Question

The osmotic pressure of a solution of $\mathrm{NaCl}\mathrm{is}0.10\mathrm{atm}$ and that of a glucose solution is $0.20\mathrm{atm}$. The osmotic pressure of a solution formed by mixing $1\mathrm{L}$ of the sodium chloride solution with $2\mathrm{L}$ of the glucose solution is $\mathrm{x}\times {10}^{-3}\mathrm{atm}$. $\mathrm{x}$ is

Answer 1

Osmotic Pressure:

• The osmotic pressure is the lowest pressure needed to seal off a semipermeable membrane from the inward flow of a solution's pure solvent.
• The osmosis index, or another name for it, gauges a solution's propensity to absorb a pure solvent.
• Potential osmotic pressure is the maximal osmotic pressure that a solution may produce if cut off from its pure solvent by a semipermeable membrane.

Osmotic Pressure expression:

$\mathrm{\pi }=\mathrm{i}\times \mathrm{C}\times \mathrm{RT}$

And, $\mathrm{For},\mathrm{NaCl}\mathrm{i}=2$

Putting values in the above expression:

$\begin{array}{rcl}{\mathrm{\pi }}_{\mathrm{NaCl}}& =& \mathrm{i}\times {\mathrm{C}}_{\mathrm{NaCl}}\times \mathrm{RT}\\ \mathrm{o}.1& =& 2\times {\mathrm{C}}_{\mathrm{NaCl}}\times \mathrm{RT}\\ {\mathrm{C}}_{\mathrm{NaCl}}& =& \frac{0.5}{\mathrm{RT}}\\ \mathrm{For}\mathrm{glucose},\mathrm{i}& =& 1\\ \mathrm{so},{\mathrm{\pi }}_{\mathrm{Glucose}}& =& \mathrm{i}\times {\mathrm{C}}_{\mathrm{Glucose}}\times \mathrm{RT}\\ 0.2& =& 1\times {\mathrm{C}}_{\mathrm{Glucose}}\times \mathrm{RT}\\ {\mathrm{C}}_{\mathrm{Glucose}}& =& \frac{0.2}{\mathrm{RT}}\\ {\mathrm{\eta }}_{\mathrm{NaCl}}\mathrm{in}1\mathrm{L}& =& {\mathrm{C}}_{\mathrm{NaCl}}\times {\mathrm{V}}_{\mathrm{Litre}}\\ & =& \frac{0.05}{\mathrm{RT}}\\ {\mathrm{\eta }}_{\mathrm{Glucose}}\mathrm{in}2\mathrm{L}& =& {\mathrm{C}}_{\mathrm{Glucose}}\times {\mathrm{V}}_{\mathrm{Glucose}}\\ & =& \frac{0.4}{\mathrm{RT}}\\ {\mathrm{V}}_{\mathrm{Total}}& =& 1+2\\ & =& 3\mathrm{L}\\ \mathrm{So},\mathrm{Final}\mathrm{Conc}.\mathrm{NaCl}& =& \frac{0.05}{\mathrm{RT}}\\ \mathrm{Final}\mathrm{Conc}.\mathrm{Glucose}& =& \frac{0.4}{\mathrm{RT}}\\ {\mathrm{\pi }}_{\mathrm{Total}}& =& {\mathrm{\pi }}_{\mathrm{NaCl}}+{\mathrm{\pi }}_{\mathrm{Glucose}}\\ & =& \left[\mathrm{i}\times {\mathrm{C}}_{\mathrm{NaCl}}+{\mathrm{C}}_{\mathrm{Glucose}}\right]\times \mathrm{RT}\\ & =& \left(\frac{2\times 0.05}{3\mathrm{RT}}+\frac{0.4}{3\mathrm{RT}}\right)\times \mathrm{RT}\\ & =& \frac{0.5}{3}\mathrm{atm}\\ & =& 0.1666\mathrm{atm}\\ & =& 166.6\times {10}^{-3}\mathrm{atm}\\ & =& 167\times {10}^{-3}\mathrm{atm}\end{array}$

Therefore, on comparing the value of $\mathrm{x}\mathrm{is}167$.