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Zorluk: Çok zorRelative Strength and Ionization of Acids and Bases

A 0.04 mol dm−30.04\text{ mol dm}^{-3} aqueous solution of a weak monobasic acid, HA\text{HA}, is 2.0%2.0\% ionized at 25∘C25^\circ\text{C}. If distilled water is added to this solution until its total volume is quadrupled, what is the degree of ionization of the acid in the diluted solution?

  1. A
    0.5%0.5\%
  2. B
    1.0%1.0\%
  3. 4.0%4.0\%Cevap
  4. D
    8.0%8.0\%

Cevap

The degree of ionization of the acid in the diluted solution is 4.0%4.0\%.
By Ostwald's dilution law for weak monobasic acids, Ka=α2CK_a = \alpha^2 C, which rearranges to α=KaC\alpha = \sqrt{\frac{K_a}{C}}. Since KaK_a is constant at a fixed temperature, the degree of ionization α\alpha is inversely proportional to the square root of the concentration (α∝1C\alpha \propto \frac{1}{\sqrt{C}}). Quadrupling the volume decreases the concentration by a factor of 4 (C2=C14C_2 = \frac{C_1}{4}), which increases the degree of ionization by a factor of 4=2\sqrt{4} = 2. Therefore, the new degree of ionization is 2.0%×2=4.0%2.0\% \times 2 = 4.0\%.

Adım Adım Çözüm

1
Calculate the acid dissociation constant (KaK_a) using the initial concentration and degree of ionization.
Initial concentration C1=0.04 mol dm−3C_1 = 0.04\text{ mol dm}^{-3}, initial degree of ionization α1=2.0%=0.02\alpha_1 = 2.0\% = 0.02. Using Ka≈α12C1K_a \approx \alpha_1^2 C_1, we get Ka=(0.02)2×0.04=4.0×10−4×0.04=1.6×10−5 mol dm−3K_a = (0.02)^2 \times 0.04 = 4.0 \times 10^{-4} \times 0.04 = 1.6 \times 10^{-5}\text{ mol dm}^{-3}.
The value of KaK_a depends only on temperature and remains constant upon dilution.
2
Determine the new concentration (C2C_2) after quadrupling the solution volume.
C2=C14=0.04 mol dm−34=0.01 mol dm−3C_2 = \frac{C_1}{4} = \frac{0.04\text{ mol dm}^{-3}}{4} = 0.01\text{ mol dm}^{-3}.
Diluting a solution to 4 times its original volume reduces its molar concentration by a factor of 4.
3
Calculate the new degree of ionization (α2\alpha_2) in the diluted solution.
\alpha_2 = \sqrt{\frac{K_a}{C_2}} = \sqrt{\frac{1.6 \times 10^{-5}}{0.01}} = \sqrt{1.6 \times 10^{-3}} = \sqrt{16 \times 10^{-4}} = 4.0 \times 10^{-2} = 0.04 = 4.0\%$.
Applying Ostwald's dilution law to find the updated degree of dissociation at the lower concentration.

Anahtar Kavram

Ostwald's Dilution Law and the relationship between dilution, concentration, and degree of ionization of weak electrolytes.
Tahmini Süre:2m 30s
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Relative Strength and Ionization of Acids and Bases

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