# The equivalent conductance of 0.20 N solution of MgCl 2 is 97.1 mho cm 2 eq ? 1 . at 25 o C. A...

## Question:

The equivalent conductance of 0.20 N solution of MgCl{eq}_2 {/eq} is 97.1 mho cm{eq}^2 {/eq} eq{eq}^{-1} {/eq}. at 25{eq}^o {/eq}C. A cell with electrodes that are 1.50 cm" in surface area and 0.50 cm apart is filled with 0.1 N MgCI{eq}_2 {/eq} solution. How much current will flow when the potential difference between the electrodes is 5 volt?

## Electric Current:

Electric current defines the amount of flow of electric charge passing through any surface in per unit of time. From ohm's law, a current is the ratio of voltage to the resistance applied in an electrical circuit.

Given Data

• Equivalent conductance is, {eq}{C_{eq}} = 97.1\;{\rm{mho}} \cdot {\rm{c}}{{\rm{m}}^2}{\rm{e}}{{\rm{q}}^{ - 1}} {/eq}.
• Distance between cell electrodes, {eq}l = 0.50\;{\rm{cm}} {/eq}.
• Potential difference is, {eq}V = 5\;{\rm{V}} {/eq}.
• The area is, {eq}A = 1.50\;{\rm{c}}{{\rm{m}}^2} {/eq}.

The expression for cell constant is,

{eq}C = \dfrac{l}{A} {/eq}

Substituting the values in above expression.

{eq}C = \dfrac{{0.50}}{{1.50}} {/eq}

The expression for equivalent conductance is,

{eq}\begin{align*} {C_{eq}} &= k \times V\\ k &= \dfrac{{{C_{eq}}}}{V} \end{align*} {/eq}

Here, k is specific conductance and V is volume in cc.

Substituting the values in above expression.

{eq}\begin{align*} k &= \dfrac{{97.1}}{{10000}}\\ k &= 0.0097\;{\rm{mho/cm}} \end{align*} {/eq}

The expression for specific conductance is,

{eq}\begin{align*} k &= \dfrac{1}{R} \times C\\ R &= \dfrac{C}{k} \end{align*} {/eq}

Here, R is the resistance.

Substituting the values in above expression.

{eq}\begin{align*} R &= \dfrac{{0.33}}{{0.00971}}\\ R &= 33.98\;{\rm{\Omega }} \end{align*} {/eq}

The expression for current is,

{eq}I = \dfrac{V}{R} {/eq}

Substituting the values in above expression.

{eq}\begin{align*} I &= \dfrac{5}{{33.98}}\\ I &= 0.145\;{\rm{A}} \end{align*} {/eq}

Thus, the flow of current is 0.145 A. 