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 $R=0.082\, L\, atm\, K^{-1}mol^{-1}$)

0.16 mol/L

The correct answer is Option (1) → 0.16 mol/L

To determine the concentration of an aqueous NaCl solution that can be used in the bloodstream based on the average osmotic pressure, we can use the formula for osmotic pressure:

\(\pi = i C R T\)

Where:

\( \pi \) is the osmotic pressure (in atm).

\( i \) is the van 't Hoff factor (for NaCl, \( i = 2 \) since it dissociates into Na⁺ and Cl⁻).

\( C \) is the concentration of the solution (in mol/L).

\( R \) is the ideal gas constant (\( 0.082 \, \text{L atm K}^{-1} \text{mol}^{-1} \)).

\( T \) is the temperature (in Kelvin).

Given:

\( \pi = 7.8 \, \text{atm} \)

\( T = 27^\circ C = 27 + 273 = 300 \, \text{K} \)

\( R = 0.082 \, \text{L atm K}^{-1} \text{mol}^{-1} \)

\( i = 2 \) for NaCl

Rearranging the Formula

We can rearrange the formula to find \( C \):

\(C = \frac{\pi}{i R T}\)

Substituting the Values

\(C = \frac{7.8}{2 \times 0.082 \times 300}\)

Calculating the denominator:

\(2 \times 0.082 \times 300 = 49.2\)

Now, calculate \( C \):

\(C = \frac{7.8}{49.2} \approx 0.16 \, \text{mol/L}\)

Conclusion
Thus, the concentration of aqueous NaCl solution that can be used in the bloodstream is approximately: 0.16 mol/L