Rearrange the van der Waals equation of state, p = nRT/(V − nb) − n2a/V2(Topic 1C) to give an expression for T as a function of p and V (with n constant). Calculate (∂T/∂p)V and confirm that (∂T/∂p)V = 1/(∂p/∂T)V.

Rearrange the van der Waals equation of state, p = nRT/(V − nb) − n2a/V2(Topic 1C) to give an expression for T as a function of p and V (with n constant). Calculate (∂T/∂p)V and confirm that (∂T/∂p)V = 1/(∂p/∂T)V.

Chemistry: The Molecular Science

5th Edition

ISBN:9781285199047

Author:John W. Moore, Conrad L. Stanitski

Publisher:John W. Moore, Conrad L. Stanitski

Chapter9: Liquids, Solids, And Materials

Section: Chapter Questions

Problem 45QRT: At the critical point for carbon dioxide, the substance is very far from being an ideal gas. Prove...

See similar textbooks

Related questions

Q: 2) The equation of state of a certain gas is given by p where a and b are constants. Find Vm 4),

A: The equation given is, => To find :

Q: Hot-air balloons gain their lift from the lowering of density of air that occurs when the air in the…

Q: The maximum in the Maxwell–Boltzmann distribution occurs when df(v)/dv = 0. Find, by…

Q: A diving bell has an air space of 3.0 m3 when on the deck of a boat. What is the volume of the air…

A: pressure exerted by fluid when an object is immersed in a fluid is a hydrostatic pressure. this…

Q: 20.7 cm3 of a pure vapour, at 1.136 atm, and 98.3 °C has a mass of 0.0603 g. Calculate the molar…

Q: What is the equivalent value of T = 50° C in kelvins?We can use Equation (11.9) :T(K) T( C)+ 273 =…

A: The relation between temperature in degree C°C and degree Fahrenheit°F is, T(K)=T(°C) + 273.15

Q: A sample of helium (perfect gas) undergoes a following two-step process.1. Isothermal reversible…

A: According to the first law of thermodynamics, A) For a reversible isothermal process, the…

Q: A sample of nitrogen initially at T = 25 oC and p = 4.0 atm triples its initial volume. What will be…

Q: The cohesive energy density, U, is defined as U/V, where U is the mean potential energy of…

Q: 17.6 cm3 of a pure vapour, at 1.153 atm, and 98.5 °C has a mass of 0.0520 g. Calculate the molar…

A: Given :- pressure = 1.153 atm Volume = 17.6 cm3 Temperature = 98.5°C mass = 0.0520 g To…

Q: Justify the formulation of the van der Waals equation of state.

A: There are two types of gases are studied in gaseous phase. One is ideal and other is real gas. A gas…

Q: 3) Derive the Joule -Tuomson coefficiant for Virial eguation of state in terms of volume expausion.

A: Answer is explained below.

Q: The Prandtl number of common gases at 1 atm

A: Prandtl number is a dimensionless quantity and gives the relation between momentum diffusivity and…

Q: In the following balanced reaction: 2Al(s) + 6HCl(aq) → 2AlCl3(s) + 3H2(g) 2.32 g of Al react…

A: Given: The temperature of H2 gas, (T) = 25oC = (25 + 273) = 298 K. The molar mass of Hydrogen atom =…

Q: The energy of the van der Waals bond, which is responsible for a number of the characteristics of…

A: (a) It is given that the van der Waals bond energy for water is 0.50 eV. The expression for…

Q: Consider Argon (Ar) gas at a pressure of 1 bar and temperature of 300 K. The equivalent hard sphere…

A: We will be using the following formulae for solving the given problems: 1. PV=nRT .. (1) Here, 'P'…

Q: be shipped as a liquid. Suppose 2.62 × 10° ft of methane is oxidized to methanol at 1.00 atm and 25…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use the virial equation of state to calculate the pressure exerted by 1.00 mol CH4, at 273 K…

A: GIVEN: Vm=1.00 cm3 =0.001 Litre R=0.082057 L atm K-1mol-1 T=273K n=1 mol CH4 B2(T)=-53.6 cm3…

Q: Derive an expression for ⟨vn⟩1/n from the Maxwell–Boltzmann distribution of speeds.

Q: Considering the first law of thermodynamics, obtain the fluid equation when dE + p.dV = T.dS is…

A: Solution -

Q: Calculate the pressure exerted by 1.0 mol C2H6 behaving as a van der Waals gas when it is confined…

Q: When dealing withsolving a question using the Clausis-Clapeyron Equasion does it matter if you solve…

Q: Q2: Calculate the mole fraction of 15 % (w/w) C6H1206?

Q: 4. Consider a sample of gas at 393 K and 22 atm. (a) Calculate the molar volume V (L/mol) of the…

Q: Express the van der Waals equation of state as a virial expansion in powers of 1/Vm and obtain…

A: Vander wall equation for real gases is given as,(P+aVm2)(Vm-b)=RT.........1st.Re arranging the above…

Q: 圖) V- b SP (2a/RV³)(V – b)? –T

A: A van der Waal gas or a real gas is a gas that follows the van del Waal equation which will be as…

Q: (1) The relationship between C P.m and C xm can also be given by the relationship: Срт — Сут ƏT (a)…

Q: Calculate the molar change in chemical potential of an ideal gas that expands by 10 times its…

A: The molar change in chemical potential of an ideal gas that expands by 10 times its original volume…

Q: Calculate the value of Cp at 298K and 1 atm pressure predicted for CH4(g) and C2H4(g) by the…

A: The expression relating the molar heat capacity at constant pressure and molar heat capacity at…

Q: 9. Consider a sample of water vapour, which expands reversibly and adiabatically from 97.3 Torr and…

A: We have reversible adiabatic expansion of water from 97.3 torr 400 cm3 to 5 dm3 , we have to…

Q: Investigate the dependence of pV on V for real gases.

A: In case of ideal gas product of pressure and volume in isothermal process remains constant as: for…

Q: Consider a particular gas. The isothermal compressibility and coefficient of thermal expansion are…

A: Given , Isothermal compressibility : κ=Vc1T (l) Coefficient of thermal expansion : α=1T+ c2c1V…

Q: A determination of the density of a gas or vapour can provide a quick estimate of its molar mass.…

A: The ideal equation for gas is given by, PV = nRT…

Q: Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q :…

A: Factor of 1N! is usually used for indistinguishable particles, that means those particles which are…

Q: Use the tables of moist-air properties to find the enthalpy and specific volume for air at 125°F…

Q: Q2: Calculate the mole fraction of 15 % (w/w) C6H12O6?

A: Welcome to bartleby !

Q: The diameter of an Xe atom is 216 pm. What is the mean free path in nm of 0.75 mol Xe confined in 7…

A: Given Values: The diameter of Xe atom is 216 pm The mole of Xe is 0.75 and volume is 7 L and…

Q: please don't round off util the final answers. Determine the Boyle temperature of hydrogen. Pc =…

A: Solution -

Q: P2D.2 Starting from the expression Cp − CV = T(∂p/∂T)V(∂V/∂T)p, use the appropriate relations…

A: Given Cp − CV = T(∂p/∂T)v(∂V/∂T)p

Q: what will happen to the root mean square speed If the kinetic energy of ideal gas and volume…

Q: 4. The density of a gaseous compound was found to be 1.23 kg/m 3 at 330 K and 20 kPa. What is the…

Q: A certain gas obey's the following equation of state: RT P = V – b V²T a Write the constants a and b…

A: The values of a and b in Van der waals equation has to be given in terms of P,V and T.

Q: A rigid vessel of volume 0.2m3 contains 10 kg of (liquid + vapor) water at 200°C. What are the…

A: Here i have calculated pressure using ideal gas equation

Q: Is the statement true of false? Support the answer a. For a fixed amount of a perfect gas, U and H…

A: According to the first law of thermodynamics, the enthalpy change of a system is related to the…

Q: Gallium melts just above room temperature and is liquid overa very wide temperature range (30–2204…

A: In a barometer, the relationship between pressure and density is given as :

Concept explainers

Repulsive and Total Interactions Between Molecules

Intermolecular forces are the repulsive or attractive interaction between the molecules. Due to the coulomb’s law, there will be a coulomb force that exists between two or more charged species. If the charge of both molecules is positive or negative, then that will lead to repulsive forces. When they have opposite charges, then the force is attractive.

Question

100%

Rearrange the van der Waals equation of state, p = nRT/(V − nb) − n²a/V²
(Topic 1C) to give an expression for T as a function of p and V (with n constant). Calculate (∂T/∂p)V and confirm that (∂T/∂p)V = 1/(∂p/∂T)V.

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Repulsive and Total Interactions Between Molecules

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

The van der Waals coefficients of monatomic krypton gas are a=0.2318m^6Pa/mol^2 and b=39.78×10^6 m^3/mol. What is the change in temperature, ΔT, when one mole of krypton gas undergoes a Joule free expansion from 0.1 L to 10 L?
P1C.4 Calculate the volume occupied by 1.00 mol N2 using the van der Waals equation expanded into the form of a virial expansion at (a) its critical temperature, (b) its Boyle temperature. Assume that the pressure is 10 atm throughout. At what temperature is the behaviour of the gas closest to that of a perfect gas? Use the following data: Tc = 126.3 K, TB = 327.2 K,a = 1.390 dm6 atm mol−2, b = 0.0391 dm3 mol−1.
The Dieterici equation of state is similar to the van der Waals equation in that they both employ gas-specific constants a and b to attempt to account for the interaction between molecules and the nonzero volume of the individual molecules of gas. However, the Dieterici equation of state has a significantly different functional form: ?(? − ?) = ??? -a ⁄ (RVT) Note that a and b are constants (n is implicitly constant as volume is expressed as molar volume). What are the following partial derivatives for the Diererici equation of state? a) (∂P/∂T)V b) (∂V/∂P)T
2. (a) Calculate the compression factor for carbon dioxide at its critical point given that Tc = 31∘C ,pc = 72.9 atm and vc= 94.0 cm3 mol−1.
P2D.2 Starting from the expression Cp − CV = T(∂p/∂T)V(∂V/∂T)p, use theappropriate relations between partial derivatives (The chemist’s toolkit 9 inTopic 2A) to show thatC CT V TV p( / )( / ) p VpT2− = ∂ ∂∂ ∂ Use this expression to evaluate Cp − CV for a perfect gas.
Calculate the amount of energy in the form of heat that is produced when a volume of 4.37 L of SO2(g) is converted to 4.37 L of SO3(g) according to this process at constant pressure and temperature of 1.00 bar and 25.0 ° C. Assume ideal gas behavior.
Calculate the pressure exerted by 1.0 mol C2H6 behaving as a van der Waals gas when it is confined under the following conditions: (i) at 273.15 K in 22.414 dm3, (ii) at 1000 K in 100 cm3. Use the data in Table 1C.3 of the Resource section.
Use the virial equation of state to calculate the pressureexerted by 1.00 mol CH4, at 273 K confined to a volumeof 1.00 cm3, given the value of the second virial coefficient.B = -53.6 cm3 mol·'. at this temperature. You may assumethat the expansion may be truncated after the second term.
13. (a). ] Determine the reduced temperature, reduced pressure and reduced molar volume of a sample of argon with a molar volume of 4.518 L at 10.0°C and 3.00 bar pressure. For Ar, T=150.86 K, Vc = 74.57 x 10-³ L, P = 48.98 bar (b) [Calculate the P and I values for which NH3 is in a corresponding state with Ar. For NH3, Tc-405.40 K, P. 113.53 bar
Cylinders of compressed gas are typically filled to a pressure of 200 bar. For oxygen, what would be the molar volume at this pressure and 25 °C based on (i) the perfect gas equation, (ii) the van der Waals equation? For oxygen, a = 1.364 dm6 atm mol−2, b = 3.19 × 10–2 dm3 mol−1.
1) Write out the Ideal Gas Law equation and the van der Waals equation. 2) List each variable in both equations. Then provide the identity and units for each variable in your list. 3) It is possible to show how the units all cancel out for the Ideal Gas Law by showing every unit on both sides of the equation like this: P V = n R T (atm) (L) = (mol) (L atm/mol K) (K) Please show that all units in the van der Waals equation cancel out in the same way
13. (a) ] Determine the reduced temperature, reduced pressure and reduced molar volume of a sample of argon with a molar volume of 4.518 L at 10.0°C and 3.00 bar pressure. For Ar, T=150.86 K, Vc = 74.57 x 10-³ L, P = 48.98 bar (b) [ Calculate the P and I values for which NH3 is in a corresponding state with Ar. For NH3, Tc=405.40 K, Pc = 113.53 bar