Question

6) The density of water is 1.0 g/cm and the density of Hg is 13.6 g/cm'. How high can the osmotic pressure generated by placing an aqueous 1.OM MgCl, solution against pure water raise a column of water that is at standard pressure?

Answer 1

In aqueous solution, one molecule of magnesium(II) chloride dissociates to form 3 ions.

MgCl2 + Mg2+ + 2C1-

Hence, the vant Hoff factor $i=3$

Assume room temperature of 298 K.

The osmotic pressure $\left ( \pi \right )$ is related to the vant Hoff factor$\left ( i \right )$, the concentration $\left ( C \right )$ , the ideal gas constant $\left ( R \right )$ and absolute temperature $\left ( T \right )$ by the following expression:

$\pi=i \times C \times R \times T$                          

Substitute 3 for i, 1.0 M for C, $0.08206 \ \dfrac { L \cdot atm}{mol \cdot K}$ for R and 298 K for T.   

$\pi=3 \times 1.0 \ M \times 0.08206 \ \dfrac { L \cdot atm}{mol \cdot K} \times 298 \ K$

$\pi=73.36 \ atm$

Hence, the osmotic pressure of solution is 73.36 atm.

Convert the unit from atm to cm Hg

$73.36 \ atm \times \dfrac {76 \ cm \ Hg}{1 \ atm}=5575 \ cm \ Hg$

Convert 5575 cm of Hg to cm of water.

$5575 \ cm \ Hg \times \dfrac {13.6 \ g \ cm^3 \ Hg}{ 1.0 \ g/cm^3 \ water }=75827 \ cm \ water$

Hence, the height of water column will be raised by 75827 cm