A saturated solution of silver bromide is made in 10−7M AgNO3 solution Given: Ksp of AgBr=3×10−13 λm∞(Ag+)=6×10−3Sm2mol−1 λm∞(NO3−)=7×10−3Sm2mol−1 λm∞(Br−)=8×10−3Sm2mol−1For water, k=7.5×10−6Sm−1The conductivity of solution is x×10−7Sm−1. The value of x/10 is…..

Let solubility of AgBr(s) in AgNO3 solution be s(M)AgBr(s) ⇌ Ag+ + Br−(s+107)s (s+107)=3×10−13 or s2+10-7s−30×10−14=0 or s2+6×10-7s−5×10−7(s2+6×10-7)=0 s(s+6×10-7)−5×10−7(s+6×10-7)=0 or s(s-5×10-7)(s+6×10-7)=0 s=5×10-7(M)πm∞(AgNO3)=λm∞(Ag+)+λm∞(NO3−)=13×10−3sm2mol−1 πm∞(AgBr)=λm∞(Ag+)+λm∞(Br−)=14×10−3s m2mol−1 k(AgBr)=[πm∞(AgBr)]C=70×10−7s m−1 ksolution=k(AgNO3)+k(AgBr)+k(H2O)=(13×10−7+70×10−7+75×10−7) =158×10−7s m−1)⇒x10=15.8

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A saturated solution of silver bromide is made in $10^{- 7} M A g N O_{3}$ solution
Given: $K_{s p} o f A g B r = 3 \times 10^{- 13}$
$λ_{m}^{\infty} (A g^{+}) = 6 \times 10^{- 3} S m^{2} m o l^{- 1} λ_{m}^{\infty} (N O_{3}^{-}) = 7 \times 10^{- 3} S m^{2} m o l^{- 1} λ_{m}^{\infty} (B r^{-}) = 8 \times 10^{- 3} S m^{2} m o l^{- 1}$
For water, $k = 7.5 \times 10^{- 6} S m^{- 1}$
The conductivity of solution is $x \times 10^{- 7} S m^{- 1}$ . The value of $x / 10$ is…..

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answer is 15.7.

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Detailed Solution

Let solubility of $AgBr (s) {in AgNO}_{3}$ solution be s(M)

$AgBr (s) ⇌ {Ag}^{+} + {Br}^{-}$

${({s+10}^{7})}_{s} ({s+10}^{7}) = 3 \times 10^{- 13} o r s^{2} {+10}^{-7} s - 30 \times 10^{- 14} = 0 o r s^{2} +6 \times 10^{-7} s - 5 \times 10^{- 7} (s^{2} +6 \times 10^{-7}) = 0 s (s+6 \times 10^{-7}) - 5 \times 10^{- 7} (s+6 \times 10^{-7}) = 0 o r s (s-5 \times 10^{-7}) (s+6 \times 10^{-7}) = 0 {s=5×10}^{-7} (M)$

$π_{m}^{\infty} (A g N O_{3}) = λ_{m}^{\infty} (A g^{+}) + λ_{m}^{\infty} (N O_{3}^{-}) = 13 \times 10^{- 3} s m^{2} m o l^{- 1} π_{m}^{\infty} (A g B r) = λ_{m}^{\infty} (A g^{+}) + λ_{m}^{\infty} (B r^{-}) = 14 \times 10^{- 3} s m^{2} m o l^{- 1} k (A g B r) = [π_{m}^{\infty} (A g B r)] C = 70 \times 10^{- 7} s m^{- 1} k_{s o l u t i o n} = k (A g N O_{3}) + k (A g B r) + k (H_{2} O) = (13 \times 10^{- 7} + 70 \times 10^{- 7} + 75 \times 10^{- 7}) = 158 \times 10^{- 7} s m^{- 1}) \Rightarrow \frac{x}{10} = 15.8$