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Chapter 5: Problem 113

Construct a table with the headings \(q, w, \Delta U,\) and \(\Delta H\). For each of the following processes, deduce whether each of the quantities listed is positive \((+),\) negative (-), or zero (0): (a) freezing of benzene, (b) reaction of sodium with water, (c) boiling of liquid ammonia, (d) melting of ice, (e) expansion of a gas at constant temperature.

Short Answer

Expert verified
For each process: (a) q<0, w=0, 螖U<0, 螖H<0; (b) q<0, w<0, 螖U<0, 螖H<0; (c) q>0, w=0, 螖U>0, 螖H>0; (d) q>0, w=0, 螖U>0, 螖H>0; (e) q>0, w<0, 螖U=0, 螖H=0.

Step by step solution

01

Understanding the Exercise

We need to construct a table with headings \(q\), \(w\), \(\Delta U\), and \(\Delta H\). For each process, we will assess whether these quantities are positive, negative, or zero. The processes include freezing of benzene, reaction of sodium with water, boiling of liquid ammonia, melting of ice, and expansion of a gas at constant temperature.
02

Thermodynamic Definitions

Let's define the terms: \(q\) is the heat exchanged, \(w\) is the work done, \(\Delta U\) is the change in internal energy, and \(\Delta H\) is the change in enthalpy. Heat absorbed by the system corresponds to \(q > 0\) and released corresponds to \(q < 0\). Similarly, work done on the system corresponds to \(w > 0\) and done by the system corresponds to \(w < 0\).
03

Processing Each Process

We'll analyze each process in terms of \(q\), \(w\), \(\Delta U\), and \(\Delta H\).
04

Process (a): Freezing of Benzene

During freezing, the system releases heat so \(q < 0\). There is no work done since it's a phase change at constant pressure, so \(w = 0\). The internal energy and enthalpy decrease during freezing, hence \(\Delta U < 0\) and \(\Delta H < 0\).
05

Process (b): Reaction of Sodium with Water

This is an exothermic reaction, so \(q < 0\). The reaction is also accompanied by the release of gas, which typically indicates expansion, so \(w < 0\). Both \(\Delta U\) and \(\Delta H\) will be negative because exothermic reactions release energy.
06

Process (c): Boiling of Liquid Ammonia

During boiling, heat is absorbed so \(q > 0\). No work is done since it's a conversion of phase at constant pressure, so \(w = 0\). Both \(\Delta U > 0\) and \(\Delta H > 0\), as energy is absorbed during the phase change.
07

Process (d): Melting of Ice

Melting is endothermic, hence \(q > 0\). Since it is a phase change at constant pressure, \(w = 0\). Both \(\Delta U > 0\) and \(\Delta H > 0\) as energy is required to overcome the solid structure.
08

Process (e): Expansion of a Gas at Constant Temperature

For an isothermal expansion of an ideal gas, \(q > 0\) because heat is added to maintain temperature. The gas does work on the surroundings, so \(w < 0\). \(\Delta U = 0\) as temperature remains constant, and \(\Delta H = 0\) since enthalpy change at constant temperature for an ideal gas is zero.

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Key Concepts

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

Thermal Energy Exchange
In thermodynamics, thermal energy exchange refers to the transfer of heat between systems or a system and its surroundings. Heat, denoted as "\(q\)," can either be absorbed by the system or released to the surroundings. This exchange is vital in understanding various processes.

For instance:
  • When a substance like benzene freezes, it releases heat, making \(q < 0\).
  • Conversely, when ice melts or ammonia boils, the system absorbs heat, resulting in \(q > 0\).
  • During the isothermal expansion of a gas, heat is typically added to maintain constant temperature, hence \(q > 0\).
Recognizing whether heat is absorbed or released helps deduce the energy flow in processes, aiding in deeper thermodynamic analysis.
Phase Change
A phase change refers to the transformation from one state of matter to another, such as solid to liquid or liquid to gas. It plays a significant role in thermodynamics as it involves the exchange of energy without altering the temperature at equilibrium pressure.

  • Freezing of Benzene: A phase change from liquid to solid, releasing energy.
  • Boiling of Liquid Ammonia: The transformation from liquid to gas, requiring the absorption of heat.
  • Melting of Ice: Solid to liquid conversion, which absorbs energy.
In constant pressure systems, phase changes do not involve work (\(w = 0\)). Analysis of these transitions helps us understand energy changes like heat and enthalpy but not work.
Enthalpy
Enthalpy (\(\Delta H\)) represents the total heat content of a system, an essential property in assessing energy changes especially during phase transitions or reactions. \(\Delta H\) is positive if heat is absorbed and negative if heat is released.

  • Freezing of Benzene: Since heat is released, \(\Delta H < 0\).
  • Boiling of Ammonia: Here, energy is absorbed, making \(\Delta H > 0\).
  • Melting of Ice: Energy requirement for melting results in \(\Delta H > 0\).
Enthalpy provides insight into the heat exchange without the influence of work done, crucial for physicochemical studies.
Internal Energy
Internal energy (\(\Delta U\)) of a system accounts for the microscopic kinetic and potential energies of molecules. Changes in it reflect the net energy change from heat exchange and work done.

  • Exothermic Reactions (e.g., Sodium with Water): Result in \(\Delta U < 0\) as energy is released.
  • Endothermic Processes (e.g., Melting of Ice): Lead to \(\Delta U > 0\) since energy is absorbed.
  • Isothermal Expansion: \(\Delta U = 0\) because there is no change in temperature thus no net energy change.
Understanding internal energy helps to describe system behavior under specific thermodynamic conditions.
Work Done
Work done (\(w\)) in thermodynamics refers to energy transfer due to a volume change under external pressure. The sign of work, whether positive or negative, indicates whether the system does work on the surroundings or vice versa.

  • Work Done by System: In the expansion of gases, like in sodium reacting with water, the system does work, thus \(w < 0\).
  • Phase Changes: Like freezing or melting, have no volume change because of constant pressure, hence \(w = 0\).
  • Isothermal Gas Expansion: In this, work is done by the expanding gas, making \(w < 0\).
Assessing work done is essential in calculating the energy dynamics of thermodynamic systems, helping predict system responses to changes in pressure or volume.

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Most popular questions from this chapter

At \(25^{\circ} \mathrm{C}\), the standard enthalpy of formation of \(\mathrm{HF}(a q)\) is \(-320.1 \mathrm{~kJ} / \mathrm{mol} ;\) of \(\mathrm{OH}^{-}(a q),\) it is \(-229.6 \mathrm{~kJ} / \mathrm{mol} ;\) of \(\mathrm{F}^{-}(a q)\) it is \(-329.1 \mathrm{~kJ} / \mathrm{mol} ;\) and of \(\mathrm{H}_{2} \mathrm{O}(l),\) it is \(-285.8 \mathrm{~kJ} / \mathrm{mol}\). (a) Calculate the standard enthalpy of neutralization of \(\mathrm{HF}(a q)\) \(\mathrm{HF}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{F}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (b) Using the value of \(-56.2 \mathrm{~kJ}\) as the standard enthalpy change for the reaction \(\mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\) calculate the standard enthalpy change for the reaction \(\mathrm{HF}(a q) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)\)

You are given the following data: \(\begin{aligned} \mathrm{H}_{2}(g) & \longrightarrow 2 \mathrm{H}(g) & & \Delta H^{\circ}=436.4 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{Br}_{2}(g) & \longrightarrow 2 \mathrm{Br}(g) & & \Delta H^{\circ}=192.5 \mathrm{~kJ} / \mathrm{mol} \\\ \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) & \longrightarrow 2 \mathrm{HBr}(g) & \Delta H^{\circ} &=-72.4 \mathrm{~kJ} / \mathrm{mol} \end{aligned}\) Calculate \(\Delta H^{\circ}\) for the reaction\(\mathrm{H}(g)+\mathrm{Br}(g) \longrightarrow \mathrm{HBr}(g)\).

When \(1.034 \mathrm{~g}\) of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) is burned in a constant-volume bomb calorimeter at \(298 \mathrm{~K}, 41.56 \mathrm{~kJ}\) of heat is evolved. Calculate \(\Delta U\) and \(w\) for the reaction on a molar basis.

The enthalpy of combustion of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) is commonly used as the standard for calibrating constant-volume bomb calorimeters; its value has been accurately determined to be \(-3226.7 \mathrm{~kJ} / \mathrm{mol}\). When \(1.9862 \mathrm{~g}\) of benzoic acid are burned in a calorimeter, the temperature rises from \(21.84^{\circ} \mathrm{C}\) to \(25.67^{\circ} \mathrm{C}\). What is the heat capacity of the bomb? (Assume that the quantity of water surrounding the bomb is exactly \(2000 \mathrm{~g} .\) )

A man ate 0.50 pound of cheese (an energy intake of \(4 \times 10^{3} \mathrm{~kJ}\) ). Suppose that none of the energy was stored in his body. What mass (in grams) of water would he need to perspire in order to maintain his original temperature? (It takes \(44.0 \mathrm{~kJ}\) to vaporize 1 mole of water.)
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