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Chapter 5: Problem 33

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

Short Answer

Expert verified
(a) Measuring ΔE is harder than measuring ΔH because both heat exchange (q) and work done (w) need to be determined for ΔE, while only heat exchange at constant pressure (q_p) needs to be measured for ΔH. (b) Internal energy (E) is a state function because it depends solely on the initial and final states of the system, but heat (q) is not a state function because it depends on the path taken by the system during a process. (c) If ΔH is negative at constant pressure, the process is exothermic because the system is releasing heat to the surroundings.

Step by step solution

01

(a) Difficulty in measuring ΔE and ΔH

(a) The change in internal energy (ΔE) of a system depends on the heat exchange with the surroundings (q) and the work done by/on the system (w). Mathematically, it can be represented as: \( \Delta E = q + w \) On the other hand, the change in enthalpy (ΔH) of a system at constant pressure is related to the heat exchange and is given by: \( \Delta H = q_p \) (where q_p is the heat exchange at constant pressure) Measuring ΔE is usually harder than measuring ΔH because both heat exchange (q) and work done (w) need to be determined for ΔE. In contrast, only heat exchange at constant pressure (q_p) needs to be measured for ΔH which is relatively simpler.
02

(b) State function

(b) A state function is a property that depends only on the current state of the system and not on the path taken to reach that state. Internal energy (E) is a state function because it depends solely on the initial and final states of the system. Heat (q), however, depends on the path taken by the system during a process. Different processes involving different paths can result in the same change of state, but in general, the amount of heat exchanged (q) would not be the same. Therefore, heat (q) is not a state function.
03

(c) Endothermic or exothermic process

(c) If the change in enthalpy (ΔH) is negative for a given process at constant pressure, it means that the system is releasing heat to the surroundings. This release of heat implies that the process is exothermic. In contrast, a process would be endothermic if it absorbs heat from the surroundings, which would result in a positive ΔH value.

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Most popular questions from this chapter

A 2.20-g sample of phenol $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)$ was burned in a bomb calorimeter whose total heat capacity is \(11.90 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} .\) The temperature of the calorimeter plus contents increased from 21.50 to $27.50^{\circ} \mathrm{C} .(\mathbf{a})$ Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol and per mole of phenol?

When an 18.6-g sample of solid potassium hydroxide dissolves in $200.0 \mathrm{~g}$ of water in a coffee-cup calorimeter (Figure 5.18), the temperature rises from 23.7 to \(44.5^{\circ} \mathrm{C}\). (a) Calculate the quantity of heat (in kJ) released in the reaction. (b) Using your result from part (a), calculate \(\Delta H\) (in kJ/mol KOH) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

A magnesium ion, \(\mathrm{Mg}^{2+}\), with a charge of $3.2 \times 10^{-19} \mathrm{C}\( and an oxide ion, \)\mathrm{O}^{2-},\( with a charge of \)-3.2 \times 10^{-19} \mathrm{C},\( are separated by a distance of \)0.35 \mathrm{nm}$. How much work would be required to increase the separation of the two ions to an infinite distance?

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing \(0.655 \mathrm{~kJ}\) of heat. It shrinks on cooling, and the atmosphere does \(382 \mathrm{~J}\) of work on the balloon. (b) A 100.0-g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) during which it absorbs \(322 \mathrm{~J}\) of heat. Assume the volume of the gold bar remains constant.

It is interesting to compare the "fuel value" of a hydrocarbon in a hypothetical world where oxygen is not the combustion agent. The enthalpy of formation of \(\mathrm{CF}_{4}(g)\) is \(-679.9 \mathrm{~kJ} / \mathrm{mol}\). Which of the following two reactions is the more exothermic? $$ \begin{aligned} \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \\ \mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) & \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g) \end{aligned} $$
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