Concentration of $H _2 SO _4$ and $Na _2 SO _4$ in a solution is $1 M$ and $1.8 \times 10^{-2} M$, respectively. Molar solubility of $PbSO _4$ in the same solution is $X \times 10^{- Y } M$ (expressed in scientific notation). The value of $Y$ is ________. [Given: Solubility product of $PbSO _4\left(K_{s p}\right)=1.6 \times 10^{-8}$ For $H _2 SO _4, K_{a l}$ is very large and $\left[K_{a 2}=1.2 \times 10^{-2}\right]$
Correct Answer: 6
Solution and Explanation
Concentration of $H _2 SO _4$ and $Na _2 SO _4$ in a solution is $1 M$ and $1.8 \times 10^{-2} M$
\(H_2SO_4\rightarrow H^++HSO^-_4\)
\(HSO^-_4\rightleftharpoons H^++SO^{2-}_4 \\ \begin{matrix} 1 && 1 & 1.8\times10^{-2} \\1+x && 1-x & (1.8\times10^{-2}-x) \end{matrix}\)
\(x\approx1 \; x\lt1.8\times10^{-2}\)
\(k_{a_2}=1.2\times10^{-2}\)
\(1.2\times10^{-2}=\frac{1\times[SO^{2-}_4]}{1}\)
\([SO^{2-}_4]=1.2\times10^{-2}M\)
\(PbSO_4 \rightleftharpoons Pb^{2+}+SO^{2-}_4 \\ \begin{matrix} &&&&&s && 1.2\times10^{-2}\end{matrix}\)
\(s=\frac{K_{sp}}{1.2\times10^{-2}}\)
\(s=\frac{1.6\times10^{-8}}{1.2\times10^{-2}}\)
\(s=1.33\times10^{-6}\)
\(Y=6\)
So, the answer is 6.
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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.