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The website http://www.windows2universe.org/earth/Water/density.html (Links to a

ID: 700899 • Letter: T

Question

The website http://www.windows2universe.org/earth/Water/density.html (Links to an external site.)Links to an external site. gives the density profile below for ocean water as a function of depth. What is the pressure 2000 m into the ocean, given this profile? Do this problem in two ways: First, assume a uniform SG = 1.025 for the whole depth, and find the pressure. Second, approximate the density as linear up to a depth of 1000 m, then uniform below that. What is the % difference?  answer = 1) 200.9 » 201 bar, 2) 201.3 » 201 bar, 3) % dif = 0.22%. They are very close. It would have been a good approximation to use either SG = 1.025 or 1.028 for the whole calculation.

Polystyrene (PS) is essentially insoluble in water, but dissolves in toluene readily. We have a PS-toluene solution at 27 C that is 10.0% by mass PS, has a solution density of 878.76 kg/m3, and a measured PS molecular weight of 190,000. Pure toluene has a density of 860.52 kg/m3.  What is the specific gravity of the PS-toluene solution? What is the molarity of the PS-toluene solution?

Explanation / Answer

Ans 2

specific gravity of the PS-toluene solution

= density of the PS-toluene solution/density of water

= 878.76 / 1000

= 0.87876

For 100 kg solution

Mass of PS = 10 kg

Molecular weight of PS = 190000 kg/kmol

Moles of PS = mass/molecular weight

= 10/190000

= 5.263 x 10^-5 kmol

Mass of toluene = 90 kg

Moles of toluene = 90/92.14 = 0.977 kmol

Mol fraction of PS, X1 = 5.386 x 10^-5

Mol fraction of toluene, X2 = 0.9999

Average molecular weight

M avg = X1 * M1 + X2 * M2

= 5.386 x 10^-5 x 190000 + 0.9999 x 92.14

= 102.28 kg/kmol

molarity of the PS-toluene solution

= (878.76 kg/m3)/(102.28 kg/kmol)

= 8.591 kmol/m3

= 8.591 mol/L

= 8.591 M