Question

Choose the correct option(s) regarding transport number:
Here,
$t_{+}\text{is the transport number of cation}$
$t_{-}\text{is the transport number of anion}$
${\Lambda }_{+}\text{is the molar conductance of cation}$
${\Lambda }_{-}\text{is the molar conductance of anion}$

• A. For an ionic solution, current carried by an ion depends upon the speed of the ion.
• B. For an ionic solution, current carried by an ion does not depend upon the speed of the ion.
• C. $\frac{t_{+}}{t_{-}}=\frac{{\Lambda }_{+}}{{\Lambda }_{-}}$
• D. $\frac{t_{+}}{t_{-}}=\frac{{\Lambda }_{-}}{{\Lambda }_{+}}$

Answer 1

Answer: (A), (C)

$\frac{t_{+}}{t_{-}}=\frac{{\Lambda }_{+}}{{\Lambda }_{-}}$

Transport number:
For electrolytic conductors, the current is carried by both cations and anions. Transport number of any ion is the fraction of total current (by all the ions) carried by that ion.
For an ionic solution
Current carried by an ion depends upon the speed of the ion.
$t_{+}\propto v_{+}$
$t_{-}\propto v_{-}$
where,
$v_{+}\text{is the speed of cation}$
$v_{-}\text{is the speed of anion}$
Also, speed of an ion is directly proportional to its molar conductance. So,
$\frac{t_{+}}{t_{-}}=\frac{v_{+}}{v_{-}}=\frac{{\Lambda }_{+}}{{\Lambda }_{-}}$