We have taken a saturated solution of AgBr. K_sp of AgBr is 12 × 10^-¹⁴. If 10^-⁷ mole of AgNO₃ are added to 1 litre of this solution find conductivity (specific conductance) of this solution in terms of 10^-⁷ S m^-¹ units.

Given: $λ_{(A g^{+})}^{o} = 6 \times 1 0^{- 3} S m^{2} m o l^{- 1}$

$λ_{(B r^{-})}^{o} = 8 \times 1 0^{- 3} S m^{2} m o l^{- 1}$

$λ_{(N O_{3}^{-})}^{o} = 7 \times 1 0^{- 3} S m^{2} m o l^{- 1}$

Option 1 -

Option 2 -

Option 3 -

Option 4 -

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Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 1

Detailed Solution:

$A g B r ? A g^{+} + B r^{-}$

S + 10^-7 S

(S + 10^-7) S = 12 × 10^-14

$∴ S = 3 \times 1 0^{- 7} M$

$κ_{t o t e l} = [6 \times 4 \times 1 0^{- 7}] + [8 \times 3 \times 1 0^{- 7}] + [7 \times 1 \times 1 0^{- 7}]$

= 55 × 10^-7 S m^-1

<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1819026632"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mi>A</mi> <mi>g</mi> <mi>B</mi> <mi>r</mi> <mo>? </mo> <mi>A</mi> <msup> <mrow> <mi>g</mi> </mrow> <mrow> <mo>+</mo> </mrow> </msup> <mtext> </mtext> <mo>+</mo> <mtext> </mtext> <mi>B</mi> <msup> <mrow> <mi>r</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msup> </mrow> </math>                S + 10-7                        S (S + 10-7) S = 12 × 10-14  <math> <mrow> <mo>∴</mo> <mi>S</mi> <mo>=</mo> <mn>3</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>7</mn> </mrow> </msup> <mi>M</mi> </mrow> </math>        <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1819026633"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <msub> <mrow> <mi>κ</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo> [</mo> <mrow> <mn>6</mn> <mo>×</mo> <mn>4</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>7</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <mrow> <mo> [</mo> <mrow> <mn>8</mn> <mo>×</mo> <mn>3</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>7</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <mrow> <mo> [</mo> <mrow> <mn>7</mn> <mo>×</mo> <mn>1</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>7</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mrow> </math>         <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1819026634"> </o:OLEObject></xml><! [endif]-> = 55 × 10-7 S m-1

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