Homework+4+Solutions

# Homework+4+Solutions - BME 221 Homework#4(50 pts Due...

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Unformatted text preview: BME 221 Homework #4 (50 pts) Due: Beginning of class on November 13 th 1. Calculate (a) the (molar) Gibbs energy of mixing (b) the (molar) entropy of mixing when the two major components of air (nitrogen and oxygen) are mixed to form air at 25°C. The mole fractions of N 2 and O 2 are 0.78 and 0.22, respectively. Is the mixing spontaneous? (4 pts) a) ∆ mix G = nRT(x 1 ln x 1 + x 2 ln x 2 ) ∆ mix G/n = RT(x 1 ln x 1 + x 2 ln x 2 ) = (8.314 J mol-1 K-1 )(298.15 K)(0.78 ln 0.78 + 0.22 ln 0.22) ∆ mix G/n = -1306 J/mol b) ∆ mix S/n = -(∆ mix G/n)/T = (-1306 J/mol)/(298.15 K) = +4.38 J/mol/K c) yes, mixing is spontaneous because ∆ mix G < 0 2. a) Assuming ideality, estimate the vapor pressure of seawater at 20°C given that the vapor pressure of pure water is 2.338 kPa at that temperature and the solute is largely Na + and Cl- ions, each present at about 0.50 mol/dm 3 . Assume the density of seawater is approximately 1 g/mL. b) Based on your result, does the water in seawater have a lower or a greater tendency to evaporate than pure water? Explain (i) based on chemical potential and (ii) based on the molecules present at the surface of pure water and on the surface of seawater. (5 pts) a) Vapor pressure of seawater can be estimated by Raoult’s law: P seawater = X water P* water 98 . . 1 5 . 55 5 . 55 X water = + = + = mol mol mol n n n solute water water , where n solute = 0.50 mol Na + +0.50 mol Cl- p seawater = 0.98(2.338 kPa) = 2.30 kPa b) The vapor pressure of seawater is lower; therefore it has a lower tendency to evaporate. (i) Water in the salt solution is more stable (has a lower chemical potential) than water in its pure form. At equilibrium, the chemical potential of water in the vapor phase of the salt solution will also be lower (since at equilibrium both chemical potentials have to be the same). Thus, it will have a lower tendency to evaporate. (ii) Some molecules at the surface of seawater will be Na + or Cl- ions instead of H 2 0 molecules. Hence fewer water molecules can escape to the vapor phase per time interval, while still the same number of water molecules can condense from the vapor phase on the surface of the liquid phase per time interval, hence lowering the vapor pressure. 3. What is the ionic strength of a solution that contains 0.1 m KCl and 0.05 m MgCl 2 . (2 pts) [K + ] = 0.1 m , [Mg 2+ ] = 0.05 m , [Cl- ] = 0.1 + 2*0.05 = 0.2 m I = ∑ i i i z m 2 2 1 = 0.5(0.1*1 2 + 0.05*2 2 + 0.2*(-1) 2 ) = 0.25 m 4. a) Why do extremely dilute charged particles in an electric field move slower in an aqueous that contains other ions at much higher concentration in solution compared to the same particles in the same field in a non-aqueous, non-conducting medium (i.e. no ions present in this non- conducting solution)? Assume that the viscosity of both media is the same. Give two reasons. b) Why does the conductance of an aqueous solution of NaCl initially increase with conc of NaCl and then decrease? (3 pts) a) In ionic solution, the ions of solution of opposite charge shield the charged particles by...
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Homework+4+Solutions - BME 221 Homework#4(50 pts Due...

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