TBR gas passage

[premedicine555]

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passage III, Q 19
for a ball that is 60% submerged, what is observed when compared to ball in figure 1 (it is 50% submerged. initial volume of ball is 36 liters), under same conditions.
I narrowed it down to C and D. and don't know what to do from then on..
C: Depth at which density of ball =density of water is below -32 feet
DDepth at which density of ball =density of water is above -32 feet

question: why is the answer D? I thought since it is 60% submerged, that it's volume needs to be decreased by 6 (and 36/6 is 6 as the new volume, at which the depth >50ft [from table]) in order for the density of the ball to equal density of surrounding water.

 

[loveoforganic]

I don't have the book and don't fully understand your question, but I have a feeling the issue is that you're dealing with real, not ideal, gases, so your compressed volume will be slightly larger than predicted

 

[premedicine555]

Sorry, just realized the wording was confusing.

The questions asks: "For a ball that is 60% submerged, what is observed when compared to ball in figure 1 under same conditions?
Background info: the ball in figure 1 is 50% submerged. The initial volume of the ball is 36 liters. Also, the water has salt added to it, which is more dense than freshwater.

C) The depth at which the density of the ball equals the density of surrounding water is below -32 feet, because the ball is denser than the orignal ball in the experiment
D) The depth at which the density of the ball equals the density of surrounding water is above-32 feet, because the ball is denser than the orignal ball in the experiment

Answer is D

There is also a table that has the depth, pressure, and volume of the ball. Except the depths range from 5 to 50--which are POSITIVE values. I don't understand why the choice has a negative "-32" value.

 

[MedPR]

Bump. I didn't get this problem either.

 

[BerkReviewTeach]

If the ball is 50% submerged at the surface, then it has 50% the density of water (the surrounding medium), making it 0.50 g/mL. When you submerge the ball to 32 ft below the surface, the surrounding pressure goes from 1 atm (at the surface) to 2 atm (the surface + 1 atm from the water above). When the external pressure doubles, the volume of the ball is cut in half. This means that the ball would occupy 18 mL at a depth of 32 ft and have a density of 1.00 g/mL. It is thus equal to the density of water at a depth of 32 ft.

The new ball is 60% submerged at the surface, so it has a density that is 60% that of water = 0.60 g/mL. To raise the density to 1.00 g/mL, its volume would need to decrease to 60% x 36 L = 21.6 L. This would require that the external presure increase to a value less than 2.00 atm (the exact value is 1.67 atm). To get to 1.67 atm external pressure, you'd need to submerge the ball to about 21 to 22 ft (where total pressurer is 1 atm due to air and 21-22/32 x 1 atm due to the water above).

Was this explanation clear and helpful? I hope it worked.

 

[chiddler]

Besides the very helpful explanation above, my thought process was as follows:

32 feet is required for the original 50% ball. (this is given in the passage, if i remember correctly).

The 60% ball is more dense. Does it need more or less pressure to make its density equal to surrounding water compared to the 50% ball?

It needs less pressure, because it already (innately) contains more density. Therefore, the depth can be above 32 feet.

 

[premedicine555]

Thank you BerkeleyReviewTeach! For some reason I kept multiplying by 6 instead of 0.60! And the whole negative values threw me off.. -32=32ft in the table, they just changed up the signs to make it "below" the surface. Make sense now!

And thanks Chidder--I thought that pressure would increase for some reason since it was more dense because more density = less volume = more pressure. but i realize that it's wrong because even though you decrease your volume by 60% of the original, that doesn't mean your pressure is 60% of the original.

 

[BerkReviewTeach]

Thank you BerkeleyReviewTeach! For some reason I kept multiplying by 6 instead of 0.60! And the whole negative values threw me off.. -32=32ft in the table, they just changed up the signs to make it "below" the surface. Make sense now!

And thanks Chidder--I thought that pressure would increase for some reason since it was more dense because more density = less volume = more pressure. but i realize that it's wrong because even though you decrease your volume by 60% of the original, that doesn't mean your pressure is 60% of the original.

Chiddler's approach is way better for the MCAT than my explanation, so hopefully my explanation helped clear up the numbers but people will use Chiddler's approach on the actual MCAT.