Practicing Success
Vapour pressure of pure liquids 'A' and 'D' at \(50^oC\) are \(500\, \ mm\) Hg and \(800\, \ mm\) Hg respectively. The binary solution of 'A' and 'D' boils at \(50^oC\) and \(700\, \ mm\)Hg pressure. The mole percentage of 'D' in the solution is |
33.33 mole percent 66.67 mole percent 25.75 mole percent 75.25 mole percent |
66.67 mole percent |
The correct answer is option 2. 66.67 mole percent. Given, \(p^o_A = 500\, \ mm\, \ Hg\) \(p^o_D = 800\, \ mm\, \ Hg\) \(p_{total} = 700\, \ mm\, \ Hg\) We know, from Raoult's law \(p_A = p^o_A\chi _A\) \(p_D = p^o_D\chi _D\, \ = p^o_D(1 - \chi _A)\) Therefore, total pressure, \(p_{total} = p_A + p_D\) \(⇒ p_{total} = p^o_A\chi _A + p^o_D(1 - \chi _A)\) \(⇒ p_{total} = p^o_A\chi _A + p^o_D - p^o_D\chi _A\) \(⇒ p_{total} = (p^o_A - p^o_D)\chi _A + p^o_D\) \(⇒ 700 = (500 - 800)\chi _A + 800\) \(⇒ -100 = -300\chi _A\) \(\chi _A = \frac{100}{300}\) \(⇒ \chi _A = 0.3333\) Therefore, \(\chi _D = 1 - \chi _A\) \(⇒ \chi _D = 1 - 0.3333\) \(⇒ \chi _D = 0.6667\) Therefore, \(\% \chi _D = 0.6667 × 100\) or, \(\% \chi _D = 66.67\text{ mole percent}\) |