A) \[\frac{{{S}_{1}}}{{{S}_{2}}}=1\]
B) \[{{S}_{1}}-{{S}_{2}}>0\]
C) \[{{S}_{1}}-{{S}_{2}}<0\]
D) \[\frac{{{S}_{1}}}{{{S}_{2}}}>1\]
Correct Answer: C
Solution :
| [c] \[{{S}_{1}}=\frac{{{K}_{sp}}}{{{0.5}^{2}}},\,{{S}_{2}}=\sqrt{\frac{{{K}_{sp}}}{0.5}}\] |
| \[\frac{{{S}_{1}}}{{{S}_{2}}}=\frac{{{K}_{sp}}}{{{0.5}^{2}}}\times \sqrt{\frac{0.5}{{{K}_{sp}}}}=\frac{\sqrt{{{K}_{sp}}}}{0.5\times \sqrt{0.5}}=\frac{\sqrt{{{K}_{sp}}}}{0.707\times 0.5}\] |
| But \[\because \] \[{{K}_{sp}}<<<1\] |
| \[\therefore \] \[\frac{{{S}_{1}}}{{{S}_{2}}}<1\] \[\therefore \] \[{{S}_{1}}<{{S}_{2}}\] |
| \[\therefore \] \[{{S}_{1}}-{{S}_{2}}<0\] |
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