At 25Degree Centigrate the equivalent conductance of 0.1M benzoic acid is 8.9Ω^-1cm^2eqiv^-1. The ionic conductance at infinite dilution of the hydrogen ion and benzoc ion are 349.8 and 32.3ohm^-1cm^2 respectively.Calculate the degree of dissociation of 0.1M benzoic acid?

To calculate the degree of dissociation of 0.1M benzoic acid, we can use the concept of equivalent conductance and the values provided for the ionic conductance at infinite dilution. The degree of dissociation (α) indicates how much of the acid has dissociated into its ions in solution. Let's break this down step by step.

Understanding the Components

We have the following information:

• Equivalent conductance of 0.1M benzoic acid (Λ) = 8.9 Ω^-1cm²equiv^-1
• Ionic conductance at infinite dilution of hydrogen ion (Λ_H+) = 349.8 Ω^-1cm²
• Ionic conductance at infinite dilution of benzoate ion (Λ_C6H5COO-) = 32.3 Ω^-1cm²

Calculating the Total Ionic Conductance

The total ionic conductance at infinite dilution for benzoic acid can be calculated using the formula:

Λ_total = Λ_H+ + Λ_C6H5COO-

Substituting the values:

Λ_total = 349.8 + 32.3 = 382.1 Ω^-1cm²

Finding the Degree of Dissociation

The degree of dissociation (α) can be calculated using the formula:

α = (Λ / Λ_total)

Substituting the known values:

α = (8.9 / 382.1)

Calculating this gives:

α ≈ 0.0233

Interpreting the Result

This means that approximately 2.33% of the benzoic acid has dissociated into its ions in a 0.1M solution. This relatively low degree of dissociation is typical for weak acids like benzoic acid, which do not fully ionize in solution.

Conclusion

In summary, the degree of dissociation of 0.1M benzoic acid is about 0.0233, indicating that only a small fraction of the acid molecules dissociate into ions. This is an important concept in understanding the behavior of weak acids in solution.