chemistry
Calorimetry is a fascinating field in chemistry that focuses on measuring the amount of heat released or absorbed during a chemical reaction. While it sounds technical, it's the base of understanding energy content in food. Here's how it works:
  • A calorimeter, the tool for this process, measures the heat flow during reactions.
  • In food, calorimetry results help calculate the calories or energy available.
Why does this matter? Because knowing the energy contributed by food components like carbohydrates, proteins, and fats helps you grasp nutritional content. With accurate calorimetry data, nutritional labels can provide energy content in kcal or kJ, ensuring better dietary decisions.

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Most popular questions from this chapter

Nitrogen monoxide, a gas recently found to be involved in a wide range of biological processes, reacts with oxygen to give brown \(\mathrm{NO}_{2}\) gas. $$2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-114.1 \mathrm{kJ}$$ Is this reaction endothermic or exothermic? If \(1.25 \mathrm{g}\) of NO is converted completely to \(\mathrm{NO}_{2}\), what quantity of heat is absorbed or evolved?

Adding \(5.44 \mathrm{g}\) of \(\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s})\) to \(150.0 \mathrm{g}\) of water in a coffee-cup calorimeter (with stirring to dissolve the salt) resulted in a decrease in temperature from \(18.6^{\circ} \mathrm{C}\) to \(16.2^{\circ} \mathrm{C} .\) Calculate the enthalpy change for dissolving \(\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s})\) in water, in \(\mathrm{kJ} / \mathrm{mol}\). Assume that the solution (whose mass is \(155.4 \mathrm{g}\) ) has a specific heat capacity of \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .\) (Cold packs take advantage of the fact that dissolving ammonium nitrate in water is an endothermic process.)

For each of the following, define a system and its surroundings and give the direction of heat transfer between system and surroundings. (a) Methane is burning in a gas furnace in your home. (b) Water drops, sitting on your skin after a dip in a swimming pool, evaporate. (c) Water, at \(25^{\circ} \mathrm{C},\) is placed in the freezing compartment of a refrigerator, where it cools and eventually solidifies. (d) Aluminum and \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})\) are mixed in a flask sitting on a laboratory bench. A reaction occurs, and a large quantity of heat is evolved.

A 0.692 -g sample of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) is burned in a constant volume calorimeter. The temperature rises from \(21.70^{\circ} \mathrm{C}\) to \(25.22^{\circ} \mathrm{C} .\) The calorimeter contains \(575 \mathrm{g}\) of water and the bomb has a heat capacity of \(650 \mathrm{J} / \mathrm{K}\). What quantity of heat is evolved per mole of glucose?

Suppose that an inch of rain falls over a square mile of ground. (A density of \(1.0 \mathrm{g} / \mathrm{cm}^{3}\) is assumed.) The heat of vaporization of water at \(25^{\circ} \mathrm{C}\) is \(44.0 \mathrm{kJ} / \mathrm{mol} .\) Calculate the quantity of heat transferred to the surroundings from the condensation of water vapor in forming this quantity of liquid water. (The huge number tells you how much energy is "stored" in water vapor and why we think of storms as such great forces of energy in nature. It is interesting to compare this result with the energy given off, \(4.2 \times 10^{6} \mathrm{kJ},\) when a ton of dynamite explodes.)
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