Student Solutions Manual for Ball's Physical Chemistry, 2nd
Student Solutions Manual for Ball's Physical Chemistry, 2nd
2nd Edition
ISBN: 9798214169019
Author: David W. Ball
Publisher: Cengage Learning US
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Chapter 4, Problem 4.1E

List the sets of conditions that allow d S , d U , and d H of a process in a system act as a spontaneity condition.

Expert Solution & Answer
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Interpretation Introduction

Interpretation:

The sets of conditions that allow dS, dU and dH of a process in a system to act as a spontaneity condition are to be stated.

Concept introduction:

The spontaneous process can be defined as the process in which the free energy is released and the system moves to an energy state which is thermodynamically more stable.

Answer to Problem 4.1E

The spontaneity condition in terms of entropy is given at the constant internal energy and constant volume by the expression,

(dS)U,V>0

At constant volume and constant entropy, the condition for spontaneity is given in terms of internal energy as,

(dU)V,S0

At constant pressure and entropy, the condition for spontaneity is given in terms of enthalpy as,

(dH)P,S0

Explanation of Solution

The derivation of the spontaneity condition ΔS>0 is applicable to the systems in which no pressure-volume work is done and the processes are adiabatic, that is, both q and w is zero. The first law of thermodynamics is dU=dqpdV.

Thus, according to the first law of thermodynamics ΔU is also zero.

Thus, ΔS>0 is valid when U and V are held constant.

The infinitesimal change in entropy is given by the expression,

(dS)U,V>0

According to the Clausius theorem, the entropy change is given by the expression,

dqTdS

This expression can be rewritten using the dq=dU+pdV as shown below.

dU+pdVTdS0

dU+pdVTdS0 …(1)

At constant volume and constant entropy, the condition for spontaneity is given in terms of internal energy as,

(dU)V,S0

For enthalpy the expression, dH=dU+d(pV) can be substituted for the value of dU in the equation (1) as shown below.

dHd(pV)+pdVTdS0dHpdVVdp+pdVTdS0

dHVdpTdS0 …(2)

At constant pressure and entropy, the condition for spontaneity is given in terms of enthalpy as,

(dH)P,S0

Conclusion

The spontaneity condition in terms of entropy is given at the constant internal energy and constant volume by the expression,

(dS)U,V>0

At constant volume and constant entropy, the condition for spontaneity is given in terms of internal energy as,

(dU)V,S0

At constant pressure and entropy, the condition for spontaneity is given in terms of enthalpy as,

(dH)P,S0

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Chapter 4 Solutions

Student Solutions Manual for Ball's Physical Chemistry, 2nd

Ch. 4 - Consider a piston whose compression ratio is 10:1;...Ch. 4 - When one dives, water pressure increases by 1atm...Ch. 4 - Calculate G(25C) for this chemical reaction, which...Ch. 4 - Thermodynamic properties can also be determined...Ch. 4 - Calculate G in two different ways for the...Ch. 4 - Calculate G in two different ways for the...Ch. 4 - For the reaction C(graphite)C(diamond) at 25C,...Ch. 4 - Determine G for the following reaction at 0C and...Ch. 4 - What is the maximum amount of electrical that is,...Ch. 4 - When a person performs work, it is non-pV work....Ch. 4 - Can non-pV work be obtained from a process for...Ch. 4 - Can pV work be obtained from a process for which...Ch. 4 - Batteries are chemical systems that can be used to...Ch. 4 - The value of G for any phase change at constant p...Ch. 4 - The value of G for any phase change at constant p...Ch. 4 - Under what conditions is A=0 for a phase change?...Ch. 4 - Example 4.2 calculated A for one step of a Carnot...Ch. 4 - Can CV and Cp be easily defined using the natural...Ch. 4 - Analogous to equation 4.26, what is the expression...Ch. 4 - Prob. 4.30ECh. 4 - Prob. 4.31ECh. 4 - Prob. 4.32ECh. 4 - Although ideally, U=H=0 for a gas-phase process at...Ch. 4 - Use equations 4.21 and 4.25 to explain why H and G...Ch. 4 - Prob. 4.35ECh. 4 - Which of the following functions are exact...Ch. 4 - Prob. 4.37ECh. 4 - Prob. 4.38ECh. 4 - Prob. 4.39ECh. 4 - Equation 4.19 says that (UV)S=p If we are...Ch. 4 - For an isentropic process, what is the approximate...Ch. 4 - Use the ideal gas law to demonstrate the cyclic...Ch. 4 - Prob. 4.43ECh. 4 - Prob. 4.44ECh. 4 - Evaluate (U/V)T for an ideal gas. Use the...Ch. 4 - Evaluate (U/V)T for a van der Waals gas. Use the...Ch. 4 - Repeat the previous exercise for a gas that...Ch. 4 - Determine an expression for (p/S)T for an ideal...Ch. 4 - Determine the value of the derivative {[(G)]/T}p...Ch. 4 - Prob. 4.50ECh. 4 - Prob. 4.51ECh. 4 - A 0.988-mole sample of argon expands from 25.0L to...Ch. 4 - A 3.66-mol sample of He contracts from 15.5L to...Ch. 4 - Prob. 4.54ECh. 4 - Prob. 4.55ECh. 4 - Use the Gibbs-Helmholtz equation to demonstrate...Ch. 4 - For the equation 2H2(g)+O2(g)2H2O(g)...Ch. 4 - Use equation 4.46 as an example and find an...Ch. 4 - What is the value of G when 1.00mol of water at...Ch. 4 - Prob. 4.60ECh. 4 - Prob. 4.61ECh. 4 - Prob. 4.62ECh. 4 - Prob. 4.63ECh. 4 - Prob. 4.64ECh. 4 - What is the change in the chemical potential of a...Ch. 4 - Prob. 4.66ECh. 4 - Prob. 4.67ECh. 4 - Prob. 4.68ECh. 4 - Prob. 4.69ECh. 4 - Can equation 4.62 be used to calculate for an...Ch. 4 - Prob. 4.71ECh. 4 - Of helium and oxygen gases, which one do you...Ch. 4 - Prob. 4.73ECh. 4 - Use equation 4.39 to determine a numerical value...Ch. 4 - Prob. 4.75ECh. 4 - Prob. 4.76E
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