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Question: Concentration of the \(A{{g}^{+}}\) ions in a saturated solution of \(A{{g}_{2}}{{C}_{2}}{{O}_{4}}\)...

Concentration of the Ag+A{{g}^{+}} ions in a saturated solution of Ag2C2O4A{{g}_{2}}{{C}_{2}}{{O}_{4}} is 2.2×10−4molL−12.2\times {{10}^{-4}}mol{{L}^{-1}}. Solubility product of Ag2C2O4A{{g}_{2}}{{C}_{2}}{{O}_{4}} is __________.
A. 5.3×10−125.3\times {{10}^{-12}}
B. 2.42×10−82.42\times {{10}^{-8}}
C. 2.66×10−122.66\times {{10}^{-12}}
D. 4.5×10−114.5\times {{10}^{-11}}

Explanation

Solution

Solubility product is a constant or equilibrium constant for the dissociation of solid substances into aqueous solution. It depends on temperature and is represented by Ksp.

Complete step by step answer:
The property of the body by which the solute dissolves in a solvent to form a solution is called solubility.
Solubility product is the equilibrium constant which increases with increase in temperature since solubility increases with temperature.
Solubility product also depends upon lattice energy of salt and salvation enthalpy of ions. Most salts dissociate into ions when they dissolve.
Solubility is different for different salts:
Soluble Solubility>0.1M>0.1M
Slightly soluble 0.01M<0.01M< Solubility<0.1M<0.1M
Sparingly soluble Solubility <0.1M<0.1M
The presence of a common ion lowers the value of the solubility product that is the common-ion effect.
If the ions are uncommon among the solute Ksp will be high due to diverse-ion effect. The presence of ion pairs will also affect Ksp value.
The reaction in the question will take place in the following way:Ag2C2O4⇌2Ag++C2O42−A{{g}_{2}}{{C}_{2}}{{O}_{4}}\rightleftharpoons 2A{{g}^{+}}+{{C}_{2}}{{O}_{4}}^{2-}
Therefore, 22 moles of Ag+A{{g}^{+}} will give us 0.50.5 moles of C2O42−{{C}_{2}}{{O}_{4}}^{2-}. This indicates that the concentration of C2O42−{{C}_{2}}{{O}_{4}}^{2-} will be 0.50.5 times that of Ag+A{{g}^{+}}ions.
The solubility product of Ag2C2O4A{{g}_{2}}{{C}_{2}}{{O}_{4}} will be
Ksp=[Ag+]2[C2O42−]{{K}_{sp}}={{[A{{g}^{+}}]}^{2}}[{{C}_{2}}O_{4}^{2-}]
Now, we have given the concentration of Ag+A{{g}^{+}} ions is 2.2×10−4molL−12.2\times {{10}^{-4}}mol{{L}^{-1}}
the concentration of C2O42−{{C}_{2}}{{O}_{4}}^{2-} will be 0.5[Ag+]=0.5×2.2×10−4molL−1=1.1×10−4molL−10.5[A{{g}^{+}}]=0.5\times 2.2\times {{10}^{-4}}mol{{L}^{-1}}=1.1\times {{10}^{-4}}mol{{L}^{-1}}
Ksp=(2.2×10−4molL−1)2×1.1×10−4molL−1 Ksp=5.3×10−12 \begin{aligned} & {{K}_{sp}}={{(2.2\times {{10}^{-4}}mol{{L}^{-1}})}^{2}}\times 1.1\times {{10}^{-4}}mol{{L}^{-1}} \\\ & {{K}_{sp}}=5.3\times {{10}^{-12}} \\\ \end{aligned}

Note: We squared the concentration of Ag ions since we obtained twice the Ag ions in the products. If it would have been three or four or any other number the power would be 33 or $$ 44 or the other number.