$1 \times 10^{-5}\,M \textrm {AgNO } _ { 3 }$ ને $AgBr$ના $1\,L$ સંતૃપ્ત દ્રાવણમાં ઉમેરવામાં આવે છે.$298\,K$ આ દ્રાવણની વાહકતા $.........\times 10^{-8}\,S\,m ^{-1}$ છે.

$\left[\right.$ આપેલ : $K _{ sp }( AgBr )=4.9 \times 10^{-13}$ at $298 K$

$\lambda_{ Ag ^{+}}^0=6 \times 10^{-3} Sm ^2\,mol ^{-1}$

$\lambda_{ Br ^{-}}^0=8 \times 10^{-3} Sm ^2\,mol ^{-1}$

$\left.\lambda_{ NO _3^{-}}^0=7 \times 10^{-3} Sm ^2\,mol ^{-1}\right]$

Question

$1 \times 10^{-5}\,M \textrm {AgNO } _ { 3 }$ ને $AgBr$ના $1\,L$ સંતૃપ્ત દ્રાવણમાં ઉમેરવામાં આવે છે.$298\,K$ આ દ્રાવણની વાહકતા $.........\times 10^{-8}\,S\,m ^{-1}$ છે.

$\left[\right.$ આપેલ : $K _{ sp }( AgBr )=4.9 \times 10^{-13}$ at $298 K$

$\lambda_{ Ag ^{+}}^0=6 \times 10^{-3} Sm ^2\,mol ^{-1}$

$\lambda_{ Br ^{-}}^0=8 \times 10^{-3} Sm ^2\,mol ^{-1}$

$\left.\lambda_{ NO _3^{-}}^0=7 \times 10^{-3} Sm ^2\,mol ^{-1}\right]$

JEE MAIN 2023, Medium

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Solution

b
${\left[ Ag ^{+}\right]=10^{-5}}$

${\left[ NO _3^{-}\right]=10^{-5}}$

${\left[ Br ^{-}\right]=\frac{ Ksp }{\left[ Ag ^{+}\right]}=4.9 \times 10^{-8}}$

$\Lambda_{ m }=\frac{ k }{1000 \times M }$

For $Ag ^{+}$

$6 \times 10^{-3}=\frac{ K _{ Ag ^{+}}}{1000 \times 10^{-5}}$

$K _{ Ag +}=6 \times 10^{-5}$

$\Rightarrow 6000 \times 10^{-8}$

$\text { for } Br ^{-}$

$8 \times 10^{-3}=\frac{ K _{ Br ^{-}}}{1000 \times 4.9 \times 10^{-8}}$

$K _{ BI -}=39.2 \times 10^{-8}$

$\text { for } NO _3^{-}$

$7 \times 10^{-3} =\frac{ K _{ No -}^3}{1000 \times 10^{-5}}$

$K _{ No _3} =7 \times 10^{-5}$

$=7000 \times 10^{-8}$

Conductivity of solution

$\Rightarrow(6000+7000+39.2) \times 10^{-8}$

$\Rightarrow 13039.2 \times 10^{-8} S m ^{-1}$

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