Question

The solubility of $\mathrm{\Lambda }\mathrm{gCl}$ in water at ${10}^{\circ }\mathrm{C}$ is $6.2\times$ ${10}^{-6}\mathrm{mol}/$ litre. The $K_{\mathrm{p}}$ of $\mathrm{\Lambda }\mathrm{gCl}$ is (1) ${[6.2\times {10}^6]}^2$ (2) ${[6.2\times {10}^{-6}]}^2$ (3) $6.2\times {\left({10}^{-6}\right)}^2$ (4) $(6.2{)}^2\times {10}^{-6}$

Short answer

Option (2) \left(6.2 \times 10^{-6}\right)^2.

Step-by-step solution

- Identify given information

The solubility of the compound $\mathrm{\Lambda }gCl$ in water at ${10}^{\circ }\mathrm{C}$ is $6.2\times {10}^{-6}$ mol/litre. This is the concentration of ${\mathrm{\Lambda }}^{+}$ and ${\mathrm{Cl}}^{-}$ in the solution when it is saturated.

- Define Solubility Product Constant (Kp)

$K_p$ represents the solubility product constant. For a general ionic compound $AB$ that dissociates into $A^{+}$ and $B^{-}$, the solubility product constant is given by $K_p=[A^{+}][B^{-}]$.

- Calculate the solubility product constant

Given the solubility $s=6.2\times {10}^{-6}$ mol/litre for $\mathrm{\Lambda }gCl$, we have $[{\mathrm{\Lambda }}^{+}]=s$ and $[{\mathrm{Cl}}^{-}]=s\text{.}Hence,K_p=[{\mathrm{\Lambda }}^{+}][{\mathrm{Cl}}^{-}]=(6.2\times {10}^{-6})(6.2\times {10}^{-6})={(6.2\times {10}^{-6})}^2$.

- Select the correct option

Compare the calculated solubility product ${(6.2\times {10}^{-6})}^2$ with the given options. The correct option is (2).

Key concepts

chemical equilibrium

Chemical equilibrium refers to the state in which the concentrations of the reactants and products remain constant over time in a closed system. At this point, the rate of the forward reaction equals the rate of the backward reaction. This means that the reaction has reached a balance where the amount of the substances involved does not change, although the reactions continue to occur at a microscopic level. Equilibrium is crucial in understanding solubility because when a solid ionic compound dissolves in water, it reaches a point where the maximum amount of solute has dissolved in the solvent. The system is now at equilibrium, and any additional solute will not dissolve until some of the dissolved solute precipitates out or a change in conditions occurs.

ionic compounds

Ionic compounds are formed when atoms transfer electrons from one to another, resulting in the creation of ions: positively charged cations and negatively charged anions. These ions are held together by strong electrostatic forces known as ionic bonds. When ionic compounds, like AgCl, dissolve in water, they dissociate into their constituent ions. For example, AgCl dissociates into Ag+ and Cl-. Understanding the properties and behavior of ionic compounds in aqueous solutions is essential for grasping the concept of solubility and the solubility product constant. Ionic compounds typically dissociate completely in water, creating a balanced number of positive and negative ions, which is vital for calculating equilibrium constants.

solubility

Solubility refers to the maximum amount of a solute that can dissolve in a solvent at a specific temperature and pressure to form a saturated solution. For ionic compounds in water, solubility is the concentration of the solute in its ionic form in the solution. The solubility product constant ($K_p$), is a measure of the solubility of ionic compounds. It is calculated by multiplying the molar concentrations of the ions, each raised to the power of its coefficient in the balanced equation. For example, for an ionic compound \ AB \ dissociating into \ A^+ \ and \ B^- \, \ K_p = [A^+][B^-]. Knowing how to calculate the solubility product constant allows us to predict whether a precipitate will form in a given solution and understand the factors affecting solubility.