If the solubility product of PbS is 8 × 10–28, then the solubility of PbS in pure water at 298 K is x × 10–16 mol L–1. The value of x is ________. (Nearest integer)
[given : \(\sqrt2=1.41\)]
[given : \(\sqrt2=1.41\)]
Correct Answer: 282
Approach Solution - 1
The solubility product \(K_{sp}\) of PbS is given as \(8 \times 10^{-28}\). For the compound PbS, the dissociation in water can be represented as:
\[ \text{PbS(s)} \rightleftharpoons \text{Pb}^{2+}(\text{aq}) + \text{S}^{2-}(\text{aq}) \]
Let the solubility of PbS be \(s\) mol L–1. Then, the concentration of Pb2+ and S2– ions will both be \(s\) mol L–1.
Thus, the \(K_{sp}\) expression is given by:
\[ K_{sp} = [\text{Pb}^{2+}][\text{S}^{2-}] = s \cdot s = s^2 \]
Substituting the \(K_{sp}\) value we have:
\[ s^2 = 8 \times 10^{-28} \]
Taking the square root of both sides gives:
\[ s = \sqrt{8 \times 10^{-28}} = \sqrt{8} \times 10^{-14} \]
We know: \(\sqrt{8} = 2 \times \sqrt{2}\)
Using \(\sqrt{2} = 1.41\), we get:
\[ \sqrt{8} = 2 \times 1.41 = 2.82 \]
Thus, the solubility \(s\) is:
\[ s = 2.82 \times 10^{-14} \text{ mol L}^{-1} \]
Therefore, the solubility in the form \(x \times 10^{-16}\) mol L–1 is:
\[ s = 282 \times 10^{-16} \text{ mol L}^{-1} \]
Hence, the value of \(x\) is 282.
The calculated value of \(x\) falls within the provided range of 282,282, confirming its correctness.
Approach Solution -2
\(\text{PbS(s)} \rightleftharpoons \text{Pb}^{2+}(\text{aq}) + \text{S}^{2-}(\text{aq})\)
\(Ksp = S2\)
\(8 \times 10^{-28} = \text{S}^{2}\)
\(S = 2\sqrt{2} \times 10^{-14} \, \text{mol/L}\)
\(2.82 \times 10^{-14} \, \text{mol/L} = 282 \times 10^{-16} \, \text{mol/L}\)
Hence, \(x = 282\)\(\)
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.