The degree of dissociation of Ca ( NO 3 ) 2 in a dilute aqueous solution containing 7 gm of the salt per 100 gm of water at 100°C is 70%. Calculate the vapour pressure (in mm Hg) of the solution a

Question

The degree of dissociation of Ca ( NO 3 ​ ) 2 ​ in a dilute aqueous solution containing 7 gm of the salt per 100 gm of water at 100°C is 70%. Calculate the vapour pressure (in mm Hg) of the solution at 100°C.

TestHub · Accepted Answer

Step 1: Find the moles of solute Ca(NO₃)₂ ( $M = 164 g / m o l$ ) and solvent H₂O:

$n_{2} = \frac{7}{164} = 0.0427 m o l, n_{1} = \frac{100}{18} = 5.556 m o l$

Step 2: Calculate the Van 't Hoff factor ( $i$ ) for dissociation ( $n = 3, α = 0.70$ ):

$i = 1 + (n - 1) α = 1 + (3 - 1) (0.70) = 2.4$

Step 3: Use the vapor pressure of pure water at its boiling point (100 °C), which is $P^{\circ} = 760 mm H g$ .

Step 4: Apply Raoult's Law for relative lowering of vapor pressure:

$\frac{P ^{\circ} - P}{P ^{\circ}} = \frac{i \cdot n _{2}}{n _{1} + i \cdot n _{2}} ⟹ \frac{760 - P}{760} = \frac{2.4 \times 0.0427}{5.556 + ( 2.4 \times 0.0427 )} = 0.0181$

Step 5: Solve for the vapor pressure of the solution ( $P$ ):

$760 - P = 760 \times 0.0181 = 13.76 ⟹ P = 746.24mmHg$

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