a. If mercury has a S.G. of 13.6, what is it\'s density in Ibm/ft^3? b. A storag

Question

a. If mercury has a S.G. of 13.6, what is it's density in Ibm/ft^3? b. A storage tank is pressurized with ethane to 450 psi. At the top of the tank are two ports. The first has a diameter of 10 , and the second has a diameter of 2 . What force (lbt) is exerted on each port? C. A new lab tech, upon evaluating the contents of a solution, declared that it was a 32 molar solution of ethanol in water. Discuss his conclusion. d. The planet Arethia has quicksilver seas and no atmosphere to speak of. Your Exploracraft^Tm IV spaceship can withstand pressures of up to 2000 psi. If the gravity on planet Arethia is 2.56 times as strong as the gravity on earth, how deep (in meters) can your Exploracraft^Tm IV delve into the seas? c. 20 L of a 5 molar solution of acetic acid is added to 3 L of isopropyl alcohol. What are the mole fractions of each species?

Explanation / Answer

3.a. Hg has a density 13.6 times the density of H2O, which gives (13.6)( 1.0 g/cm3 ) or 13.6 g/cm3 . We now need to convert these metric units to lbm/ft3 .

( 13.6 g/cm3)( 1 kg/ 1000 g) ( 2.205 lbm / kg) (2.54 cm/in)3 (12 in /ft)3 = 849.2 lbm/ ft3 .

3. b. Both pressures, P, are the same according to Pascal's Law.   Force F = (P) (A), where P = 450 lbf / in2 .

For the large port, diameter = 10 in and Radius R = 5 in.    A = pi R2 = pi (5 in)2 = 78.54 in2 .

F = (450 lbf /in2 )(78.54 in2 ) = 35,342.9 lbf.  

For small port, diameter = 2 in and R = 1 in.   A = pi (1 in )2 = 3.142 in2 . F = (450 lbf/in2)(3.142 in2)= 1,413.7 lbf.

3.c. Molarity means the number of moles of solute (ethanol in this case) per Liter of soln. Ethanol has a molecular mass (MW) of approx 46 grams/mole, so a 32 Molar soln would consist of (32 moles)(46 g/mole) = 1,472 grams of ethanol dissolved in water so as to make 1 Liter of solution.

3. d. "Quicksilver" means liquid Hg. We found the mass density of Hg in part (a) to be 849.2 lbm/ ft3 .

Pressure P in a liquid of depth h is     P   = (density ) g h .

               (2000 lbf / in2)(144 in2 / 1 ft2 ) =   (849.2 lbm/ ft3)(2.56)(32) h .   Solve for h in units of ft to get h = 4239.3 ft

and then convert that to meters, as requested:   (4239.3 ft )( 0.3048 m/ft) =   1292.1 m = h

3.e.   In this question, the molarity of the isopropyl alcohol is not given , so we cannot answer the question.

However, assuming a molarilty of 5M also for isopropyl alcohol, here is the calculation.  

#moles of acetic acid = (5 moles/L)(20 L) = 100 moles.

# moles of isopropyl alcohol = ( 5 moles/L) (3 L) = 15 moles

thus , the total number of moles is 115 moles.

mole fraction of acetic acid = 100 / 115 = 0.87

mole fraction of isopropyl alcohol = 15/ 115 = 0.13

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