Answered: Derive an expression for pressure in…

Derive an expression for pressure in terms of the canonical partition function Q, and then obtain an expression for the Gibbs energy in terms of the canonical partition function Q.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

See similar textbooks

Related questions

Q: is the study of transformations of energy and matter as they approach the state of equilibrium…

A: Definition :

Q: The differential for the Gibbs function, G, at constant composition is: ?G = −S?T + Vdp Using the…

A: Maxwell Relation and Differential Equations

Q: The variation of free energy with pressure at constant temperature is given by

Q: Calculate the change in the entropies of the system and the surroundings, and the total change in…

A: for an isothermal reversible compression or expansion the entropy of is given by , ⊿S=nRlnVfVin=no…

Q: Suggest a physical interpretation of the dependence of the Gibbs energy on the pressure.

Q: A sample of Ar of mass 8.30 g occupies 1.75dm3 at 330 K. (a) Calculate the work done when the gas…

A: Answer:In this problem, in first case we have to find out the work done in isothermal irreversible…

Q: Calculate the standard molar Gibbs energy of neon gas at 298 K.

A: The standard molar Gibbs energy at any temperature T can be expressed as follows:

Q: Estimate the vibrational contribution to the molar entropy of the most common isotopomer of bromine,…

A: First the vibrational partition function is calculated.

Q: sider a chem reacti R has two states separated by 2.0x 10-22 J. P has a doubly degenerate level that…

A: The partition function of a system, Q, measures the possibility of a system occupying a state i. A…

Q: Determine the heat capacity at constant pressure (in joules per kelvin per mole) for an ideal…

Q: Use the equipartition principle to estimate the value of γ = Cp/CV for carbon dioxide. Do this…

Q: system A with 100,000 molecules is at equilibrium at 400k with a boltzmann partition function of…

Q: Calculate the vibrational, rotational, and translational contributions to the constant volume heat…

Q: Without carrying out an explicit calculation, explain there lative values of the standard molar…

A: Standard Molar Entropy In chemistry, the standard molar entropy is the entropy content of one mole…

Q: (1) The molecules in a thermally equilibrated isolated system are confined to just the two…

A: For two molecules present in just two energy levels represented by ε0 and ε1 where ε0 indicates zero…

Q: Calculate the difference in Gibbs energy of a perfect gas if the pressure is increased by 20% at…

A: Gibbs free Energy (ΔG): In a reversible system at constant temperature and pressure, Gibbs energy is…

Q: Describe enthropy. What the entropy describes about a system, the statistical (boltzmann) definition…

A: A thermodynamic state property which measures the degree of disorderness or randomness of the…

Q: What is the reversible work, in joules, for the expansion of 2.50 mol of an ideal gas from 4.7 bar…

Q: Give examples of chemical systems that are (a) open, (b) closed, (c) isolated.

A: Open system: An open system can exchange energy and matter with environment. Example: Cup of water (…

Q: Determine the work done in an isothermal, reversible expansion of a real gas obeying the virial…

Q: At temperature T, the internal energy of 1mol rigid diatomic molecules is =......

A: Internal energy can be calculated on the basis of degree of freedom.

Q: The fugacity of a monatomic gas is found to obey the relation ?(?, ?) = ????. Write expressions for…

A: Fugacity is a sort of fictitious pressure which is used in order to retain for real gases. Molar…

Q: The molar constant pressure heat capacity of an ideal diatomic gas is R. Calculate Cy for 6.10 mol…

A: Heat capacity is defined as the amount of heat needed for a substance to increase the temperature by…

Q: Exactly one mole of a monatomic ideal gas (C,=R) undergoes isothermal expansion from 24.4 L to 34.4…

A: For the isothermal process, the change in entropy can be calculated by using following equation:…

Q: Calculate the molar entropy of Ar under conditions of T=298K and V=24.5L. Use the ideal gas law to…

A: Molar entropy calculation requires some more data which is missing here. Calculation of pressure is…

Q: A. Consider the following gas phase reaction: H20 (g) → H2(g) +02(g). Using the tabulated…

Q: What molar constant-volume heat capacities would you expect under classical conditions for the…

A: According to equipartition theorem, the contribution of degree of freedom to the heat capacity is ½…

Q: Derive the generalized Gibbs equations, considering chemical potentials and more than one phase.

A: The Gibbs-Duhem equation is a fundamental relationship in thermodynamics that describes the…

Q: Calculate the molar internal energy of a monatomic gas.

Q: Consider an ideal monatomic gas consisting of N atoms. Initially, it is contained in a volume of V.…

A: We have given - isothermal Process, So temperature is constant. Which also means dH = 0 , dU =…

Q: The internal energy of a system A None of these B is the sum of the rotational, vibrational, and…

A: Internal energy of system is denoted by U.

Q: Calculate the change of entropy in the system: Delta S of the surrounding=251 kJ/mol, Gibbs free…

A: It is considered that the given system and its surrounding are in thermal equilibrium, then…

Q: Determine the work involved when one mole of an ideal gas is compressed isothermally from 1.00 bar…

A: Let P1 be the initial pressure exerted on the gas and P2 be the final pressure exerted on the gas.…

Q: Discuss the relations between: the entropy (particularly of the universe), the standard Gibbs' free…

A: The standard free energy change (∆G○) of a reaction is calculated from the corresponding enthalpy…

Q: Name the thermodynamic state function that is a measure of randomness or can also be defined as…

A: Given that a thermodynamic state function that is a measure of randomness or can also be defined as…

Question

The translational canonical partition function Qtrs of an ideal monoatomic gas is given by:
3N
2T
alnQtrs
ƏT
√²
=
Justify mathematically why the translational contribution to the molar constant-volume
heat capacity is:
Cy = 3Nk
3
- Nk
Derive an expression for pressure in terms of the canonical partition function Q, and
then obtain an expression for the Gibbs energy in terms of the canonical partition
function Q.
Consider the mixing of two perfectly miscible (ideal) organic solvents A and B. Calculate
their respective mole fractions needed to obtain the greatest entropy of mixing.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: 1. Translational Contribution to Molar

VIEW

Step 3: 2. Expression for Pressure and Gibbs Energy in terms of Canonical Partition Function Q

VIEW

Step 4: Thermodynamics parameters

VIEW

Solution

VIEW

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

Derive an expression showing how entropy can be related to thermodynamic probability.
Derivation Calculate the entropy of HBr at 298 K and 1.00 bar, given that the bond length is 1.41 Å and the masses of ¹H and 79Br are 1.008 amu and 78.92 amu, respectively. The vibrational wavenumber is 2649 cm-¹. Step 1 of 7 Provide the equation needed to calculate the translational contribution to the total entropy. (Use the following as necessary: h, kB, m to represent the mass, P, T, and T.) (²³1) (2πmkT) h³ Strans = R In kµT (²/2) e P (2πmkBT) ³ kBT h³ P Step 2 of 7 Substitute numerical values into the equation from Step 1 to obtain a numerical calculation for the translational entropy contribution. Strans = 163.61 163.484901080763 J.K-1.mol-1 Step 3 of 7 Provide the equation needed to calculate the rotational contribution to the total entropy. (Use the following as necessary: h, I, kB, 7, σ, and T.) Srot = R In 8n²lkpT oh² + R 87² IkBT oh² Step 4 of 7 Substitute numerical values into the equation from Step 3 to obtain a numerical calculation for the rotational entropy…
Res translational degrees rotational degrees electronic energetic degrees vibrational degrees Contribution is equal to the theorem's prediction Contribution is not equal to the theorem's prediction
Answer this please
Beginning from the Clausius inequality, derive for us several (two or more) units of entropy
The absolute entropy of Kr at 298.15 K is 163.97 J/mol-K. What is its absolute entropy at 200.00 K if the volume remains unchanged? Assume that the heat capacity is constant.
Differentiate between distribution ratio (D) and partition coefficient (K,).
18. Which of the following is the definition of internal energy of a system? a.it is the sum of the kinetic energy of all of its components b.it is the sum of the rotational, vibrational, and translational energies of all of its components c.lt refers only to the energies of the nuclei of the atoms of the component molecules d.It is the sum of the potential and kinetic energies of the components
Half a mole of a perfect gas expands isothermally and at 298.15 K from a volume of 10 L to avolume of 20 L. (a) What is the change in the entropy of the gas? (b) How much work is doneon the gas? (c) What is the heat of Surroundings ? (d) What is the change in the entropy of the surroundings? (e)What is the change in the entropy of the system plus the surroundings?
Are the law of conservation of energy in dynamics and the First Law of thermodynamics identical? If not, describe the difference.
Derive the work expression for the reversible isothermal expansion of a van der Waals gas, assuming initial and final molar volumes, ?m1 and ?m2 , respectively. Show your derivation steps.
7:53 PM Mon Nov 21 < TOA 5.) A sample of 2.00 mol of a perfect gas is initially at a pressure of 111 kPa and temperature of 277 K. The sample is heated reversibly to 356 K at a constant volume. The constant volume molar heat capacity is 2.5R. Calculate the final pressure, AU, q, and w. n= 2.00 mol AT= 356 K-277 K= 79 K P= 111 kPa 1.11x 10³ Pa Cp.m= 2.5R = 2.5.8.314 / mcl.k= 20.79 J/mol K F w=0 AU= q Reversible pressure inside is same as pressure outside = m CSAT @87% q= 4 8