Molar conductivity of $AgNO_{3}$, $HCl$ and $HNO_{3}$ at infinite dilution are $a$, $b$, $c$ $S$ $cm^{2}$…

Molar conductivity of $AgNO_{3}$, $HCl$ and $HNO_{3}$ at infinite dilution are $a$, $b$, $c$ $S$ $cm^{2}$ $mol^{-1}$, respectively. If the conductivity of saturated $AgCl$ solution is $Z$ $S$ $cm^{-1}$, then $K_{sp}$ of $AgCl$ will be:
  1. $\frac{1000Z}{a+b-c}$
  2. $\left[\frac{1000\,Z}{a+b-c}\right]^2$
  3. $[\frac{a+b-c}{Z}]$
  4. $\left[\frac{a+b-c}{Z \times 1000}\right]^2$

Solution

ΛAgNO3∘=λAg+∘+λNO3-∘=aΛHCl∘=λH+∘+λCl-∘=bΛHNO3∘=λH+∘+λNO3-∘=c
Also, ΛAgCl∘=λAg+∘+λCl-∘=a+b-c

Also, ΛAgCl∘=K×1000M
a+b-c=Z×1000M
∴ M=1000 Za+b-c
Now,  K sp = Ag +   Cl - = M 2 = 1 0 0 0  Z a + b - c 2

Asked in: MHT CET Full Test 2

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