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If concentration of two weak bases are s...

If concentration of two weak bases are same and D.O.D `(alpha)` are very less their ralative strength can be compared by :

A

`([OH^(-)]_(1))/([OH^(-)]_(2))`

B

`(Kb_(1))/(Kb_(2))`

C

`(alpha1)/(alpha2)`

D

`(sqrt(Kb_(1)))/(sqrt(Kb_(2)))`

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To solve the problem of comparing the relative strength of two weak bases with the same concentration and very low degrees of dissociation, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Weak Bases**: - Weak bases partially dissociate in solution. For example, if we have two weak bases, AOH and BOH, they dissociate as follows: - AOH ⇌ A⁺ + OH⁻ - BOH ⇌ B⁺ + OH⁻ 2. **Concentration and Degree of Dissociation**: - Let the concentration of both bases be C molar. - Let the degree of dissociation (α) for AOH be α₁ and for BOH be α₂. Since the degrees of dissociation are very small, we can assume that the concentration of undissociated base is approximately equal to C (i.e., 1 - α ≈ 1). 3. **Calculating Concentrations of Ions**: - The concentration of hydroxide ions (OH⁻) produced by each base can be expressed as: - For AOH: [OH⁻] = Cα₁ - For BOH: [OH⁻] = Cα₂ 4. **Equilibrium Constants**: - The base dissociation constant (K_b) for each base can be expressed as: - K_b₁ = [A⁺][OH⁻] / [AOH] = (Cα₁)(Cα₁) / (C(1 - α₁)) ≈ Cα₁² (since α₁ is small) - K_b₂ = [B⁺][OH⁻] / [BOH] = (Cα₂)(Cα₂) / (C(1 - α₂)) ≈ Cα₂² 5. **Relating K_b Values**: - From the above, we have: - K_b₁ ≈ Cα₁² - K_b₂ ≈ Cα₂² - Therefore, we can relate the two constants: - K_b₁ / K_b₂ = (Cα₁²) / (Cα₂²) = α₁² / α₂² 6. **Comparing Relative Strengths**: - The relative strength of the bases can be compared using the concentration of hydroxide ions produced: - Relative strength = [OH⁻]₁ / [OH⁻]₂ = (Cα₁) / (Cα₂) = α₁ / α₂ - Thus, we can conclude that: - α₁ / α₂ = K_b₁ / K_b₂ 7. **Final Conclusion**: - Since K_b values are directly related to the strength of the bases, we can compare the relative strength of the two weak bases based on their K_b values.
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