Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 4, Problem 4.44E
Interpretation Introduction
Interpretation:
The expression
Concept introduction:
The Maxwell relations are the equations showing the relation between
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Since we will be dealing with partial derivatives later in the semester, this is a good opportunity to review this topic (see appendix C). Then evaluate the following partial derivatives
(a) PV = nRT; (∂ P/∂V)T
(b) r = (x2 + y2 + z 2 )1/2; (∂ r/∂y)x,z
(a) Express (∂Cp/∂P)T as a second derivative of H and find its relation to (∂H/∂P)T. (b) From the relationships found in (a), show that (∂Cp/∂V)T=0 for a perfect gas.
Calculate V−1(∂V/∂T)p,n for an ideal gas?
Chapter 4 Solutions
Physical Chemistry
Ch. 4 - List the sets of conditions that allow dS, dU, and...Ch. 4 - Explain why conditions for using S>0 as a strict...Ch. 4 - Explain how the equation dU+pdVTdS0 is consistent...Ch. 4 - Explain why the spontaneity conditions given in...Ch. 4 - Prove that the adiabatic free expansion of an...Ch. 4 - Derive equation 4.6 from equation 4.5.Ch. 4 - Derive equation 4.8 from equation 4.7.Ch. 4 - The third part of equation 4.9 mentions a...Ch. 4 - Calculate A for a process in which 0.160mole of an...Ch. 4 - What is the maximum amount of non-pV work that can...
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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- Show that CP = VT α (∂P/∂T) Sarrow_forwardRearrange 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.arrow_forwardA 0.250 mol nitrogen initially at 50 °C with a volume of 8.00 L is allowed to expand reversibly and adiabatically until its volume has doubled. Calculate the value of ΔHwhen Cp = 7/2R.arrow_forward
- (a) Write expressions for dV and dp given that V is a function of p and T and p is a function of V and T. (b) Deduce expressions for d ln V and d ln p in terms of the expansion coefficient and the isothermal compressibility.arrow_forwardWhat is Isothermal Expansion of a van der Waals Gas?arrow_forwardThe density of lead is 1.13 ✕ 104 kg/m3 at 20.0°C. Find its density (in kg/m3) at 100°C. (Use ? = 29 ✕ 10−6 (°C)−1 for the coefficient of linear expansion. Give your answer to at least four significant figures.)arrow_forward
- The cohesive energy density, U, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that U = 1/2N2∫V(R)dτ where N is the number density of the molecules and V(R) is their attractive potential energy and where the integration ranges from d to infinity and over all angles. Go on to show that the cohesive energy density of a uniform distribution of molecules that interact by a van der Waals attraction of the form −C6/R6 is equal to −(2π/3)(NA2/d3M2)ρ2C6, where ρ is the mass density of the solid sample and M is the molar mass of the molecules.arrow_forwardA sample of 2.2 mol CO2(g) is originally confined in 15 dm3 at 280 K and then undergoes adiabatic expansion against a constant pressure of 78.5 kPa until the volume has increased by a factor of 4.0. Calculate ΔT. (The final pressure of the gas is not necessarily 78.5 kPa.)arrow_forwardP2D.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.arrow_forward
- Use the virial equation of state to calculate the pressure exerted by 1.00 mol CH4, at 273 K confined to a volume of 1.00 cm3 , given the value of the second virial coefficient, B = -53.6 cm3 mol-1, at this temperature. You may assume that the expansion may be truncated after the second term.arrow_forwardCp− ̄Cv=T ̄V β^2/κ reduces to ̄CP− ̄CV=R for an ideal gas.arrow_forwardCalculate the work done during the isothermal reversible expansion of a gas that satisfies the virial equation of state (eqn 1C.3b) written with the first three terms. Evaluate (a) the work for 1.0 mol Ar at 273 K (for data, see Table 1C.3) and (b) the same amount of a perfect gas. Let the expansion be from 500 cm3 to 1000 cm3 in each case.arrow_forward
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