Which of the following pair of solutions is isotonic? A. $18 \mathrm{~g} / \mathrm{L}$ of glucose of…
Which of the following pair of solutions is isotonic?
A. $18 \mathrm{~g} / \mathrm{L}$ of glucose of solution and $6 \mathrm{~g} / \mathrm{L}$ of Urea solution
B. $10 \mathrm{~g} / \mathrm{L}$ of glucose solution and $10 \mathrm{~g} / \mathrm{L}$ of Urea solution
C. $\quad 0.01 \mathrm{M} \mathrm{NaOH}$ solution and $0.02 \mathrm{M}$ glucose solution
D. $0.01 \mathrm{M} \mathrm{NaCl}$ solution and $0.01 \mathrm{M}$ glucose solution
(Assume that $\mathrm{NaCl}$ undergoes complete dissociation)
$A$ and $B$
$\mathrm{A}$ and $\mathrm{C}$
$B$ and $D$
$B$ and $C$
Solution
Osmotic pressure $\pi=\mathrm{CRT}$; $\mathrm{C}$ is in moles/L.
$\mathrm{C}=\frac{\mathrm{n}}{\mathrm{V}}=\frac{\mathrm{m}}{\mathrm{MV}}$
$\mathrm{m}=$ mass of solute and $\mathrm{M}=\mathrm{mol}$. wt. of solute $\mathrm{V}=$
Volume in $\mathrm{L}$.
At a given $\mathrm{T}$, isotonic solution; $\pi_1=\pi_2 ; \mathrm{C}_1 \mathrm{RT}=\mathrm{C}_2 \mathrm{RT}$
(A) $18 \mathrm{~g} / \mathrm{L}$ of glucose $=(18 / 180) / \mathrm{L}=0.1 \mathrm{~mol} / \mathrm{L}=0.1(\mathrm{M})$
and $6 \mathrm{~g} / \mathrm{L}$ of Urea $=(6 / 60) / \mathrm{L}=0.1 \mathrm{~mol} / \mathrm{L}=0.1(\mathrm{M})$
(B.) $10 \mathrm{~g} / \mathrm{L}$ of glucose $=\left(\frac{10}{180}\right) / \mathrm{L}=(1 / 18) / \mathrm{L}=0.06(\mathrm{M})$
$10 \mathrm{~g} / \mathrm{L}$ of urea $=\left(\frac{10}{60}\right) / \mathrm{L}=(1 / 6) / \mathrm{L}=0.17(\mathrm{M})$
$\therefore \quad \mathrm{C}_1 \neq \mathrm{C}_2$
(C) $0.01(\mathrm{M}) \quad \mathrm{NaOH}$ solution and $0.02(\mathrm{M})$ glucose solution are isotonic.
$\begin{aligned} & \pi_{\mathrm{NaOH}}=2 \times 0.01 \times \mathrm{RT}=0.02 \mathrm{RT} \\ & \pi_{\text {glucose }}=0.02 \mathrm{RT}\end{aligned}$
$\begin{aligned} & \therefore \pi_{\mathrm{NaOH}}=\pi_{\text {glucose }} \\ & \therefore \quad \mathrm{C}_1 \neq \mathrm{C}_2\end{aligned}$
(D) $0.01(\mathrm{M}) \mathrm{NaCl}$ solution are $0.01(\mathrm{M})$ glucose solution
$\begin{aligned} & \pi_{\mathrm{NaCl}}=2 \times 0.01 \times \mathrm{RT} \\ & \pi_{\text {glucose }}=0.01 \times \mathrm{R} \times \mathrm{T}\end{aligned}$
$\therefore \quad \pi_{\mathrm{NaCl}} \neq \pi_{\text {glucose }}$