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Question: \[M{{(OH)}_{x}}\] has \[{{K}_{sp}}\] = \[27\times {{10}^{-12}}\] and solubility in water is \[{{10}^...

M(OH)xM{{(OH)}_{x}} has Ksp{{K}_{sp}} = 27×10−1227\times {{10}^{-12}} and solubility in water is 10−3{{10}^{-3}} M. Calculate the value of x.

Explanation

Solution

The solubility product is a type of equilibrium constant and its value depends on temperature of the solution. It is denoted with a symbol Ksp{{K}_{sp}}. Ksp{{K}_{sp}} usually increases with an increase in temperature due to increased solubility.

Complete Solution :
Whenever we are going to add M(OH)xM{{(OH)}_{x}} into water. It is going to convert into ions as follows.
M(OH)x→Mx++X OH−M{{(OH)}_{x}}\xrightarrow{{}}{{M}^{x+}}+X\text{ }O{{H}^{-}}

- The Solubility product of the above equation is as follows.
Ksp= !![!! Mx+] [OH−]x{{K}_{sp}}=\text{ }\\!\\![\\!\\!\text{ }{{M}^{x+}}]\text{ }{{[O{{H}^{-}}]}^{x}}
We know that the solubility product for any reaction is equal to the product of concentration of the products.
- In the question it is given that Ksp{{K}_{sp}} = 27×10−1227\times {{10}^{-12}}, !![!! Mx+]\text{ }\\!\\![\\!\\!\text{ }{{M}^{x+}}]= 10−3{{10}^{-3}} M . Substitute all these values in the above formula to get the value of x.

& 27\times {{10}^{-12}}=({{10}^{-3}}){{(X{{10}^{-3}})}^{x}} \\\ & {{X}^{x}}{{({{10}^{-3}})}^{x+1}}=27\times {{10}^{-12}} \\\ & {{X}^{x}}{{({{10}^{-3}})}^{x+1}}={{(3)}^{3}}\times {{({{10}^{-3}})}^{3+1}} \\\ & X=3 \\\ \end{aligned}$$ \- By comparing the both sides in the above expression we will get the value of X = 3. So, the molecular formula of the compound is $$M{{(OH)}_{3}}$$. **Additional Information:** \- If the value of a solubility product is small, the lower the solubility. Solubility products are useful in predicting whether a precipitate will form under specified conditions or not. \- Solubility products are also helpful in choosing conditions for the reaction. Under which two chemical substances in solution can be separated by fractional precipitation. \- The solubility product of a number of compounds has been experimentally determined and can be used to calculate solubility at a specified temperature. **Note:** Don’t be confused with the terms solubility product and Solubility. Both are not the same. \- Solubility product: The solubility product is a type of equilibrium constant and its value depends on the temperature of the solution. \- Solubility: “The amount of a substance that will dissolve in a given amount of solvent to give a saturated solution under specified conditions”.