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Question
(10 of 10)
you have two beakers labeled a and b. beaker a has a 3.0 m nacl solution inside and beaker b has a 2.0 m mgcl2 solution. you take two dialysis bags (permeable to water but not glucose or any ions), and each are filled with a 1.5 osm glucose solution and place one in beaker a and one in beaker b, at the same time. which of the following is true?
- the rate of osmosis in beaker a is slower than beaker b
- water will flow out of both dialysis sacs, into their respective beakers, at the same rate until equilibrium is achieved.
- the osmolarity of the solution in beaker a = 3.0 osm
- both bags in the beakers will swell
- two of these are correct
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- Analyze Beaker A: \( \text{NaCl} \) dissociates into \( \text{Na}^+ \) and \( \text{Cl}^- \), so 3.0 M \( \text{NaCl} \) has an osmolarity of \( 3.0 \times 2 = 6.0 \) Osm. The dialysis bag has 1.5 Osm glucose (glucose doesn't dissociate). So water will flow into the bag (from beaker to bag) in Beaker A.
- Analyze Beaker B: \( \text{MgCl}_2 \) dissociates into \( \text{Mg}^{2+} \) and \( 2\text{Cl}^- \), so 2.0 M \( \text{MgCl}_2 \) has an osmolarity of \( 2.0 \times 3 = 6.0 \) Osm. The dialysis bag has 1.5 Osm glucose. So water will flow into the bag (from beaker to bag) in Beaker B.
- Check osmolarity of Beaker A solution: Beaker A has 3.0 M \( \text{NaCl} \) (osmolarity 6.0 Osm), not 3.0 Osm. So that option is wrong.
- Rate of osmosis: Depends on osmotic gradient. In Beaker A, gradient is \( 6.0 - 1.5 = 4.5 \) Osm. In Beaker B, \( 6.0 - 1.5 = 4.5 \) Osm? Wait, no: Wait, Beaker B has 2.0 M \( \text{MgCl}_2 \), osmolarity \( 2\times3 = 6 \) Osm. Bag has 1.5 Osm. So gradient is 6 - 1.5 = 4.5. Beaker A: 3 M NaCl (osmolarity 6) - 1.5 = 4.5. Wait, maybe I miscalculated earlier. Wait, no, the question's Beaker A: 3.0 M NaCl (osmolarity 6), bag: 1.5 Osm glucose. Beaker B: 2.0 M MgCl₂ (osmolarity 6), bag: 1.5 Osm glucose. Wait, but the options: "Two of these are correct"? Wait, let's re - evaluate:
Wait, the dialysis bags are filled with 1.5 Osm glucose. So in Beaker A (3.0 M NaCl, osmolarity 6.0 Osm), the bag has lower osmolarity, so water flows into the bag (bag swells). In Beaker B (2.0 M MgCl₂, osmolarity 6.0 Osm), the bag has lower osmolarity, so water flows into the bag (bag swells). So "Both bags in the beakers will swell" is correct. Also, let's check the osmolarity of Beaker A solution: 3.0 M NaCl, each NaCl gives 2 particles, so osmolarity is \( 3\times2 = 6 \) Osm, so the option "The osmolarity of the solution in Beaker A = 3.0 Osm" is wrong. The rate of osmosis: since both have the same osmotic gradient (6 - 1.5 = 4.5 Osm), the rate should be same? Wait, no, maybe I made a mistake in dissociation. Wait, NaCl dissociates into 2 ions, MgCl₂ into 3 ions. But the beaker solutions: Beaker A: 3.0 M NaCl (osmolarity 6), Beaker B: 2.0 M MgCl₂ (osmolarity 6). The bags: 1.5 Osm glucose. So the osmotic gradient (beaker osmolarity - bag osmolarity) is 6 - 1.5 = 4.5 for both. So the rate of osmosis should be same? But the option "The rate of osmosis in Beaker A is slower than Beaker B" is wrong. The option "Water will flow out of both dialysis sacs, into their respective beakers" is wrong (water flows into the sacs). The option "Both bags in the beakers will swell" is correct. Also, let's check the osmolarity of Beaker A: 3.0 M NaCl, osmolarity is 6.0 Osm, so that option is wrong. Wait, but the option "Two of these are correct" - maybe I missed. Wait, the osmolarity of Beaker A solution: 3.0 M NaCl, osmolarity is 6.0 Osm, so that option is wrong. The "Both bags..." is correct. Is there another correct? Wait, maybe my initial analysis of osmolarity was wrong. Wait, the question says "Beaker A has a 3.0 M NaCl solution" - NaCl dissociates into 2 ions, so osmolarity is 32 = 6 Osm. The bag has 1.5 Osm glucose. So water flows into the bag (bag swells). Beaker B: 2.0 M MgCl₂, dissociates into 3 ions, so osmolarity is 23 = 6 Osm. Bag has 1.5 Osm glucose. Water flows into the bag (bag swells). So "Both bags in the beakers will swell" is correct. Also, is the osmolarity of Beaker A solution 3.0 Osm? No, it's 6.0 Osm. The rate of osmosis: since both have the same gradient, rate is same, so that option is wrong. The water flow direction: into…
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The option "Both bags in the beakers will swell" is correct. So the answer is the option labeled "Both bags in the beakers will swell".