Question

A \[5\%\] solution of cane sugar (molar weight\[=342\]) is isotonic with \[1\%\] solution of unknown solute. The molar mass of unknown solute in grams:
A. \[171.2\]
B. \[68.4\]
C. \[34.2\]
D. \[136.8\]

Answer 1

Hint: As we know, an isotonic solution is one that has a similar osmolality, or solute concentration, as another solution. On the off chance that these two solutions are isolated by a semipermeable layer, water will stream in equivalent parts out of every solution and into the other.

Complete step by step solution:
Isotonic solutions are those solutions which have the same osmotic pressure. If osmotic pressures are equal at the same temperature, concentrations must also be equal. Isotonic solution has the same O.P below the same conditions, hence concentration of 2 solutions must be the same.
Apparently, Osmotic pressure of cane sugar is equal to that of solution of solute, Let the solute be X .That is \[{{\pi }_{1}}={{\pi }_{2}}\]
For Isotonic solution:
\[
   \pi =MRT \\
  {{\pi }_{1}}={{\pi }_{2}} \\
  {{M}_{1}}RT={{M}_{2}}RT \\
  {{M}_{1}}={{M}_{2}}
\]
\[\Rightarrow 5\%\] solution \[\equiv 5\;gm\] solute in \[100\;ml\] solution
\[\Rightarrow 1\%\] solution \[\equiv 1\;gm\] solute in \[100\;ml\] solution
\[
\Rightarrow \dfrac{5}{342}\times \dfrac{1000}{100}=\dfrac{1}{M.wt}\times \dfrac{1000}{100} \\
\Rightarrow {{\left( M.wt \right)}_{2}}=\dfrac{342}{5} \\
  =68.4
\]

Hence, the molecular weight of \[X\] is \[68.4\], so the correct option is B.

Additional Information:
Isotonic arrangements have a grouping of broken up particles like plasma, and an osmolality. These liquids stay inside the extracellular compartment and are conveyed between intravascular (veins) and interstitial (tissue) spaces, expanding intravascular volume. Isotonic solutions are utilized to build the Extracellular fluid volume due to blood loss, surgery, dehydration, fluid loss that has been lost extracellularly.

Note:
While solving this question, we just need to remember that at the constant temperature molar concentration of one substance will be equal to that of another substance. Then, we need to apply the formula of concentration correctly, the molecular formula will occur.