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  • The molar conductivity of 0.007 M acetic acid is <img alt="\mathrm{20 \ S \; cm^{2}mol^{-1}.}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B20%20%5C%20S%20%5C%3B%20cm%5E%7B2%7Dm

The molar conductivity of 0.007 M acetic acid is \mathrm{20 \ S \; cm^{2}mol^{-1}.}  What is the dissociation constant of acetic acid? Choose the correct option.

\left[\begin{array}{l} \Lambda_{\mathrm{H}^{+}}^{\circ}=350 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1} \\ \Lambda_{\mathrm{CH}_{3} \mathrm{COO}^{-}}^{\circ}=50 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1} \end{array}\right]
 

Option: 1

\mathrm{1.75 \times 10^{-4}\; mol\; L^{-1}}


Option: 2

\mathrm{2.50 \times 10^{-4}\; mol\; L^{-1}}


Option: 3

\mathrm{1.75 \times 10^{-5}\; mol\; L^{-1}}

 


Option: 4

\mathrm{2.50 \times 10^{-5}\; mol\; L^{-1}}


Answers (1)

best_answer

Given,

\Lambda_{\mathrm{m}}=20 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}

\Lambda_{\mathrm{m}}^{\circ} \mathrm{CH}_{3} \mathrm{COOH}=\Lambda_{\mathrm{CH}_{3} \mathrm{COO}^{-}}^{0}+\Lambda_{\mathrm{m}^{+}}^{\mathrm{o}}

\Lambda_{\mathrm{m}}^{\circ} \mathrm{CH}_{3} \mathrm{COOH}=50+350=400 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}

\alpha=\frac{\Lambda_{\mathrm{m}}}{\Lambda_{\mathrm{m}}^{\circ}}=\frac{20}{400}=\frac{1}{20}

\mathrm{K}_{\mathrm{a}}=\frac{\mathrm{C} \alpha^{2}}{1-\alpha} \simeq \mathrm{C} \alpha^{2}=7 \times 10^{-3} \times\left(\frac{1}{20}\right)^{2}

\mathrm{K}_{\mathrm{a}}=7 \times 10^{-3} \times \frac{1}{4} \times 10^{-2}

\mathrm{K}_{\mathrm{a}}=1.75 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1}

Therefore, the correct option is (3).

Posted by

Kuldeep Maurya

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