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Chemistry Question on Acids and Bases

Which of the following salts is most soluble?

A

Bi2S3(Ksp=1×10−17)B i_{2} S_{3}\left(K_{s p}=1 \times 10^{-17}\right)

B

MnS(Ksp=7×10−16)M n S\left(K_{s p}=7 \times 10^{-16}\right)

C

CuS(Ksp=8×10−37)C u S\left(K_{s p}=8 \times 10^{-37}\right)

D

Ag2S(Ksp=6×10−51)A g_{2} S\left(K_{s p}=6 \times 10^{-51}\right)

Answer

Bi2S3(Ksp=1×10−17)B i_{2} S_{3}\left(K_{s p}=1 \times 10^{-17}\right)

Explanation

Solution

Bi2S3222si3++33s2−B i_{2} S_{3} 2 \underset{2 s}{2} i^{3+}+3 \underset{3 s}{ }^{2-} Ksp=(2s)2(3s)3=108s5K_{s p}=(2 s)^{2}(3 s)^{3}=108 s^{5} 108s5=1×10−17108 s^{5}=1 \times 10^{-17} s=(1×10−17108)1/5=1.56×10−4s=\left(\frac{1 \times 10^{-17}}{108}\right)^{1 / 5}=1.56 \times 10^{-4} MnSMn2+s+S2−sM n S \underset{s}{M n^{2+}}+\underset{s}{S^{2-}} Ksp=s2s=Ksp=7×10−16K_{s p}=s^{2} s=\sqrt{K_{s p}}=\sqrt{7 \times 10^{-16}} =2.64×10−8CuSCu2+s+S2−s=2.64 \times 10^{-8} CuSC\underset{s}{u ^{2+}}+\underset{s}{S^{2-}} Ksp=s28×10−37=s2K_{s p}=s^{2} 8 \times 10^{-37}=s^{2} s=8×10−37=0.89×10−18s=\sqrt{8 \times 10^{-37}}=0.89 \times 10^{-18} Ag2S2Ag+2s+S2−sKsp=4s3A g_{2} S 2 \underset{2 s}{ Ag ^{+}}+\underset{s}{S^{2-}} K_{s p}=4 s^{3} 4s3=6×10−51s=6×10−51434 s^{3}=6 \times 10^{-51} s=\sqrt[3]{\frac{6 \times 10^{-51}}{4}} =1.5×10−513=1.14×10−17=\sqrt[3]{1.5 \times 10^{-51}}=1.14 \times 10^{-17} The solubility of Bi2S3Bi _{2} S _{3} is maximum. Hence, it is the most soluble.