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Chapter 5: Problem 93

The heat of combustion of fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) is \(-2812 \mathrm{kJ} / \mathrm{mol} .\) If a fresh golden delicious apple weighing 4.23 oz \((120 \mathrm{g})\) contains 16.0 \(\mathrm{g}\) of fructose, what caloric content does the fructose contribute to the apple?

Short Answer

Expert verified
The fructose in the apple contributes approximately 59.7 calories to the apple's total caloric content.

Step by step solution

01

Convert heat of combustion to caloric content

To convert the heat of combustion of fructose to caloric content, we will use the fact that 1 cal is equal to 4.184 J. So, we have to divide the given heat of combustion by 4.184. Heat of combustion in calories/mol = \(\frac{-2812 \: kJ}{4.184 \: J/cal} = -672\: cal/mol\)
02

Calculate the number of moles of fructose

Now, we need to find the number of moles of fructose in the 16.0 g of fructose contained in the apple. The molecular weight of fructose is \(C_6H_{12}O_6\), which is equal to 6(12.01) + 12(1.01) + 6(16.00) = 180.18 g/mol. Number of moles of fructose = \(\frac{16.0 \: g}{180.18 \: g/mol} = 0.0888 \: mol\)
03

Calculate the caloric content contributed by the fructose

Finally, we can calculate the total caloric content provided by the fructose using the heat of combustion (in calories/mol) and the number of moles. Caloric content of fructose = Heat of combustion (cal/mol) x Number of moles Caloric content of fructose = \(-672 \: cal/mol \times 0.0888 \: mol = -59.7 \: cal\) Note that the caloric content is a negative value because heat is released during combustion, which is an exothermic process. Thus, the fructose in the apple contributes approximately 59.7 calories to the apple's total caloric content.

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Most popular questions from this chapter

(a) Under what condition will the enthalpy change of a process equal the amount of heat transferred into or out of the system? (b) During a constant- pressure process, the system releases heat to the surroundings. Does the enthalpy of the system increase or decrease during the process? (c) In a constant-pressure process, \(\Delta H=0 .\) What can you conclude about \(\Delta E, q,\) and \(w ?\)

Ozone, \(\mathrm{O}_{3}(g),\) is a form of elemental oxygen that plays an important role in the absorption of ultraviolet radiation in the stratosphere. It decomposes to \(\mathrm{O}_{2}(g)\) at room temperature and pressure according to the following reaction: $$2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g) \quad \Delta H=-284.6 \mathrm{kJ}$$ (a) What is the enthalpy change for this reaction per mole of \(\mathrm{O}_{3}(g) ?\) (b) Which has the higher enthalpy under these conditions, 2 \(\mathrm{O}_{3}(g)\) or 3 \(\mathrm{O}_{2}(g) ?\)

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is blended with gasoline as an automobile fuel. (a) Write a balanced equation for the combustion of liquid ethanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming \(\mathrm{H}_{2} \mathrm{O}(g)\) as a product. (c) Calculate the heat produced per liter of ethanol by combustion of ethanol under constant pressure. Ethanol has a density of 0.789 \(\mathrm{g} / \mathrm{mL}\) (d) Calculate the mass of \(\mathrm{CO}_{2}\) produced per ky of heat emitted.

The standard enthalpies of formation of gaseous propyne \(\left(\mathrm{C}_{3} \mathrm{H}_{4}\right),\) propylene \(\left(\mathrm{C}_{3} \mathrm{H}_{6}\right),\) and propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) are \(+185.4,+20.4,\) and \(-103.8 \mathrm{kJ} / \mathrm{mol}\) , respectively.(a) Calculate the heat evolved per mole on combustion of each substance to yield \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) (b) Calculate the heat evolved on combustion of 1 \(\mathrm{kg}\) of each substance. (c) Which is the most efficient fuel in terms of heat evolved per unit mass?

A sample of a hydrocarbon is combusted completely in \(\mathrm{O}_{2}(g)\) to produce \(21.83 \mathrm{g} \mathrm{CO}_{2}(g), 4.47 \mathrm{g} \mathrm{H}_{2} \mathrm{O}(g),\) and 311 \(\mathrm{kJ}\) of heat. (a) What is the mass of the hydrocarbon sample that was combusted? (b) What is the empirical formula of the hydrocarbon? (c) Calculate the value of \(\Delta H_{f}^{\circ}\) per empirical-formula unit of the hydrocarbon. (d) Do you think that the hydrocarbon is one of those listed in Appendix C? Explain your answer.
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