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Chapter 6: Problem 53

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

Short Answer

Expert verified
The 2.5 kJ/mol quantity represents the work done by the system due to the expansion of the gas during the process, which is the PΔV term. This means that the process involves the conversion of 2.5 kJ/mol of energy into work against the external pressure during the transformation of liquid water into water vapor.

Step by step solution

01

Recall the formula relating ΔH, ΔE, and work done by the system

The relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔE) of a system is given by the following formula: ΔH = ΔE + PΔV where P is the pressure and ΔV is the change in volume during the process.
02

Rearrange the formula

We are given that ΔH is more positive than ΔE by 2.5 kJ/mol. We can represent this using the above equation and solve for PΔV: ΔH - ΔE = PΔV
03

Plug in the given values

We are given that ΔH - ΔE is 2.5 kJ/mol. Therefore, we have: 2.5 kJ/mol = PΔV
04

Interpret the result

From the last equation, we can see that the 2.5 kJ/mol quantity represents the work done by the system due to the expansion of the gas during the process, which is PΔV term. Thus, the process involves the conversion of 2.5 kJ/mol of energy into work against the external pressure during the transformation of liquid water into water vapor.

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Most popular questions from this chapter

The equation for the fermentation of glucose to alcohol and carbon dioxide is: $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g) $$ The enthalpy change for the reaction is \(-67 \mathrm{kJ} .\) Is this reaction exothermic or endothermic? Is energy, in the form of heat, absorbed or evolved as the reaction occurs?

In a coffee-cup calorimeter, 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M}\) NaOH and 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M} \mathrm{HCl}\) are mixed. Both solutions were originally at \(24.6^{\circ} \mathrm{C}\) . After the reaction, the final temperature is \(31.3^{\circ} \mathrm{C}\) . Assuming that all the solutions have a density of 1.0 \(\mathrm{g} / \mathrm{cm}^{3}\) and a specific heat capacity of \(4.18 \mathrm{J} / \mathrm{C} \cdot \mathrm{g},\) calculate the enthalpy change for the neutralization of \(\mathrm{HCl}\) by NaOH. Assume that no heat is lost to the surroundings or to the calorimeter.

A system absorbs 35 \(\mathrm{J}\) of heat and has 25 \(\mathrm{J}\) of work performed on it. The system then returns to its initial state by a second step. If 5 \(\mathrm{J}\) of heat are given off in the second step, how much work is done by the system in the second step?

Consider the following reaction: $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-572 \mathrm{kJ} $$ a. How much heat is evolved for the production of 1.00 mole of $\mathrm{H}_{2} \mathrm{O}(l) ?$ b. How much heat is evolved when 4.03 g hydrogen are reacted with excess oxygen? c. How much heat is evolved when 186 \(\mathrm{g}\) oxygen are reacted with excess hydrogen? d. The total volume of hydrogen gas needed to fill the Hindenburg was $2.0 \times 10^{8} \mathrm{L}\( at 1.0 atm and \)25^{\circ} \mathrm{C} .$ How much heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted?

The specific heat capacity of silver is 0.24 $\mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}$ a. Calculate the energy required to raise the temperature of 150.0 g Ag from 273 \(\mathrm{K}\) to 298 \(\mathrm{K}\) . b. Calculate the energy required to raise the temperature of 1.0 mole of \(\mathrm{Ag}\) by \(1.0^{\circ} \mathrm{C}\) (called the molar heat capacity of silver). c. It takes 1.25 \(\mathrm{kJ}\) of energy to heat a sample of pure silver from \(12.0^{\circ} \mathrm{C}\) to \(15.2^{\circ} \mathrm{C}\) . Calculate the mass of the sample of silver.
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