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Two elements A and B form compounds having formula AB2 and AB4. When dissolved in 20 g of benzene (C6H6), 1 g of AB2 lowers the freezing point by 2.3 Kwhereas 1.0 g of AB4 lowers it by 1.3 K. - CBSE (Science) Class 12 - Chemistry

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Question

Two elements A and B form compounds having formula AB2 and AB4. When dissolved in 20 g of benzene (C6H6), 1 g of AB2 lowers the freezing point by 2.3 Kwhereas 1.0 g of AB4 lowers it by 1.3 K. The molar depression constant for benzene is 5.1 Kkg mol−1. Calculate atomic masses of A and B.

Solution

We know that,

`M_2 = (1000xxw_2xxk_f)/(triangleT_fxxw_1)`

Then `M_(AB_2) = (1000xx1xx5.1)/(2.3 xx 20)`

= 110.87 gmol-1

`M_(AB_4) = (1000xx 1xx5.1)/(1.3xx20)`

= 196.15 g mol−1

Now, we have the molar masses of AB2 and AB4 as 110.87 g mol−1 and 196.15 g mol−1 respectively.

Let the atomic masses of A and B be x and y respectively.

Now, we can write:

x + 2y = 110.87 (i)

x +4y = 196.15 (ii)

Subtracting equation (i) from (ii), we have

2y = 85.28

⇒ y = 42.64

Putting the value of ‘y’ in equation (1), we have

x + 2 × 42.64 = 110.87

⇒ x = 25.59

Hence, the atomic masses of A and B are 25.59 u and 42.64 u respectively.

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Solution Two elements A and B form compounds having formula AB2 and AB4. When dissolved in 20 g of benzene (C6H6), 1 g of AB2 lowers the freezing point by 2.3 Kwhereas 1.0 g of AB4 lowers it by 1.3 K. Concept: Expressing Concentration of Solutions.
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