Question

The equation for the solubility product constant of $A{g_2}Cr{O_4}$ is:
A.${K_{sp}} = \left[ {A{g^{2 + }}} \right]\,.\,\left[ {Cr{O^{2 - }}} \right]$
B.${K_{sp}} = \left[ {A{g^ + }} \right]{\,^2}.\,\left[ {C{r^{6 + }}} \right]\,.\left[ {O_4^{8 - }} \right]$
C.${K_{sp}} = \left[ {A{g^ + }} \right]\,.\,\left[ {C{r^{6 + }}} \right]\,.\left[ {O_4^{8 - }} \right]$
D.${K_{sp}} = {\left[ {A{g^ + }} \right]^2}\,.\,\left[ {Cr{O_4}^{2 - }} \right]$

Answer 1

In this question, we have to predict the correct solubility product from the given options. Solubility product or solubility constant $\left( {{K_{sp}}} \right)$ is used for equations when a solid substance is dissolving in an aqueous solution. It is used for the solutes that are only slightly soluble and do not completely dissolve in solution. It represents how much of the solute will dissolve in the solution.

Complete step by step answer:
$A{g_2}Cr{O_4}$ dissociates as –
$A{g_2}Cr{O_4}\,(s) \rightleftharpoons 2\,A{g^ + }\,(aq) + \,CrO_4^{2 - }(aq)$
The stoichiometric coefficient of $A{g^ + }$ is 2 and its charge is $+ 1$.
The stoichiometric coefficient of $CrO_4^{2 - }$ is 1 and its charge is $- 2$.
We know that the solubility product or solubility constant $\left( {{K_{sp}}} \right)$ is equal to the concentrations of the constituents ions present in salt their powers which is their respective stoichiometric coefficient.
Therefore the solubility product ${K_{sp}}$ of $A{g_2}Cr{O_4}$ is
${K_{sp}} = {\left[ {A{g^ + }} \right]^2}\,.\,\left[ {Cr{O_4}^{2 - }} \right]$
Thus, the correct option is (D).

Note:
Factors affecting solubility product $\left( {{K_{sp}}} \right)$
Temperature: Most solutes become more soluble in a liquid as the temperature is increased. If we talk about the proof regarding this statement, then we see how well instant coffee mixes in a cup of cold water compared to a cup of hot water. The temperature shows its effect on the solubility of gases as well as solids but the effect on the solubility of liquids is yet not determined properly.
Pressure: Pressure can also show its effect on solubility, but only for gases that exist in the form of liquids. Henry’s law is defined in terms of solubility and partial pressure of a gas.
Henry’s law is written as $p = kc$, where
p is the partial pressure of the gas above the liquid
k is the Henry’s law constant
c is the concentration of gas in the liquid
Henry’s law shows that, as partial pressure decreases, the concentration of gas in the liquid also decreases, due to which its solubility decreases. So less pressure results in less solubility, and more pressure results in more solubility.
Molecular size: The solutes having smaller molecules are considered to be more soluble than the solutes with the larger molecules. It’s easier for the solvent to surround smaller molecules, so those molecules can be dissolved faster than larger molecules.