Question

Molar conductivity of a weak acid HA at infinite dilution is \[345.8{\text{ S c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\]. Calculate molar conductivity of \[0.05{\text{ M HA}}\] solution. Given that \[\alpha = 5.8 \times {10^{ - 6}}\].

Answer 1

Hint: For this we must know the relation between the molar conductivity at infinite solution. Substituting the known values in the formula we will get the molar conductivity of the weak acid.
Formula used:
 \[{\Lambda ^{\text{c}}} = \Lambda ^\circ \times \alpha \]
Here \[{\Lambda ^{\text{c}}}\] is the molar conductance of weak acid at any concentration, \[\Lambda ^\circ \] is the molar conductance of weak acid at infinite dilution and \[\alpha \] is the degree of dissociation.

Complete step by step answer:
The value of \[\Lambda ^\circ \] is given to us that is \[345.8{\text{ S c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\]
The value of \[\alpha \] is \[5.8 \times {10^{ - 6}}\]
Using the formula we will get:
\[{\Lambda ^{\text{c}}} = 345.8{\text{ S c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}} \times 5.8 \times {10^{ - 6}}\]
Hence solving the above equation we will get:
\[{\Lambda ^{\text{c}}} = 0.002005{\text{ S c}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\]

Additional information:
At infinite dilution the weak acid also becomes or behaves as strong acid. Infinite solution is a point when conductance of electrolyte gets saturated and at that point the molar conductance is known as limiting molar conductance. The force of attraction due to dilution becomes very less and hence they also dissociate completely at infinite solution. Molar conductivity is the conductance of a solution that contains one mole of electrolyte or simply it is the conductance of one mole of electrolyte. Molar conductivity of both strong and weak electrolytes increases with decrease in concentration. Alpha is the degree of dissociation of an electrolyte which states that the amount of electrolyte dissociates per unit amount of electrolyte that was taken initially.

Note:
Electrolytes are the substance which does not conduct electricity. In the solid state but is an electric conductor in their molten or aqueous state. This happens because of the presence of free ions in electrolyte when they dissociate and the movement of these ions will carry current.