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Chapter 7: Problem 123

For the process \(\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)\) at \(298 \mathrm{K}\) and 1.0 atm, \(\Delta H\) is more positive than \(\Delta E\) by 2.5 kJ/mol. What does the \(2.5 \mathrm{kJ} / \mathrm{mol}\) quantity represent?

Short Answer

Expert verified
The 2.5 kJ/mol difference between ΔH and ΔE for the process \(\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)\) at 298 K and 1.0 atm represents the work done by the system on its surroundings as the water molecules transform from a liquid phase to gaseous phase, at constant pressure and temperature.

Step by step solution

01

Understanding the Terms

Enthalpy (H) and Internal Energy (E) are state functions that describe the energy content of a system. Here, we deal with their changes (ΔH and ΔE) in conversion from liquid water to water vapor. Enthalpy represents the amount of heat energy transferred at constant pressure and accounts for the work done by the system on its surroundings. On the other hand, internal energy represents the total energy within a system (including kinetic and potential energy). The relationship between ΔH, ΔE, and the work done during the process is: \( \Delta H = \Delta E + P \Delta V\) where P is the constant pressure and ΔV is the change in volume for the process.
02

Analyze the Given Information

We are given that ΔH is 2.5 kJ/mol more positive than ΔE. We can rewrite the relationship in step 1 as: \( \Delta H - \Delta E = P \Delta V \) The 2.5 kJ/mol represents the difference between ΔH and ΔE, so we can say: \( 2.5 \, \text{kJ/mol} = P \Delta V \)
03

Relate the Quantity to the Process

Since \( P \Delta V \) represents the work done by the system on its surroundings during the process, the 2.5 kJ/mol difference indicates the amount of work done by the system as it expands and the liquid water transformed into water vapor at constant pressure and temperature. This work includes doing mechanical work on the surroundings, such as displacing the atmosphere or lifting a piston.
04

Conclusion

The 2.5 kJ/mol difference between ΔH and ΔE represents the work done by the system on its surroundings as the water molecules transform from a liquid phase to gaseous phase, at constant pressure and temperature (298 K and 1.0 atm).

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Most popular questions from this chapter

The complete combustion of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g),\) produces 1300. kJ of energy per mole of acetylene consumed. How many grams of acetylene must be burned to produce enough heat to raise the temperature of 1.00 gal water by \(10.0^{\circ} \mathrm{C}\) if the process is \(80.0 \%\) efficient? Assume the density of water is \(1.00 \mathrm{g} / \mathrm{cm}^{3}\).

The enthalpy change for the reaction $$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ is \(-891 \mathrm{kJ}\) for the reaction \(a s\) written. a. What quantity of heat is released for each mole of water formed? b. What quantity of heat is released for each mole of oxygen reacted?

Combustion of table sugar produces \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) When \(1.46 \mathrm{g}\) table sugar is combusted in a constant-volume (bomb) calorimeter, \(24.00 \mathrm{kJ}\) of heat is liberated. a. Assuming that table sugar is pure sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\) write the balanced equation for the combustion reaction. b. Calculate \(\Delta E\) in \(\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) for the combustion reaction of sucrose.

Are the following processes exothermic or endothermic? a. the combustion of gasoline in a car engine b. water condensing on a cold pipe c. \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) d. \(\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{F}(g)\)

Consider the reaction $$2 \mathrm{HCl}(a q)+\mathrm{Ba}(\mathrm{OH})_{2}(a q) \longrightarrow \mathrm{BaCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \Delta H=-118 \mathrm{kJ}$$ Calculate the heat when \(100.0 \mathrm{mL}\) of \(0.500 \mathrm{M}\) HCl is mixed with \(300.0 \mathrm{mL}\) of \(0.100 M \mathrm{Ba}(\mathrm{OH})_{2} .\) Assuming that the temperature of both solutions was initially \(25.0^{\circ} \mathrm{C}\) and that the final mixture has a mass of \(400.0 \mathrm{g}\) and a specific heat capacity of \(4.18 \mathrm{J} /^{\prime} \mathrm{C} \cdot \mathrm{g},\) calculate the final temperature of the mixture.
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