7.66 (a) Consider a two-phase system, where one phase is pure liquid A and the second phase is an ideal gas mixture of A vapor with inert gas B (assumed insoluble in liquid A). The presence of gas B changes μA, the chemical potential of liquid A, because B increases the total pressure on the liquid phase. However, since the vapor is assumed ideal, the presence of B does not affect μg, the chemical potential of A in the vapor phase [see Eq. (6.4)]. Because of its effect on μ¼, gas B affects the liquid-vapor equi- librium position, and its presence changes the equilibrium vapor pressure of A. Imagine an isothermal infinitesimal change dP in the total pressure P of the system. Show that this causes a change dPA in the vapor pressure of A given by А dPA V¹m.A Vm.APA const. T (7.38) dP V8 m,A RT Equation (7.38) is often called the Gibbs equation. Because V m,A' m,A is much less than Vg the presence of gas B at low or moder- ate pressures has only a small effect on the vapor pressure of A. (b) The vapor pressure of water at 25°C is 23.76 torr. Calculate the vapor pressure of water at 25°C in the presence of 1 atm of inert ideal gas insoluble in water.

What is AG for the decomposition of CaCO3 at 298 K and a partial pressure of CO2 of 4.00x10-4 bar? CaCO3(s) → CaO(s) + CO2(g) AGrxn (298 K, Pco2 = 0.400 mbar) = ??? CO2(g) Compound AG°; (kJ mol·1) CACO3(s) СаО(s) -1129 -604 -394

Osmotic pressures are often reported in units of atmospheres or mm Hg. The latter impliesthat the height of a column of liquid can be used as a measure of pressure. This is, in fact, thebasis of the torricellian barometer from which the units of “torr” come. The pressure, P, isrelated to the height of the column by:P = ρghwhere ρ is the density of the liquid, g is the acceleration due to gravity and h is the height. Whatwill be the height (in mm) of a column of aqueous solution with a density of 0.9987 g/mL, if theosmotic pressure of the solution at 25 °C is 1.4 mm Hg? The density of mercury at thistemperature is 13.8 g/mL

Henry’s law constant for CO2 in the water at 25 °C is 3.1 * 10-2 M atm-1. (a) What is the solubility of CO2 in the water at this temperature if the solution is in contact with air at normal atmospheric pressure?

2.28(b) Set up a thermodynamic cycle for determining the enthalpy of hydration of Ca?+ ions using the following data: enthalpy of sublimation of Ca(s), +178.2 kJ mol-1; first and second ionization enthalpies of Ca(g), 589.7 kJ mol-1 and 1145 kJ mol¬1; enthalpy of vaporization of bromine, +30.91 kJ mol-1; dissociation enthalpy of Br,(g), +192.9 kJ mol-1; electron gain enthalpy of Br(g), –331.0 kJ mol-1; enthalpy of solution of CaBr,(s), –103.1 kJ mol-'; enthalpy of hydration of Br¯(g), –337 kJ mol¬!.

State whether the entropy of the system increases or de-creases in each of the following processes:(a) Pure gases are mixed to prepare an anesthetic.(b) Electronic-grade silicon is prepared from sand.(c) Dry ice (solid CO₂) sublimes.

At 20 °C, the vapor pressure of benzene (C6H6) is 75 torr,and that of toluene (C7H8) is 22 torr. Assume that benzeneand toluene form an ideal solution. (a) What is thecomposition in mole fraction of a solution that has a vaporpressure of 35 torr at 20 °C? (b) What is the mole fractionof benzene in the vapor above the solution describedin part (a)?

13.21 Two nonpolar organic liquids, hexane (C6H14) and heptane (C7H16), are mixed. (a) Do you expect AHsoln to be a large positive number, a large negative number, or close to zero? Explain. (b) Hexane and heptane are miscible with each other in all proportions. In making a solution of them, is the entropy of the system increased, decreased, or close to zero, compared to the separate pure liquids?

State whether the entropy of the system increases or decreases in each of the following processes:(a) Gasoline burns in a car engine.(b) Gold is extracted and purified from its ore.(c) Ethanol (CH3CH2OH) dissolves in 1-propanol (CH3CH2CH2OH).

The following table presents the solubilities of severalgases in water at 25 °C under a total pressure of gas andwater vapor of 1 atm. (a) What volume of CH4(g) understandard conditions of temperature and pressure is containedin 4.0 L of a saturated solution at 25 °C? (b) Thesolubilities (in water) of the hydrocarbons are as follows:methane < ethane < ethylene. Is this because ethyleneis the most polar molecule? (c) What intermolecularinteractions can these hydrocarbons have with water?(d) Draw the Lewis dot structures for the three hydrocarbons.Which of these hydrocarbons possess p bonds?Based on their solubilities, would you say π bonds aremore or less polarizable than s bonds? (e) Explain whyNO is more soluble in water than either N2 or O2. (f) H2S is more water-soluble than almost all the other gasesin table. What intermolecular forces is H2S likely to havewith water? (g) SO2 is by far the most water-soluble gasin table. What intermolecular forces is SO2 likely to havewith…