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The osmotic pressure of blood is 8.21 atm at $ {37^0} $ C. How much glucose would be used for an injection that is at the same osmotic pressure as blood?
A) 22.7 $ g{L^{ - 1}} $
B) 58.14 $ g{L^{ - 1}} $
C) 61.26 $ g{L^{ - 1}} $
D) 75.43 $ g{L^{ - 1}} $

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Last updated date: 25th Jul 2024
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Answer
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Hint :In order to solve this question, you must know the relationship between the osmotic pressure of a solution and the molar concentration of its solute. This relationship was given by the Dutch chemist Jacob van’t Hoff. This equation only holds true for solutions that behave like ideal solutions.

Complete Step By Step Answer:
 $ \pi $ = 8.21
V = 1 L
M = 180 (Molar mass of glucose)
T = 273 + 37 = 310 K
R = 0.0821
m = ?
We know that,
 $ \pi = CRT $
 $ \pi v = {m}{M}RT $
Therefore, $ {m}{v} = {{\pi M}}{{RT}} $
Now put the values, $ {m}{v} $ = $ {{8.21 \times 1 \times 180}}{{0.0821 \times 310}} $
 $ {m}{v} $ = 58.06 $ g{L^{ - 1}} $
Hence, option (B) is correct.

Note :
Osmotic pressure can be defined as the minimum pressure that must be applied to the solution to halt the flow of solvent molecules through a semipermeable membrane.