Question

The osmotic pressure of a solution of an organic substance containing $18g$ in $1lt$ of the solution at $293K$ is $2.414\times {10}^{5}N/m^2$. The molecular mass of the substance if $R=8.314J/molK$.

• A. $283$
• B. $363$
• C. $522$
• D. $182$

Answer 1

The correct option is D $182$

Osmotic pressure of the solution is given by,

π= CRT= (n/V) RT ------ (1)

where,

C = (n/V) having n = number of moles of solute

V = Volume of solution in litres

We can now substitute the value of number of moles and get the final formula

n = w/M = (Amount of substance)/(Molar mass of substance)

Now, osmotic pressure becomes,

π = (w×R×T)/(M×V)

Solving for M, we get M = (w ×R×T/(π×V))

Substituting the values,

$M=\frac{18\times 8.314\times 293}{2.414\times {10}^5\times {10}^{-3}}=182g/mol$

Thus, Molecular mass of substance = 182 g/mol​