The osmotic pressure of a living cell is 12 atm at 300 K. The strength of sodium chloride solution that is isotonic with the living cell at this temperature is
Q. The osmotic pressure of a living cell is 12 atm at 300 K. The strength of sodium chloride solution that is isotonic with the living cell at this temperature is ________ g L⁻¹. (Nearest integer)

Given : R = 0.08 L atm K⁻¹ mol⁻¹

Assume complete dissociation of NaCl

(Given: Molar mass of Na and Cl are 23 and 35.5 g mol⁻¹ respectively.)
Correct Answer: 15

Explanation (Complete Step-by-Step Calculation)

Formula for osmotic pressure:

\[ \pi = i M R T \]

Where:

π = osmotic pressure

i = van’t Hoff factor

M = molarity

R = gas constant

T = temperature


Step 1: Identify values

π = 12 atm

T = 300 K

R = 0.08 L atm K⁻¹ mol⁻¹

NaCl dissociates completely:

\[ NaCl \rightarrow Na^+ + Cl^- \]

Number of particles formed = 2

Therefore,

\[ i = 2 \]


Step 2: Substitute in formula

\[ 12 = 2 \times M \times 0.08 \times 300 \]

\[ 12 = 2 \times M \times 24 \]

\[ 12 = 48M \]

\[ M = \frac{12}{48} \]

\[ M = 0.25 \text{ mol L}^{-1} \]


Step 3: Convert molarity to strength (g L⁻¹)

Molar mass of NaCl:

\[ 23 + 35.5 = 58.5 \text{ g mol}^{-1} \]

Strength = M × molar mass

\[ = 0.25 \times 58.5 \]

\[ = 14.625 \text{ g L}^{-1} \]

Nearest integer = 15 g L⁻¹

Final Answer = 15

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