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### $AB_2$ is 10% dissociated in water to $A^{2+}$ and $B^-$ ....

$AB_2$ is 10% dissociated in water to $A^{2+}$ and $B^-$. The boiling point of a 10.0 molal aqueous solution of $AB_2$ is _ _ _ _ $^ \circ C$. (Round off to the nearest integer)

[Given: Molal elevation constant of water $K_b = 0.5 K.Kg.mol^{-1}$, boiling point of pure water = $100 ^\circ C$]

Solution

At ionic equilibrium, $\mathop {A{B_2}}\limits_{a(1 - \alpha )} \rightleftharpoons \mathop {{A^{2 + }}}\limits_{a\alpha } + \mathop {2{B^ - }}\limits_{2a\alpha }$

Total moles of particles $=a(1-\alpha) + a\alpha + 2a\alpha = a(1+2\alpha ) = 1.2a$

$\therefore i=\frac {1.2a}{a} = 1.2$

$\Delta T_b = i K_b m = 1.2 \times 0.5 \times 10 = 6$

$\therefore B.P. = 106^\circ C$

### Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$