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Chapter 5: Problem 42

Without referring to tables, predict which of the following has the higher enthalpy in each case: (a) \(1 \mathrm{~mol} \mathrm{CO}_{2}(s)\) or \(1 \mathrm{~mol}\) \(\mathrm{CO}_{2}(g)\) at the same temperature, (b) 2 mol of hydrogen atoms or \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2},\) (c) \(1 \mathrm{~mol} \mathrm{H}_{2}(g)\) and \(0.5 \mathrm{~mol} \mathrm{O}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) or \(1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(g)\) at \(25^{\circ} \mathrm{C},\) (d) \(1 \mathrm{~mol} \mathrm{~N}_{2}(g)\) at \(100{ }^{\circ} \mathrm{C}\) or \(1 \mathrm{~mol}\) \(\mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\)

Short Answer

Expert verified
(a) 1 mol of \(\mathrm{CO}_{2}(g)\) has a higher enthalpy. (b) 2 mol of hydrogen atoms have a higher enthalpy. (c) 1 mol of \(\mathrm{H}_{2}(g)\) and 0.5 mol of \(\mathrm{O}_{2}(g)\) have a higher combined enthalpy. (d) 1 mol of \(\mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\) has a higher enthalpy.

Step by step solution

01

Case (a): CO2(s) vs CO2(g)

As both the solid CO2 and gaseous CO2 are at the same temperature, the only difference between them is the phase. The enthalpy of the substance increases when it transitions from solid to liquid and then from liquid to gas. Therefore, 1 mol of \(\mathrm{CO}_{2}(g)\) will have a higher enthalpy than 1 mol of \(\mathrm{CO}_{2}(s)\) at the same temperature because it has absorbed more energy during the phase transition.
02

Case (b): 2 mol H atoms vs 1 mol H2

When 2 mol of hydrogen atoms combine to form 1 mol of \(\mathrm{H}_{2}\) molecule, a chemical bond is formed between the two hydrogen atoms. The energy is released during the formation of the bond, resulting in the decrease of enthalpy for the system. Hence, 2 mol of hydrogen atoms will have a higher enthalpy compared to 1 mol of \(\mathrm{H}_{2}\).
03

Case (c): 1 mol H2(g) + 0.5 mol O2(g) vs 1 mol H2O(g)

After the combustion reaction of hydrogen and oxygen, 1 mol of \(\mathrm{H}_{2}(g)\) and 0.5 mol of \(\mathrm{O}_{2}(g)\) would form 1 mol of \(\mathrm{H}_{2} \mathrm{O}(g)\). This reaction releases energy as enthalpy decreases: \[ \mathrm{H}_{2}(g) + \dfrac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)\] The enthalpy of 1 mol of \(\mathrm{H}_{2} \mathrm{O}(g)\) will be lower than the combined enthalpy of 1 mol of \(\mathrm{H}_{2}(g)\) and 0.5 mol of \(\mathrm{O}_{2}(g)\) at the same temperature, as energy has been released during the reaction.
04

Case (d): 1 mol N2(g) at 100 掳C vs 1 mol N2(g) at 300 掳C

As temperature increases, the enthalpy of the substance also increases because it has absorbed more energy to reach the higher temperature. The temperature is the only difference between these two cases. Therefore, 1 mol of \(\mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\) will have a higher enthalpy than 1 mol of \(\mathrm{N}_{2}(g)\) at \(100{ }^{\circ} \mathrm{C}\).

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Key Concepts

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

Phase Transition Enthalpy
When a substance undergoes a phase change, such as solid carbon dioxide (dry ice) sublimating into carbon dioxide gas (CO2), there is a change in its enthalpy. Enthalpy is essentially a measure of heat content, and when the phase transition occurs without a change in temperature, it implies that energy has been absorbed to overcome intermolecular forces.

During sublimation, solid CO2 requires energy to transition into the gaseous phase. In this endothermic process, the enthalpy increases because the molecules in the gas phase have more freedom to move and therefore have higher potential energy. This is why, at the same temperature, 1 mole of CO2 gas has a higher enthalpy than 1 mole of solid CO2.
Chemical Bond Energy
Chemical bond energy is the energy required to break a bond or the energy released when a bond is formed. When considering 2 moles of hydrogen atoms versus 1 mole of H2, we're looking at individual atoms versus bonded atoms. The diatomic molecule H2 is formed by a covalent bond between the two hydrogen atoms.

As this bond forms, energy is released, which is essentially the 'bond energy.' So, the system's enthalpy decreases. Consequently, before the formation of the H2 molecule, when the atoms are separate, the energy - and hence enthalpy - of the system is higher. This explains why 2 moles of hydrogen atoms have more enthalpy than 1 mole of H2.
Combustion Reaction Enthalpy
In a combustion reaction, substances react with oxygen to release heat, and typically, the process involves the formation of new chemical bonds. Taking the reaction where hydrogen gas combines with oxygen to form water vapor (H2O), the enthalpy change is significant.

Because the formation of water from hydrogen and oxygen releases energy - typically in the form of heat - the reaction is exothermic. This means the products, in this case, water vapor, will have a lower enthalpy than the reactants, hydrogen and oxygen gases. This is why after combustion, 1 mole of H2O(g) at 25掳C has a lower enthalpy than the combined enthalpy of 1 mole of H2(g) and 0.5 mole of O2(g) at the same temperature.
Temperature Influence on Enthalpy
Temperature effectively measures the average kinetic energy of particles in a substance. With an increase in temperature, particles move faster and tend to occupy a larger volume. This kinetic activity corresponds to an increase in the system's enthalpy.

Thus, when comparing nitrogen gas (N2) at 100掳C to nitrogen gas at 300掳C, the molecules within the warmer sample are moving with greater energy, resulting in a higher enthalpy. Hence, 1 mole of N2(g) at 300掳C has a higher enthalpy than 1 mole of N2(g) at 100掳C, illustrating the direct relationship between temperature and enthalpy.

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Most popular questions from this chapter

Two solid objects, \(A\) and \(B\), are placed in boiling water and allowed to come to temperature there. Each is then lifted out and placed in separate beakers containing \(1000 \mathrm{~g}\) water at \(10.0^{\circ} \mathrm{C}\). Object A increases the water temperature by \(3.50^{\circ} \mathrm{C}\); 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 \(\mathrm{B}\) ?

The automobile fuel called E85 consists of \(85 \%\) ethanol and \(15 \%\) gasoline. \(\mathrm{E} 85\) can be used in so-called "flex-fuel" vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of \(\mathrm{C}_{8} \mathrm{H}_{18}\) ), that the average heat of combustion of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) is \(5400 \mathrm{~kJ} / \mathrm{mol}\), and that gasoline has an average density of \(0.70 \mathrm{~g} / \mathrm{mL}\). The density of ethanol is \(0.79 \mathrm{~g} / \mathrm{mL}\). (a) By using the information given as well as data in Appendix C, compare the energy produced by combustion of \(1.0 \mathrm{~L}\) of gasoline and of \(1.0 \mathrm{~L}\) of ethanol. (b) Assume that the density and heat of combustion of \(\mathrm{E} 85\) can be obtained by using \(85 \%\) of the values for ethanol and \(15 \%\) of the values for gasoline. How much energy could be released by the combustion of \(1.0 \mathrm{~L}\) of E85? (c) How many gallons of E85 would be needed to provide the same energy as 10 gal of gasoline? (d) If gasoline costs \(\$ 3.10\) per gallon in the United States, what is the break-even price per gallon of \(\mathrm{E} 85\) if the same amount of energy is to be delivered?

What is the connection between Hess's law and the fact that \(H\) is a state function?

(a) Why is the change in enthalpy usually easier to measure than the change in internal energy? (b) \(H\) is a state function, but \(q\) is not a state function. Explain. (c) For a given process at constant pressure, \(\Delta H\) is positive. Is the process endothermic or exothermic?

Gasoline is composed primarily of hydrocarbons, including many with eight carbon atoms, called octanes. One of the cleanest-burning octanes is a compound called 2,3,4 trimethylpentane, which has the following structural formula: The complete combustion of one mole of this compound to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\) leads to \(\Delta H^{\circ}=-5064.9 \mathrm{~kJ} / \mathrm{mol}\) (a) Write a balanced equation for the combustion of \(1 \mathrm{~mol}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}(l) .(\mathbf{b})\) Write a balanced equation for the formation of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) from its elements. (c) By using the information in this problem and data in Table \(5.3,\) calculate \(\Delta H_{f}^{\circ}\) for 2,3,4 trimethylpentane.
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