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physical chemistry
Physical Chemistry 3rd edition Thomas Engel, Philip Reid - Solutions
For a gas that obeys the equation of state Vm= Rt/P + B(T) derive the result dB(T) = B(T) – Tª ән т dт ӘР
Explain why CP,m is a function of temperature for ethane, but not for argon in a temperature range in which electronic excitations do not occur.
Show that dρ/ρ = −β/dT + κ/dP, where ρ is the density ρ = m/V. Assume that the mass, m, is constant.
Explain why ethene has a higher value for CV ,m at 800. K than CO.
Make a graph of the densities of a liquid and its gas as a function of the temperature from low temperatures up to the critical point. Explain the behavior at the critical point.
A differential dz = f (x, y) dx + g(x, y) dy is exact if the integral ∫ f (x, y) dx + ∫ g(x, y) dy is independent of the path. Demonstrate that the differential dz = 2xy dx + x2 dy is exact by integrating dz along the paths (1, 1) → (1, 8) → (6, 8) and (1, 1) → (1, 3) → (4, 3) → (4,
Why is ΔH sublimation = ΔH fusion + ΔH vaporization ?
A student gets up from her chair and pushes a stack of books across the table. They fall to the floor. Is the work associated with each part of this process positive, negative, or zero?
An athlete at high performance inhales ~3.75 L of air at 1.00 atm and 298 K. The inhaled and exhaled air contain 0.50 and 6.2% by volume of water, respectively. For a respiration rate of 32 breaths per minute, how many moles of water per minute are expelled from the body through the lungs?
Derive the following relation,for the internal pressure of a gas that obeys the Redlich€“Kwong equation of state, За aU av т /T 2TV, т + b) || RT 1 V — в тиИ, + b)
A perfectly insulating box is partially filled with water in which an electrical resistor is immersed. An external electrical generator converts the change in potential energy of a mass m which falls by a vertical distance h into electrical energy which is dissipated in the resistor. What value do
As the pressure is increased at −45°C, ice I is converted to ice II. Which of these phases has the lower density?
Under what conditions are ΔH and ΔU for a reaction involving gases and/or liquids or solids identical?
Use (∂U/∂V)T = (βT - kP)k to calculate (∂U/∂V)T for an ideal gas.
A bowling ball (a) Rolls across a table(b) Falls on the floor. Is the work associated with each part of this process positive, negative, or zero?
Explain how the ideal gas law can be deduced for the measurements shown in Figures 1.5 and 1.8.Figure 1.5Figure 1.8 0.1 L 2.5 2.0 1.5 0.2 L 1.0 0.3 L 0.4 L 0.5 L 0.6 L '0.5 тп -200 –100 0 100 200 300 400 Temperature/Celsius Pressure/bar 700 K 200 K Tпт 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Volume/10-2
Why does water have several different solid phases, but only one liquid and one gaseous phase?
Consider the equilibrium in the reaction 3O2(g) ⇋ 2O3(g). Assume that ΔHoR is independent of temperature.a. Without doing a calculation, predict whether the equilibrium position will shift toward reactants or products as the pressure is increased.b. Without doing a calculation, predict
In this problem, you calculate the error in assuming that ΔHoRis independent of T for the reaction2CuO(s) ‡‹ 2Cu(s) + O2(g).The following data are given at 25°C:
Under anaerobic conditions, glucose is broken down in muscle tissue to form lactic acid according to the reaction: C6H12O6(s) †’ 2CH3CHOHCOOH(s). Thermodynamic data at T = 298 K for glucose and lactic acid are given below.Calculate ΔS for the system, the
A 0.1429 g sample of sucrose, C12H22O11, is burned in a bomb calorimeter. In order to produce the same temperature rise in the calorimeter as the reaction, 2353 J must be expended.a. Calculate ΔU and ΔH for the combustion of 1 mole of sucrose.b. Using the data tables and your answer to (a),
Starting with the van der Waals equation of state, find an expression for the total differential dP in terms of dV and dT. By calculating the mixed partial derivatives (∂(∂P/∂V) ∂/∂T)V and (∂ (∂P/∂T)V/∂V)T , determine if dP is an exact differential.
Why does the triple point in a P–T diagram become a triple line in a P–V diagram?
Because U is a state function, (∂/∂V (∂U/∂T)V)T = (∂/∂T (∂U/∂V)T)V . Using this relationship, show that (∂CV/∂V)T = 0 for an ideal gas.
An ideal gas is expanded adiabatically into a vacuum. Decide which of q, w, ΔU and ΔH is positive, negative, or zero.
You get a P–T phase diagram by projecting a P–V–T phase diagram on the P–T plane.
You have containers of pure O2 and N2 at 298 K and 1atm pressure. Calculate ΔG mixing relative to the unmixed gases ofa. A mixture of 10.mol of O2 and 10.mol of N2b. A mixture of 10.mol of O2 and 20.mol of N2c. Calculate ΔG mixing if 10 mol of pure N2 is added to the mixture of 10 mol of O2 and
At 295 k, ∆HoR = 131.28 kJ mol-1 for the reaction C (graphite) + H2O(g) → CO(g), with CP,m = 8.53, 33.58, 29.12, and 28.82 J K-1 mol-1 for graphite. H2O(g), CO(g), and H2(g) respectively. Calculate ∆HoR at 240 oC form this information. Assume that the heat capacities are independent
Derive an expression for the internal pressure of a gas that obeys the Bethelot equation of state, P = RT/Vm – b – a TV2 m.
An ideal gas is expanded reversibly and isothermally. Decide which of q, w, ΔU, and ΔH is positive, negative, or zero.
Why does the liquid–gas coexistence curve in a P–T phase diagram end at the critical point?
A sample containing 2.50 mol of an ideal gas at 325 K is expanded from an initial volume of 10.5 L to a final volume of 60.0 L. Calculate ΔG and ΔA for this process for a. An isothermal reversible pathb. An isothermal expansion against a constant external pressure equal to the final
Show that the expression (ˆ‚U/ˆ‚V)T= T(ˆ‚P/ˆ‚T)V ˆ’ P can be written in the form т2 /т av ३
An ideal gas is expanded reversibly and adiabatically. Decide which of q, w, ΔU, and ΔH is positive, negative, or zero.
Calculate ΔGR???? for the reaction CO(g) + 1/2O2(g) → CO at 298.15 K. Calculate ΔGoR at 600. K assuming that ΔHoR is constant in the temperature interval of interest.
Is the following statement correct? If not, rewrite it so that it is correct. If ΔHoR for a chemical reaction does not change appreciably with temperature, the heat capacities for reactants and products must be small.
Using the result of Equation (3.8), (∂P/∂T)V = β /κ , express β as a function of κ and Vm for an ideal gas, and β as a function of b, κ , and Vm for a van der Waals gas.
What is the physical origin of the pressure difference across a curved liquid–gas interface?
The Joule coefficient is defined by (∂T /∂V)U = (1/CV )[P − T(∂P/∂T)V ]. Calculate the Joule coefficient for an ideal gas and for a van der Waals gas.
Discuss the following statement: Heating an object causes its temperature to increase.
Oxygen reacts with solid glycylglycine C4H8N2O3 to form urea CH4N2O, carbon dioxide, and water: 3O2(g) + C4H8N2O3(s) ⇋ CH4N2O(s) + 3CO2(g) + 2H2O(l)At T = 298 K and 1.00 atm, solid glycylglycine has the following thermodynamic properties:ΔGof = −491.5 kJ mol−1, ΔHof =
Discuss the following statement: If the temperature of the system increased, heat must have been added to it.
Can temperature be measured directly? Explain your answer.
A triple point refers to a point in a P–T phase diagram for which three phases are in equilibrium. Do all triple points correspond to a gas–liquid–solid equilibrium?
Give an example based on molecule–molecule interactions excluding chemical reactions, illustrating how the total pressure upon mixing two real gases could be different from the sum of the partial pressures.
Why are there no points in the phase diagram for sulfur in Figure 8.11 that show rhombic and monoclinic solid phases in equilibrium with liquid and gaseous sulfur?Figure 8.11 Liquid Monoclinic- solid 153°C, 1420 atm 95.39°C, 1 atm 115.21°C, 1 atm 444.6°C, 1 atm Rhombic -115.18°C, 3.2 x 10-5
Calculate the degree of dissociation of N2O4 in the reaction N2O4(g) ⇋ 2NO2(g) at 300. K and a total pressure of 1.50 bar. Do you expect the degree of dissociation to increase or decrease as the temperature is increased to 550. K? Assume that ΔHoR is independent of temperature.
The function f (x, y) is given by f (x, y) = xy sin 5x + x2ˆšy in y +3e-2x2cos y. DetermineandObtain an expression for the total differential df. 2² f af a (af ay ax of ay? ax У ay х a (af дх ду a (af әх ду .Is ay ду( дх У
A 22.0 g mass of ice at 273 K is added to 136 g of H2O(l) at 310 K at constant pressure. Is the final state of the system ice or liquid water? Calculate ΔS for the process. Is the process spontaneous?
Use the result of Problem P3.10 to derive a formula for (ˆ‚CV /ˆ‚V )Tfor a gas that obeys the Redlich€“Kwong equation of state, RT 1 a Vm - b VT VVm + b)' T VVm P:
Calculate ΔS°R for the reaction H2(g) + Cl2(g) → 2HCl (g) at 870. K. Omit terms in the temperature dependent heat capacities higher than T2 /K2.
A vessel containing a liquid is opened inside an evacuated chamber. Will you see a liquid–gas interface if the volume of the initially evacuated chamber is a. Less than the critical volume,b. A factor of 10 larger than the critical volumec. A factor of 1.05 larger than the critical volume?
Equation (3.38), CP = CV + TV (β2/κ). links CP and CV with β and κ . Use this equation to evaluate CP − CV for an ideal gas.
Assuming that ΔH°f is constant in the interval 275 K – 600. K, calculate ΔG° for the process *H2O, g, 298 K) → (H2O, g, 600, K). Calculate the relative change in the Gibbs energy.
Give a molecular level explanation as to why the surface tension of Hg(l) is not zero.
Beginning with Equation (5.5), use Equation (5.6) to eliminate Vc and Vd to arrive at the result w cycle = nR(T hot – T cold )lnVb /Va.
A sample of K(s) of mass 2.740 g undergoes combustion in a constant volume calorimeter. The calorimeter constant is 1849 J K–1, and the measured temperature rise in the inner water bath containing 1450. g of water is 1.60 K. Calculate ΔUof and ΔHof for K2O.
The parameter a in the van der Waals equation is greater for H2O than for He. What does this say about the difference in the form of the potential function in Figure 1.10 for the two gases?Figure 1.10 Ideal gas Real gas Itransition ľV=0 (1)A
Why are the triple point temperature and the normal freezing point very close in temperature for most substances?
Assuming that ΔHof is constant in the interval 275 K–600. K, calculate ΔGo for the process (H2O, g, 298 K) → (H2O, g, 600.K). Calculate the relative change in the Gibbs energy.
Calculate ΔS if the temperature of 2.50 mol of an ideal gas with CV = 5/2R is increased from 160. to 675 K under conditions of a. Constant pressureb. Constant volume.
Calculate w, q, ΔH, and ΔU for the process in which 1.75 mol of water undergoes the transition H2O(l, 373 K) → H2O(g, 610.K) at 1 bar of pressure. The volume of liquid water at 373 K is 1.89 × 10−5 m3 mol−1 and the molar volume of steam at 373 and 610.K is 3.03 and 5.06 × 10−2
Calculate ΔH and ΔS if the temperature of 1.75 moles of Hg(l) is increased from 0.00oC to 75.0oC at 1 bar. Over this temperature range, CP,m = (J K-1 mol-1) 30.093 – 4.944 × 10-3 T/K.
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