Question 6 of 29intermediate🔧 ApplyNumerical3 marks

Conductivity of 0.00241 M acetic acid is 7.896×107.896 \times 10⁻⁵ S cm⁻¹. Calculate its molar conductivity. If Λm⁰ for acetic acid is 390.5 S cm² mol⁻¹, what is its dissociation constant?

Correct Answer

To calculate the molar conductivity (Λm\Lambda_m), we use the formula Λm=κ×1000c\Lambda_m = \frac{\kappa \times 1000}{c}. Given conductivity (κ\kappa) is 7.896×10−57.896 \times 10^{-5} S cm−1^{-1} and concentration (cc) is 0.002410.00241 mol L−1^{-1}, the calculation is Λm=7.896×10−5×10000.00241=32.76\Lambda_m = \frac{7.896 \times 10^{-5} \times 1000}{0.00241} = 32.76 S cm2^2 mol−1^{-1}.

Next, we determine the degree of dissociation (α\alpha) using the relation α=ΛmΛm0\alpha = \frac{\Lambda_m}{\Lambda_m^0}. Given Λm0\Lambda_m^0 is 390.5390.5 S cm2^2 mol−1^{-1}, we find α=32.76390.5=0.0839\alpha = \frac{32.76}{390.5} = 0.0839.

Finally, the dissociation constant (KaK_a) is calculated using the formula Ka=cα21−αK_a = \frac{c\alpha^2}{1-\alpha}. Substituting the values, we get Ka=0.00241×(0.0839)21−0.0839=1.85×10−5K_a = \frac{0.00241 \times (0.0839)^2}{1 - 0.0839} = 1.85 \times 10^{-5}.

Exercise: EXERCISES | Q: 2.11 | (Chapter: Page 30)
For More Understanding

Explanation

The solution follows the standard methodology for weak electrolytes outlined in the context. First, molar conductivity is derived from conductivity and concentration using the conversion factor of 1000 to handle the liter to cm3cm^{3} unit difference. Second, the degree of dissociation is found by comparing the calculated molar conductivity to the limiting molar conductivity. Finally, the dissociation constant is determined using the concentration and degree of dissociation, consistent with the formulas provided in the text for weak electrolytes like acetic acid.

Solution Steps

  1. Step 1: Calculate Molar Conductivity (Λm\Lambda_m) using the formula Λm=κ×1000c\Lambda_m = \frac{\kappa \times 1000}{c}.

  2. Step 2: Calculate Degree of Dissociation (α\alpha) using the formula α=ΛmΛm0\alpha = \frac{\Lambda_m}{\Lambda_m^0}.

  3. Step 3: Calculate Dissociation Constant (KaK_a) using the formula Ka=cα21−αK_a = \frac{c\alpha^2}{1-\alpha}.

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