Question

If the equivalent conductance of $1M$ benzoic acid is \[12.8\]\[oh{{m}^{-1}}c{{m}^{2}}equi{{v}^{-1}}\] and if the conductance of benzoate and ${{H}^{+}}$ ions are $42$ and $288.42$\[oh{{m}^{-1}}c{{m}^{2}}equi{{v}^{-1}}\] respectively. What is its percentage of dissociation?

Answer 1

Hint: Weak electrolyte is defined as an electrolyte that cannot dissociate completely in the aqueous solution or liquid. The conductivity of the solution at infinite dilution is called as limiting molar conductance. Conductance is defined as a degree with which an object conducts electricity.

Formula used:
$\alpha =\dfrac{{{\Lambda }^{c}}_{m}}{{{\Lambda }^{\alpha }}_{m}}$
where, $\alpha $ is the degree of dissociation, ${{\Lambda }_{m}}$ is the equivalent conductance of benzoic acid and ${{\Lambda }^{\alpha }}_{m}$ is the limiting molar conductance.
${{\Lambda }^{\alpha }}_{m}={{\Lambda }^{\alpha }}_{{{C}_{6}}{{H}_{5}}CO{{O}^{-}}}+{{\Lambda }^{\alpha }}_{{{H}^{+}}}$
where, $\alpha $ is the degree of dissociation, ${{\Lambda }_{m}}$ is the equivalent conductance of benzoic acid and ${{\Lambda }^{\alpha }}_{m}$ is the limiting molar conductance.

Complete step by step answer:
Here, it is given that the equivalent conductance of benzoic acid is \[12.8\]\[oh{{m}^{-1}}c{{m}^{2}}equi{{v}^{-1}}\] .
Also,
The conductance of benzoate ion $=42~$\[oh{{m}^{-1}}c{{m}^{2}}equi{{v}^{-1}}\]
And, the conductance of ${{H}^{+}}$ ion $=~$$288.42$\[oh{{m}^{-1}}c{{m}^{2}}equi{{v}^{-1}}\]
Let us see the formula to calculate the degree of dissociation
$\alpha =\dfrac{{{\Lambda }^{c}}_{m}}{{{\Lambda }^{\alpha }}_{m}}$
where,$\alpha $ is the degree of dissociation, ${{\Lambda }_{m}}$ is the equivalent conductance of benzoic acid and ${{\Lambda }^{\alpha }}_{m}$ is the limiting molar conductance.
Firstly, you should know how to calculate limiting molar conductance. The formula can be written as:
${{\Lambda }^{\alpha }}_{m}={{\Lambda }^{\alpha }}_{{{C}_{6}}{{H}_{5}}CO{{O}^{-}}}+{{\Lambda }^{\alpha }}_{{{H}^{+}}}$
where, ${{\Lambda }^{\alpha }}_{{{C}_{6}}{{H}_{5}}CO{{O}^{-}}}$ is the conductance of benzoate ion and ${{\Lambda }^{\alpha }}_{{{H}^{+}}}$ is the conductance of ${{H}^{+}}$ ion.
Substituting the values in the above formula, we get,
${{\Lambda }^{\alpha }}_{m}=42+288.42=330.42$\[oh{{m}^{-1}}c{{m}^{2}}equi{{v}^{-1}}\]
Now, we will substitute the value of ${{\Lambda }^{\alpha }}_{m}$ and equivalent conductance in the formula to calculate degree of dissociation.
$\alpha =\dfrac{12.8}{330.42}=0.0387$\[oh{{m}^{-1}}c{{m}^{2}}equi{{v}^{-1}}\]
Now, converting it into percentage
Percentage dissociation $=0.0387\times 100\Rightarrow 3.8%$
Therefore, the percentage dissociation is $3.8%$ .

Additional Information:
Degree of dissociation for weak electrolyte is defined as the fraction of equivalent conductance to the limiting molar conductance and it is denoted with a Greek symbol $(\alpha )$ .
Limiting molar conductance is defined as the conductance when the concentration of an electrolyte approaches to zero.
Equivalent conductance is produced by $1g$ equivalent of electrolyte when dissolved to form a solution. It is an intensive property.
Electrolytic conductance is of three types:
Specific conductance
Molar conductance
Equivalent conductance

Note:
The SI unit of equivalent conductance is \[oh{{m}^{-1}}c{{m}^{2}}equi{{v}^{-1}}\] .
Conductance is defined as a degree to which an object is allowed to conduct electricity.
increase in dilution also increases the conduction of a weak electrolyte
The degree of dissociation of a weak electrolyte increases with dilution.