Question

Problem 2. You wish to determine the energy content per gram and Calories per serving of a chocolate chip cookie and a banana bread slice from the Student Union to decide which is less “fattening.” The intact cookie and banana bread slice you are analyzing weigh 72.501 g and 69.003 g, respectively. Before you can analyze the samples, the calorimeter heat capacity must be determined. It is known that combustion of 1.000 g of benzoic acid releases 26.44 kJ of heat = 26.44 kJ. Thus, you combust 1.000 g of benzoic acid in a constant-volume calorimeter and record a temperature increase of 2.52 °C.

2a. From the data given above, determine the heat capacity of the constant-volume calorimeter. To receive credit, you must show all work in a legible, highly organized manner.

2b. Now you take a 5.688 g sample of the chocolate chip cookie and burn it in the same calorimeter. During the combustion, the temperature of the water in the calorimeter increases by 11.81 °C. For the chocolate chip cookie, calculate the energy content in kJ/g and the Calories per serving. Please remember, you must show all work in a legible, highly organized manner.

2c. Finally, you take a 4.904 g sample of the banana bread and run it in the same calorimeter. During the combustion, the water temperature in the calorimeter increases by 12.29 °C. For the banana bread slice, calculate the energy content in kJ/g and the Calories per serving. Don’t forget, you must show all work in a legible, highly organized manner.

2d (3p). Based on the above Problem 2 data, is the chocolate chip cookie or banana bread slice less “fattening” in terms of the energy content in kJ/g? What about in terms of the Calories per serving? In complete sentences, clearly justify your reasoning citing the evidence.

Answer 1

Ans: As given in the question that we are using constant volume calorimeter and also it is given that combustion of 1.000 g of benzoic acid releases 26.44 kJ of heat and the rise in temperature is equal to 2.52oC.

1) Now as we know that Heat(Q) = Cv(T2-T1) where Cv is the heat capacity at constant volume and its unit is J/oC. and (T2-T1) is the temperature difference Now putting the respective values in the heat equation, we get:

26.44 KJ = Cv*2.52oC, so Cv is equal to 10.5 KJ/oC.

2) Now for chocolate chip cookie the temperature difference is 11.81oC and we have calculated that Cv for this calorimeter is 10.5KJ/oC. So putting the values in the heat equation we get, Q = 10.5 KJ/oC*11.81oC and Q is equal to 123.9 KJ. Now the sample is of 5.688 gram so the energy content is (123.9/5.688)KJ/gram and this is equal to 21.78 KJ/gram.

Now 1 calorie is equal to 4.184 Joule, so the energy we are getting after combusting chocolate chip cookie in calorie is (21.78*1000)/4.184 which is equal to 5205.5 Calories/gram. Now for Chocolate chip cookie we are analyzing 72.501 gram so Calories per serving is equal to energy content(in calorie/gram)*total weight, and this is equal to (5205.5)*(72.501) and this is equal to 3,77,407.2 Calories per serving.

3) Now for banana bread the temperature difference is equal to 12.29oC so total energy we are getting after the combustion of banana bread is equal to Q =10.5 KJ/oC*12.29oC and Q is equal to 129.05 KJ. Now the sample is of 4.904 gram so the energy content is (129.05/4.904)KJ/gram and this is equal to 26.32 KJ/gram.

Now 1 calorie is equal to 4.184 Joule, so the energy we are getting after combusting banana bread in calorie is (1000*26.32)/4.184 which is equal to 6290.6 Calories/gram. Now for Banana bread we are analyzing 69.003 gram so Calories per serving is equal to calories*total weight and this is equal to 6290.6*69.003 and this is equal to 4,34,072.41 Calories per serving.

4) Low energy content items are less as they include foods with a high water content and high energy content items tend to include foods that are high in fat and have a low water content. So from this we can say that chocolate chip cookie is less fattening in terms of energy content.

Now for calories per serving the banana bread is providing higher calories as compared to chocolate chip cookie so from this we can also conclude that the chocolate chip cookie is less fattening as fat is also a possible source of energy in the body.