The average osmotic pressure of human blood is 7.8 atm at 27°C. The concentration of aqueous \(NaCl\) solution that can be used in the blood stream. (Given \(R=0.082\, L\, atm\, K^{-1}mol^{-1}\))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.16 mol/L
A solution injected into the blood stream must be isotonic with blood, that is, it must have the same osmotic pressure (7.8 atm at 27 °C). For an electrolyte the osmotic pressure depends on the number of particles, so the van’t Hoff factor i is included:
\( \pi = i\,C\,R\,T \)
NaCl dissociates completely: NaCl → \( \ce{Na^{+}} \) + \( \ce{Cl^{-}} \), 1 + 1 = 2 ions, so i = 2. T = 27 + 273 = 300 K.
\( \displaystyle C = \frac{\pi}{i\,R\,T} = \frac{7.8}{2 \times 0.082 \times 300} = \frac{7.8}{49.2} = 0.159 \approx 0.16\,\mathrm{mol\,L^{-1}} \)
So the NaCl solution should be about 0.16 mol/L.
NCERT (2026-27 edition):
Osmosis and Osmotic Pressure – “… Two solutions having same osmotic pressure at a given temperature are called isotonic solutions. When such solutions are separated by semipermeable membrane no osmosis occurs between them. For example, the osmotic pressure associated with the fluid inside the blood cell is equivalent to that of 0.9% (mass/volume) sodium chloride solution, called normal saline solution and it is safe to inject intravenously.”