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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 \(120 \mathrm{~g}\) contains \(16.0 \mathrm{~g}\) of fructose, what caloric content does the fructose contribute to the apple?

Short Answer

Expert verified
The total caloric content of the fructose in the apple is \((\frac{2812 \mathrm{kJ/mol}}{180.18 \mathrm{g/mol}}) \times 16 \mathrm{g} \times 0.239 \mathrm{kcal/ kJ}\) = 75.3 kcal.

Step by step solution

01

Calculate the number of moles of fructose in the apple

Given mass of fructose in the apple is 16 g. We can calculate the number of moles (n) using the formula: n = mass / molar mass The molar mass of fructose, \(\mathrm{C}_{6} \mathrm{H}_{12}\mathrm{O}_{6}\), is: \(6 \times 12.01 \: (for \: Carbon) + 12 \times 1.01 \: (for \: Hydrogen) + 6 \times 16.00 \: (for \: Oxygen) = 72.06 + 12.12 + 96 = 180.18 \mathrm{g/mol}\) Now, let's find the number of moles of fructose, n = \( \frac{16}{180.18}\)
02

Convert the heat of combustion to energy content per gram of fructose

Heat of combustion of fructose is given as -2812 kJ/mol. To convert this to energy content per gram, we can divide the heat of combustion by the molar mass of fructose. Energy content per gram = \(\frac{2812 \mathrm{kJ/mol}}{180.18 \mathrm{g/mol}}\)
03

Calculate the total energy content of the fructose present in the apple

Now that we know the energy content per gram of fructose and the number of moles of fructose present in the apple, we can calculate the total energy content by multiplying these values: Total energy content = Energy content per gram × mass of fructose = \( (\frac{2812 \mathrm{kJ/mol}}{180.18 \mathrm{g/mol}}) \times 16 \mathrm{g}\) Finally, as 1 kJ is equal to 0.239 kcal, we can convert our final answer in kJ to kcal: Total caloric content = Total energy content in kJ × 0.239 kcal / kJ

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Most popular questions from this chapter

Butane \(\mathrm{C}_{4} \mathrm{H}_{10}(l)\) boils at $-0.5^{\circ} \mathrm{C} ;\( at this temperature it has a density of \)0.60 \mathrm{~g} / \mathrm{cm}^{3}\(. The enthalpy of formation of \)\mathrm{C}_{4} \mathrm{H}_{10}(g)\( is \)-124.7 \mathrm{~kJ} / \mathrm{mol},$ and the enthalpy of vaporiza- tion of \(\mathrm{C}_{4} \mathrm{H}_{10}(l)\) is $22.44 \mathrm{~kJ} / \mathrm{mol} .\( Calculate the enthalpy change when \)1 \mathrm{~L}$ of liquid \(\mathrm{C}_{4} \mathrm{H}_{10}(l)\) is burned in air to give \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) How does this compare with \(\Delta H\) for the complete combustion of \(1 \mathrm{~L}\) of liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}(l) ?\) For $\mathrm{CH}_{3} \mathrm{OH}(l),\( the density at \)25^{\circ} \mathrm{C}\( is \)0.792 \mathrm{~g} / \mathrm{cm}^{3},\( and \)\Delta H_{f}^{\circ}=-239 \mathrm{~kJ} / \mathrm{mol}$.

(a) When a 0.47-g sample of benzoic acid is combusted in a bomb calorimeter (Figure 5.19), the temperature rises by \(3.284^{\circ} \mathrm{C}\). When a 0.53 -g sample of caffeine, $\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\(, is burned, the temperature rises by \)3.05^{\circ} \mathrm{C}\(. Using the value of \)26.38 \mathrm{~kJ} / \mathrm{g}$ for the heat of combustion of benzoic acid, calculate the heat of combustion per mole of caffeine at constant volume. (b) Assuming that there is an uncertainty of \(0.002^{\circ} \mathrm{C}\) in each temperature reading and that the masses of samples are measured to \(0.001 \mathrm{~g},\) what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

(a) What is meant by the term state function? (b) Give an example of a quantity that is a state function and one that is not. (c) Is the volume of a system a state function? Why or why not?

Two solid objects, A and B, are placed in boiling water and allowed to come to the temperature of the water. Each is then lifted out and placed in separate beakers containing \(1000 \mathrm{~g}\) of water at \(10.0^{\circ} \mathrm{C}\). Object A increases the water temperature by $3.50^{\circ} \mathrm{C} ; \mathrm{B}\( increases the water temperature by \)2.60{ }^{\circ} \mathrm{C}$. (a) Which object has the larger heat capacity? (b) What can you say about the specific heats of \(\mathrm{A}\) and \(\mathrm{B}\) ?

Calculate \(\Delta E\) and determine whether the process is endothermic or exothermic for the following cases: \((\mathbf{a}) q=0.763 \mathrm{~kJ}\) and \(w=-840 \mathrm{~J}\). (b) A system releases \(66.1 \mathrm{~kJ}\) of heat to its surroundings while the surroundings do \(44.0 \mathrm{~kJ}\) of work on the system.
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