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JEE Main 20231 FebruaryEvening Shift
Exam
JEE Main
Year
2023
Date
1 February
Shift
Evening Shift
Subject
Chemistry
Chapter
Electrochemistry

JEE Main 2023 · 1 February · Evening Shift · Chemistry · Electrochemistry

1 × 10 ^ - 5 M AgNO _ 3 is added to 1L of saturated solution of...

1 \times {10}^{- 5}M{AgNO}_{3}isaddedtois added to1Lofsaturatedsolutionofof saturated solution ofAgBr.Theconductivityofthissolutionat. The conductivity of this solution at298Kisis_______ \times {10}^{- 8}S{m}^{- 1}.</p><p>[Given:.</p><p>[Given :{K}_{sp} ( AgBr ) = 4 . 9 \times {10}^{- 13}atat298K</p><p></p><p>{\lambda}_{{Ag}^{+}}^{0} = 6 \times {10}^{- 3}{Sm}^{2}{mol}^{- 1}</p><p></p><p>{\lambda}_{{Br}^{-}}^{0} = 8 \times {10}^{- 3}{Sm}^{2}{mol}^{- 1}</p><p>λNO3−0=7×10−3Sm2mol−1]</p><p>{\lambda}_{{NO}_{3}^{-}}^{0} = 7 \times {10}^{- 3}{Sm}^{2}{mol}^{- 1}]

Correct answer

13039

Step-by-step solution

The concentrations of the ions can be calculated as follows,

[Ag+]=10−5M\left[{Ag}^{+}\right] = {10}^{- 5}M

\left[{NO}_{3}^{-}\right] = {10}^{- 5}M</p><p>[Br−]=Ksp[Ag+]=4.9×10−8M</p><p>\left[{Br}^{-}\right] = \dfrac{Ksp}{\left[{Ag}^{+}\right]} = 4 . 9 \times {10}^{- 8}M

Λm=k1000×M=Specificconductance1000×Molarity{Λ}_{m} = \dfrac{k}{1000 \times M} = \dfrac{Specificconductance}{1000 \times Molarity}

For Ag+{Ag}^{+}

6×10−3=kAg+1000×10−56 \times {10}^{- 3} = \dfrac{k{Ag}^{+}}{1000 \times {10}^{- 5}}

kAg+=6×10−5Sm−1{k}_{Ag +} = 6 \times {10}^{- 5}{Sm}^{- 1}

⇒6000×10−8Sm−1⇒ 6000 \times {10}^{- 8}{Sm}^{- 1}

for Br−{Br}^{-}

8×10−3=kBr−1000×4.9×10−88 \times {10}^{- 3} = \dfrac{k{Br}^{-}}{1000 \times 4 . 9 \times {10}^{- 8}}

kBr−=39.2×10−8Sm−1{k}_{Br -} = 39 . 2 \times {10}^{- 8}{Sm}^{- 1}

for NO3−{NO}_{3}^{-}

7×10−3=kNO3−1000×10−57 \times {10}^{- 3} = \dfrac{k{NO}_{3}^{-}}{1000 \times {10}^{- 5}}

kNO3−=7×10−5Sm−1k{NO}_{3}^{-} = 7 \times {10}^{- 5}{Sm}^{- 1}

=7000×10−8Sm−1= 7000 \times {10}^{- 8}{Sm}^{- 1}

Conductivity of solution

⇒(6000+7000+39.2)×10−8⇒ ( 6000 + 7000 + 39 . 2 ) \times {10}^{- 8}

⇒13039.2×10−8Sm−1⇒ 13039 . 2 \times {10}^{- 8}S{m}^{- 1}

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