Question

The concentration in gms per litre of a solution of cane sugar $\left( M=342 \right)$ which is isotonic with a solution containing six gms of urea of molecular weight $60$ per litre is
A. 3.42
B. 34.2
C. 5.7
D. 19

Answer 1

Hint: If the effective molar concentrations of two solutions is same then it is called an isotonic solution. Here cane sugar solution has the same molar concentration with the urea solution.

Formula Used: The formula used in this case is given as-
\[\frac{{{w}_{1}}}{{{m}_{1}}\times {{V}_{1}}}=\frac{{{w}_{2}}}{{{m}_{2}}\times {{V}_{2}}}\]

Complete Step by Step Answer:
The formula for isotonic solution is given as follows:
\[\frac{{{w}_{1}}}{{{m}_{1}}\times {{V}_{1}}}=\frac{{{w}_{2}}}{{{m}_{2}}\times {{V}_{2}}}\]

Here ${{w}_{1}}$ is the weight of cane sugar that is ${{w}_{1}}=x$ .
${{m}_{1}}$ is the molecular weight of cane sugar that is ${{m}_{1}}=342$ .
${{V}_{1}}$ is the volume of the sugar solution that is one litre.
${{w}_{2}}$ is the weight of cane sugar that is ${{w}_{2}}=6$ .
${{m}_{2}}$ is the molecular weight of cane sugar that is ${{m}_{2}}=60$ .
${{V}_{2}}$ is the volume of the sugar solution that is one litre.

Putting these values we get:
$\frac{x}{1\times 342}=\frac{6}{60\times 1}$
\[x=34.2\]
Thus the correct option is B.

Note: Isotonic solutions are widely used for patients who have the fluid volume deficit which is also called hypovolemia to raise the patient’s blood pressure. It has to be noted that infusion of too much isotonic fluid can cause excessive fluid volume which is also called hypervolemia.