Zncl2 undergoes hydrolysis zncl2+2H2O givesrise to zn(oH)2+2hcl.The overall kb for zn(oh)2 is 2.5·10^-12at 25 degree c.The degree of hydrolysis of 0.001m zncl2 solution is

To determine the degree of hydrolysis of a 0.001 M ZnCl2 solution, we need to analyze the hydrolysis reaction and the equilibrium involved. The hydrolysis of ZnCl2 can be represented as follows:

The Hydrolysis Reaction

When zinc chloride (ZnCl2) dissolves in water, it dissociates into zinc ions (Zn²⁺) and chloride ions (Cl⁻). The zinc ions can then undergo hydrolysis:

• ZnCl2 → Zn²⁺ + 2Cl⁻
• Zn²⁺ + 2H2O ⇌ Zn(OH)2 + 2H⁺

In this reaction, zinc ions react with water to form zinc hydroxide (Zn(OH)2) and hydrogen ions (H⁺), which indicates that the solution will be acidic due to the release of H⁺ ions.

Understanding the Equilibrium Constant

The equilibrium constant for the hydrolysis reaction can be expressed in terms of the concentrations of the products and reactants at equilibrium. Given that the overall Kb for Zn(OH)2 is 2.5 × 10^-12 at 25 degrees Celsius, we can use this value to find the degree of hydrolysis.

Setting Up the Equilibrium Expression

The hydrolysis reaction can be represented as:

• Zn²⁺ + 2H2O ⇌ Zn(OH)2 + 2H⁺

The equilibrium expression for this reaction is:

Kb = [Zn(OH)2][H⁺]² / [Zn²⁺]

Calculating the Degree of Hydrolysis

Let’s denote the degree of hydrolysis as 'x'. In a 0.001 M solution of ZnCl2, the initial concentration of Zn²⁺ is 0.001 M. When hydrolysis occurs, 'x' moles of Zn²⁺ will react to form 'x' moles of Zn(OH)2 and '2x' moles of H⁺. Therefore, at equilibrium, we have:

• [Zn²⁺] = 0.001 - x
• [Zn(OH)2] = x
• [H⁺] = 2x

Substituting these values into the Kb expression gives:

2.5 × 10^-12 = (x)(2x)² / (0.001 - x)

This simplifies to:

2.5 × 10^-12 = (4x³) / (0.001 - x)

Assuming that x is small compared to 0.001, we can approximate (0.001 - x) as 0.001. Thus, the equation becomes:

2.5 × 10^-12 = 4x³ / 0.001

Rearranging gives:

x³ = (2.5 × 10^-12 * 0.001) / 4

x³ = 6.25 × 10^-16

Taking the cube root of both sides, we find:

x ≈ 8.55 × 10^-6

Calculating the Degree of Hydrolysis

The degree of hydrolysis (h) can be calculated as:

h = x / C

Where C is the initial concentration of ZnCl2 (0.001 M):

h = (8.55 × 10^-6) / (0.001) = 0.00855

Thus, the degree of hydrolysis of the 0.001 M ZnCl2 solution is approximately 0.00855, or 0.855%.

Final Thoughts

This calculation illustrates how the hydrolysis of metal salts can lead to the formation of acidic solutions and how to apply equilibrium concepts to determine the degree of hydrolysis. Understanding these principles is crucial for predicting the behavior of solutions in various chemical contexts.