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Two elements A and B form compounds havi...

Two elements `A` and `B` form compounds having molecular formula `AB_(2)` and `AB_(4)`. When dissolved in `20 g` of benzene, `1 g`of `AB_(2)` lowers the freezing point by `2.3 K`, whereas `1.0 g` of `AB_(4)` lowers it by `1.3 K`. The molal depression constant for benzene is `5.1 K kg mol^(-1)`. Calculate the atomic mass of `A` and `B`.

Text Solution

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Using the relation, `M_(2)=(1000xxk_(f)xxw_(2))/(w_(1)xxDelta T_(f))`
` therefore M_(AB_(2))=(1000xx5.1xx1)/(20xx2.3)=110.87 " g mol"^(-1)`
`M_(AB_(4))=(1000xx5.1xx1)/(20xx1.3)=196.15 " g mol"^(-1)`
Let the atomic masses of A and B are p and q respectively.
Then molar mass of
`AB_(2)=p+2q=110.87 " g mol"^(-1)`
And molar mass of
`AB_(4)=p+4q=196.15 " g mol"^(-1)`
Substracting equation (ii) from equation (i), we get `2q=85.28 implies q=42.64`
Putting q=42.64 in equ. (i), we get
p=110.87-85.28
p=25.59
Thus, atomic mass of `A=25.59 " g mol"^(-1)` and atomic mass of `B=42.64 " g mol"^(-1)`
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