If equal volumes of $AB_2$ and $XY$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $AY_2$ at 300 K ?
(Given $K_{sp}$ (at 300 K) for $AY_2=5.2 \times 10^{-7}$)
Precipitation Condition for
Precipitation of a sparingly soluble salt occurs when the ionic product ($Q_{sp}$) of its constituent ions exceeds its solubility product ($K_{sp}$). The salt in question is , which dissociates as:
$AY_2 \rightleftharpoons A^{2+} + 2Y^-$
The solubility product expression is:
$K_{sp} = [A^{2+}][Y^-]^2$
For precipitation to occur, the calculated ionic product ($Q_{sp}$) using the concentrations of $A^{2+}$ and $Y^-$ ions after mixing must be greater than the given $K_{sp}$ value.
Ion Concentrations After Mixing
The ions contributing to the potential precipitate are $A^{2+}$ from $AB_2$ and $Y^-$ from $XY$. The dissociation reactions are:
$AB_2 \rightarrow A^{2+} + 2B^-$
$XY \rightarrow X^{+} + Y^-$
When equal volumes of the two solutions are mixed, the concentration of each ion is effectively halved due to dilution.
- Concentration of $A^{2+}$ after mixing = $\frac{[AB_2]_{initial}}{2}$
- Concentration of $Y^-$ after mixing = $\frac{[XY]_{initial}}{2}$
Analyzing Option C for Precipitation
Let's analyze Option C, which states initial concentrations of $2.0 \times 10^{-4}$ M $AB_2$ and $0.8 \times 10^{-3}$ M $XY$.
Step 1: Calculate ion concentrations after mixing.
- Initial $[AB_2] = 2.0 \times 10^{-4}$ M
- Initial $[XY] = 0.8 \times 10^{-3}$ M
- After mixing equal volumes:
- $[A^{2+}] = \frac{2.0 \times 10^{-4} \text{ M}}{2} = 1.0 \times 10^{-4}$ M
- $[Y^-] = \frac{0.8 \times 10^{-3} \text{ M}}{2} = 0.4 \times 10^{-3}$ M
Step 2: Calculate the ionic product ($Q_{sp}$).
Using the concentrations calculated above:
$Q_{sp} = [A^{2+}][Y^-]^2$
$Q_{sp} = (1.0 \times 10^{-4} \text{ M}) \times (0.4 \times 10^{-3} \text{ M})^2$
$Q_{sp} = (1.0 \times 10^{-4}) \times (0.16 \times 10^{-6})$
$Q_{sp} = 0.16 \times 10^{-10} = 1.6 \times 10^{-11}$
Step 3: Compare $Q_{sp}$ with $K_{sp}$.
The given $K_{sp}$ for $AY_2$ is $5.2 \times 10^{-7}$ at 300 K.
$Q_{sp} = 1.6 \times 10^{-11}$
$K_{sp} = 5.2 \times 10^{-7}$
Precipitation occurs if $Q_{sp} > K_{sp}$. Comparing the values, $1.6 \times 10^{-11}$ is less than $5.2 \times 10^{-7}$.
Similar Questions
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Important Questions from Physical Chemistry
$CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + CO_2(g) + H_2O(l)$
Consider the above reaction, what mass of $CaCl_2$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $CaCO_3$ ?
(Given: Molar mass of Ca, C, O, H and Cl are 40, 12, 16, 1 and 35.5 g $mol^{-1}$, respectively)- According to Bohr's model of hydrogen atom, which of the following statement is incorrect?
Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?Which of the following graphs correctly represents the plot of $K_H$ at 1 bar for gases in water versus temperature?
On complete combustion 1.0 g of an organic compound (X) gave 1.46 g of $CO_2$ and 0.567 g of $H_2O$. The empirical formula mass of compound (X) is ________ g.
(Given molar mass in g $mol^{-1}$ C: 12, H: 1, O: 16)
