1. Tardigrade
  2. Question
  3. Chemistry
  4. Two elements A and B form compounds of formula AB2 and AB4. When dissolved in 20.0 g of benzene 1.0 g of AB2 lowers f. pt. by 2.3°C whereas 1.0 g of AB4 lowers f. pt. by 1.3°C. The Kf for benzene is 5.1. The atomic masses of A and B are

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Q. Two elements $A$ and $B$ form compounds of formula $AB_2$ and $AB_4$. When dissolved in $20.0\, g$ of benzene $1.0 \,g$ of $AB_2$ lowers f. pt. by 2.3$^{\circ}$C whereas $1.0\, g$ of $AB_4$ lowers f. pt. by 1.3$^{\circ}$C. The $K_f$ for benzene is $5.1$. The atomic masses of $A$ and $B$ are

AIIMSAIIMS 2016Solutions

Solution:

Let the masses of A and B be a and b. The mass of AB2 will be (a + 2b) g mol-1 and AB4 will be (a + 4b) g mol-1.
$\Delta T_{ f} =\frac{K_{ f} \times W_{B}\times1000}{M_{B}\times W_{A}}$
For AB$_{2}, 2.3=\frac{5.1\times1\times1000}{\left(a+2b\right)\times20}\quad\quad\quad\quad\quad...\left(i\right)$
For AB$_{4}, 1.3=\frac{5.1\times1\times1000}{\left(a+4b\right)\times20}\quad \quad \quad \quad \quad ...\left(ii\right)$
On solving (i) and (ii), we get
$\quad\quad$ a = 25.59 and b = 42.64