Question

The concentration of ${K^ + }$ in the interior and exterior of a Nerve cell are $500mM$ and $25mM$ respectively. The electrical potential (in volt) that exists across the membrane is : $[\,{\log _{10}}2\, = \,0.3,\,\,2.303RT/F\,\, = \,\,0.6\,\,]$ (Given answer be multiplying with 1000).

Answer 1

Hint : In order to answer this question, you must recall the concept of Electrochemistry. To find the electrical potential use the formula of standard ElectroMotive Force. Electrical potential is a measurement of the ability of a voltaic cell to produce an electric current. Electrical potential is typically measured in volts (V). Put the correct values and calculate the correct logarithmic values and then after calculating correctly, you will get your required values. And then finally as required in the question, multiply the value with $1000$ and the resulting value will be the required answer.

Complete Step By Step Answer:
We know that a neuron also known as a nerve cell is an electrically excitable cell that takes up, processes and transmits information through electrical as well as chemical signals. It is one of the most important elements of the nervous system.
The membrane potential of a resting neuron is primarily determined by the movement of ${K^ + }$ ions across the membrane. So, let's get a feeling for how the membrane potential works by seeing what would happen in a case where only ${K^ + }$ can cross the membrane. Due to which electric potential develops.
Step 1:Since the exterior concentration of the Nerve cell is 500 mM while interior concentration is 25 mM. Reaction coefficient is the ratio of concentration of exterior and interior concentration of Nerve cells.
We will use the formula of Electromotive force to find the required answer:
$E\,\, = \,\,{E^ \circ }\,\, - \,\,\dfrac{{0.06}}{n}\,\log \dfrac{{{{[{K^ + }]}_{ext}}}}{{{{[{K^ + }]}_{in}}}}$
$\Rightarrow \,\,E\,\, = \,\,0\,\, - \,\dfrac{{0.06}}{1}\,\log \dfrac{{25}}{{500}}\,\, = \,\,0.078\,V$
Step 2: In the question, it is given that we have to give the final answer after multiplying it with $1000$ . So we will multiply the value of $E$ by $1000$ :
$E\,\, = \,\,0.078 \times 1000\,\, = \,\,78V$
Hence, $E\,\, = \,\,78V$ is the required answer. And here in the answer, V stands for Volts.

Note :
Electrical potential is a measurement of the ability of a voltaic cell to produce an electric current. Electrical potential is typically measured in volts (V). The voltage that is produced by a given voltaic cell is the electrical potential difference between the two half-cells. It is not possible to measure the electrical potential difference between the two half-cells. It is not possible to measure the electrical potential of an isolated half-cell. For example, if only a zinc half-cell were constructed, no complete redox reaction can occur and so no electrical potential can be measured.