Answer:
a) Δπ = 1.264 atm
b) W = 128 joules
c) ΔH >> W ( a factor greater than 17,000 )
Explanation:
a) The osmotic pressure, π , is determined by :
π = nRT/V, where n= moles of solute
R= 0.0821 Latm/kmol
T = 300 K
calling π(sw) osmotic pressure for for sea water and π (fw) for fresh water,
salinity of sea water = 3.5 g / 1L water (assuming only NaCl for the salts)
salinity of fresh water = 0.5 parts per thousand (range: 0- 0.5 ppt)
πsw = (3.5 g/58.44 g/mol) (0.0821 Latm/Kmol) (300 K ) /1 L = 1.475 atm
πfw = (0.5 g/58.44 g/mol) (0.0821 Latm/Kmol) (300 K ) /1 L = 0.211 atm
d water = 1 g/cm³
Δ π = (1.475 - 0.211) = 1.264 atm
b) W = Δπ V = 1.426 atm x 1L = 1.43 L-atm
1 L-atm = 101.33 j
W = 101.33 j/ Latm x 1.43 Latm = 128 joules
c) ΔH = Q₁ + nΔH vap, where
Q₁ = heat required to bring the solution from 300 K to boiling, 373 K
ΔH vap = heat of vaporization
Q = mCΔT = 1000 g x 4.186 j x 73 K = 305.6 j = 0.3056 kj
ΔH vap = (1000 g/ 18 g/mol ) 40.7 kj/mol = 2,261 kj
ΔH = 0.3056 kj + 2,261 kj = 2,261.3 kj
Note = Q << ΔH vap and we could have neglected it.
This result shows why nobody talks about evaporation of sea water to produce fresh water ΔH >> W
) ions in aqueous solution.