# 5.4 Thermochemistry: calorimetry  (Page 6/14)

 Page 6 / 14

## Bomb calorimetry

When 3.12 g of glucose, C 6 H 12 O 6 , is burned in a bomb calorimeter, the temperature of the calorimeter increases from 23.8 °C to 35.6 °C. The calorimeter contains 775 g of water, and the bomb itself has a heat capacity of 893 J/°C. How much heat was produced by the combustion of the glucose sample?

## Solution

The combustion produces heat that is primarily absorbed by the water and the bomb. (The amounts of heat absorbed by the reaction products and the unreacted excess oxygen are relatively small and dealing with them is beyond the scope of this text. We will neglect them in our calculations.)

The heat produced by the reaction is absorbed by the water and the bomb:

$\begin{array}{l}{q}_{\text{rxn}}=-\left({q}_{\text{water}}+{q}_{\text{bomb}}\right)\\ =-\left[\left(4.184\phantom{\rule{0.2em}{0ex}}\text{J/g °C}\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(775\phantom{\rule{0.2em}{0ex}}\text{g}\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(35.6\phantom{\rule{0.2em}{0ex}}\text{°C}-23.8\phantom{\rule{0.2em}{0ex}}\text{°C}\right)+893\phantom{\rule{0.2em}{0ex}}\text{J/°C}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(35.6\phantom{\rule{0.2em}{0ex}}\text{°C}-23.8\phantom{\rule{0.2em}{0ex}}\text{°C}\right)\right]\\ =-\left(38,300\phantom{\rule{0.2em}{0ex}}\text{J}+10,500\phantom{\rule{0.2em}{0ex}}\text{J}\right)\\ =\text{−48,800 J}=\text{−48.8 kJ}\end{array}$

This reaction released 48.7 kJ of heat when 3.12 g of glucose was burned.

When 0.963 g of benzene, C 6 H 6 , is burned in a bomb calorimeter, the temperature of the calorimeter increases by 8.39 °C. The bomb has a heat capacity of 784 J/°C and is submerged in 925 mL of water. How much heat was produced by the combustion of the glucose sample?

39.0 kJ

Since the first one was constructed in 1899, 35 calorimeters have been built to measure the heat produced by a living person. Francis D. Reardon et al. “The Snellen human calorimeter revisited, re-engineered and upgraded: Design and performance characteristics.” Medical and Biological Engineering and Computing 8 (2006)721–28, http://link.springer.com/article/10.1007/s11517-006-0086-5. These whole-body calorimeters of various designs are large enough to hold an individual human being. More recently, whole-room calorimeters allow for relatively normal activities to be performed, and these calorimeters generate data that more closely reflect the real world. These calorimeters are used to measure the metabolism of individuals under different environmental conditions, different dietary regimes, and with different health conditions, such as diabetes. In humans, metabolism is typically measured in Calories per day. A nutritional calorie (Calorie)    is the energy unit used to quantify the amount of energy derived from the metabolism of foods; one Calorie is equal to 1000 calories (1 kcal), the amount of energy needed to heat 1 kg of water by 1 °C.

## Measuring nutritional calories

In your day-to-day life, you may be more familiar with energy being given in Calories, or nutritional calories, which are used to quantify the amount of energy in foods. One calorie (cal) = exactly 4.184 joules, and one Calorie (note the capitalization) = 1000 cal, or 1 kcal. (This is approximately the amount of energy needed to heat 1 kg of water by 1 °C.)

The macronutrients in food are proteins, carbohydrates, and fats or oils. Proteins provide about 4 Calories per gram, carbohydrates also provide about 4 Calories per gram, and fats and oils provide about 9 Calories/g. Nutritional labels on food packages show the caloric content of one serving of the food, as well as the breakdown into Calories from each of the three macronutrients ( [link] ).

For the example shown in (b), the total energy per 228-g portion is calculated by:

$\left(5\phantom{\rule{0.2em}{0ex}}\text{g protein}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}4\phantom{\rule{0.2em}{0ex}}\text{Calories/g}\right)+\left(31\phantom{\rule{0.2em}{0ex}}\text{g carb}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}4\phantom{\rule{0.2em}{0ex}}\text{Calories/g}\right)+\left(12\phantom{\rule{0.2em}{0ex}}\text{g fat}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}9\phantom{\rule{0.2em}{0ex}}\text{Calories/g}\right)=252\phantom{\rule{0.2em}{0ex}}\text{Calories}$

So, you can use food labels to count your Calories. But where do the values come from? And how accurate are they? The caloric content of foods can be determined by using bomb calorimetry; that is, by burning the food and measuring the energy it contains. A sample of food is weighed, mixed in a blender, freeze-dried, ground into powder, and formed into a pellet. The pellet is burned inside a bomb calorimeter, and the measured temperature change is converted into energy per gram of food.

Today, the caloric content on food labels is derived using a method called the Atwater system that uses the average caloric content of the different chemical constituents of food, protein, carbohydrate, and fats. The average amounts are those given in the equation and are derived from the various results given by bomb calorimetry of whole foods. The carbohydrate amount is discounted a certain amount for the fiber content, which is indigestible carbohydrate. To determine the energy content of a food, the quantities of carbohydrate, protein, and fat are each multiplied by the average Calories per gram for each and the products summed to obtain the total energy.

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