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Ksp of AgCl at 18C is 1.8×1010. If Ag of solution is 4×103 mol/litre, the Cl that must exceed before AgCl is precipitated would be (1) 4.5×108 mol/ litre (2) 7.2×1013 mol/ litrc (3) 4.0×103 mol/ litre (4) 4.5×107 mol/ itre

Short Answer

Expert verified
The Clconcentrationmustexceed4.5 \times 10^{-8}mol/LforAgCl$ to precipitate. The correct answer is option (1).

Step by step solution

01

Understanding the Problem

Given the solubility product constant (Ksp) of AgCl and the concentration of Ag+ ions in the solution, determine the concentration of Cl ions required to start precipitating AgCl.
02

Writing the Solubility Product Expression

The solubility product expression for AgCl is given by Ksp=[Ag+]×[Cl].
03

Substitute Given Values into Equation

Given Ksp=1.8×1010 and [Ag+]=4×103 mol/L, substitute these values into the solubility product expression: 1.8×1010=(4×103)×[Cl].
04

Solve for [Cl]

Rearrange the equation to solve for [Cl]: [Cl]=1.8×10104×103.
05

Perform the Calculation

Perform the division: [Cl]=1.8×10104×103=4.5×108 mol/L.
06

Identify the Correct Answer

Among the given options, 4.5×108 mol/L matches with option (1).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ksp (Solubility Product Constant)
In chemistry, the solubility product constant, represented as Ksp, is an equilibrium constant that applies to the solubility of ionic compounds. When an ionic compound dissolves in water, it dissociates into its constituent ions. Ksp expresses the product of the concentrations of these ions, each raised to the power of its coefficient in the balanced equation. For example, if we have a compound AB that dissolves into A⁺ and B⁻ ions, the Ksp expression is: Ksp=[A+]×[B]. This constant is specific to a particular ionic compound at a particular temperature. A low Ksp value indicates that the compound is not very soluble in water. In the original exercise, the Ksp of AgCl (Silver Chloride) at 18°C is provided as 1.8×1010.
Precipitation of Ionic Compounds
Precipitation occurs when the product of the ion concentrations in a solution exceeds the Ksp of the ionic compound. In simple terms, if the concentration of dissolved ions in a solution is too high, the excess ions will combine to form a solid precipitate, falling out of the solution. This process helps us understand at what point a certain amount of ions will start forming a solid compound again. In our provided exercise, we want to find the concentration of chloride ions (Cl⁻) that will cause AgCl to start precipitating. We use the given Ksp and the concentration of Ag⁺ ions. By rearranging and solving the Ksp expression, we can find the critical concentration of Cl⁻ that initiates precipitation.
Equilibrium Concentrations
Equilibrium concentrations refer to the steady-state concentrations of reactants and products in a chemical reaction that has reached equilibrium. In the context of solubility equilibria, such as with the dissolution of an ionic compound, equilibrium is reached when the rate of dissolution equals the rate of precipitation. For example, in the dissolution of AgCl, we write the equilibrium as follows: Ksp=[Ag+]×[Cl]. Given that the system is at equilibrium, the concentrations of Ag⁺ and Cl⁻ ions will remain constant as long as no additional ions are added or removed. Solving the provided exercise involves calculating the equilibrium concentration of Cl⁻ given the Ksp and the concentration of Ag⁺, which helps to determine when precipitation will occur.

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