The solubilities of AgCl in water, 0.01M , 0.01M NaCl and 0.05M are denoted by and respectively. Which of the following relationships is correct?

Question

The solubilities of AgCl in water, 0.01M ${CaCl}_{2}$ , 0.01M NaCl and 0.05M ${AgNO}_{3}$ are denoted by $S_{1}, S_{2}, S_{3}$ and $S_{4}$ respectively. Which of the following relationships is correct?

Smart Achievers · Accepted Answer

(2)

$Solubility of AgCl in water: AgCl ⇌ {Ag}^{+} + {Cl}^{-}$

$K_{s p} = [{Ag}^{+}] [{Cl}^{-}] = (S_{1}) (S_{1}) = S_{1}^{2}$

$∴$ $S_{1} = \sqrt{K_{s p}} = 1.34 \times 10^{- 5}$ $mole/litre$

$Solubility of AgCl in 0.01 M {CaCl}_{2}$

$[{Ag}^{+}] = S_{2}, [{Cl}^{-}] = (2 \times 0.01 + S_{2})$ $K_{s p} = [{Ag}^{+}] [{Cl}^{-}]$ $∴$ $S_{2} = 9 \times 10^{- 9}$ $mole/litre$

$Solubility of AgCl in 0.01 M NaCl$

$[{Ag}^{+}] = S_{3}, [{Cl}^{-}] = (0.01 + S_{3})$ $∴$ $1.8 \times 10^{- 10} = S_{3} (0.01 + S_{3})$ $∴$ $S_{3} = 1.8 \times 10^{- 8}$ $mole/litre$

$Solubility of AgCl in 0.05 M {AgNO}_{3}$

$[{Ag}^{+}] = (0.05 + S_{4}), [{Cl}^{-}] = S_{4}$ $∴$ $S_{4} = 3.6 \times 10^{- 9}$ $mole/litre$

$From the values of solubility we get S_{1} > S_{3} > S_{2} > S_{4}$

Solution

Q.
The solubilities of AgCl in water, 0.01M ${CaCl}_{2}$ , 0.01M NaCl and 0.05M ${AgNO}_{3}$ are denoted by $S_{1}, S_{2}, S_{3}$ and $S_{4}$ respectively. Which of the following relationships is correct

1 $S_{1} > S_{2} > S_{3} > S_{4}$

2 $S_{1} > S_{3} > S_{2} > S_{4}$

3 $S_{1} > S_{2} = S_{3} > S_{4}$

4 $S_{1} > S_{3} > S_{4} > S_{2}$

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Solution

Q. The solubilities of AgCl in water, 0.01M CaCl2, 0.01M NaCl and 0.05M AgNO3 are denoted by S1,S2,S3 and S4 respectively. Which of the following relationships is correct

1 S1>S2>S3>S4

2 S1>S3>S2>S4

3 S1>S2=S3>S4