Question

The solubility of a sparingly soluble salt $A_x{B}_y$ in water at ${25}^{0}C=1.4\times {10}^{-4}M$. The solubility product is $1.1\times {10}^{-11}$. Select the correct possible option(s):

• A. $x=1$
• B. $y=2$
• C. $\frac{x}{y}=1$
• D. $\frac{x}{y}=0.5$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $x=1$
B $y=2$
D $\frac{x}{y}=0.5$

Lets say the solubility of salt is s, then:
$K_{sp}\left(A_x{B}_y\right)$ = $x^x\times y^y\times s^{x+y}$
Now for the given value of solubility product, and solubility we have 2 variables and 1 equation. We can use the given options to backtrack the options that make sense:
For $x=1andy=2$
$K_{sp}\left(A_x{B}_y\right)$= $1^1\times 2^2\times {1.4}^3\times {10}^{-12}=1.1\times {10}^{-11}$
But we also know that equation holds true for $x=2andy=1$