Question

\(x\%\;(w/v)\) solution of urea is isotonic with \(4\%\;(w/v)\) solution of a non-volatile solute of molar mass \(120\;g\;mol^{-1}\). The value of \(x\) is

• A. \(2\)
• B. \(4\)
• C. \(3\)
• D. \(5\)

Hint:

For isotonic non-electrolyte solutions, molarity must be equal. In \(w/v\%\), the given mass is always per \(100\;mL\) of solution.

Answer 1

The Correct Option is A

Step 1: State the isotonic condition.
Isotonic solutions have equal osmotic pressure, so by $\pi = CRT$ at the same temperature they must have equal molar concentration.
Step 2: Express percentage as grams per 100 mL.
A $4\%\;(w/v)$ solution means $4\;g$ of solute in $100\;mL$ of solution, and an $x\%$ urea solution means $x\;g$ urea in $100\;mL$. Since the volume is the same, equal molarity means equal moles.
Step 3: Write moles of the unknown solute.
Its molar mass is $120\;g\;mol^{-1}$, so moles in $100\;mL$ are \[ \frac{4}{120}. \]
Step 4: Write moles of urea.
Urea has molar mass $60\;g\;mol^{-1}$, so moles in $100\;mL$ are \[ \frac{x}{60}. \]
Step 5: Equate the two and simplify.
\[ \frac{x}{60} = \frac{4}{120} \] which gives \[ \frac{x}{60} = \frac{1}{30}. \]
Step 6: Solve for $x$.
Cross multiplying, $30x = 60$, so $x = 2$. The required value is
\[ \boxed{2} \]