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Question: A solution of sodium chloride discharges \(6.1\times {{10}^{16}}\) \(\text{N}{{\text{a}}^{\text{+}}}...

A solution of sodium chloride discharges 6.1×10166.1\times {{10}^{16}} Na+\text{N}{{\text{a}}^{\text{+}}} ions and 4.6×10164.6\times {{10}^{16}} Cl−\text{C}{{\text{l}}^{-}} ions in 10 seconds. Find the current passing through the solution.
A.1.7 mA\text{1}\text{.7 mA}
B.1.8 mA\text{1}\text{.8 mA}
C.1.9 mA\text{1}\text{.9 mA}
D.1.6 mA\text{1}\text{.6 mA}

Explanation

Solution

The current flowing through any substance can be defined as the rate of flow of charge and the S.I. unit of current is ampere or Watt per second. We shall find the total charge in coulombs present in the solution and use it to find the current passing through the solution.
Formula Used: current=chargetime{\text{current}} = \dfrac{{{\text{charge}}}}{{{\text{time}}}}

Complete step by step answer:
As per the question, the Number of Na+\text{N}{{\text{a}}^{\text{+}}}ions discharged = 6.1×10166.1\times {{10}^{16}} and,
The number of Cl−\text{C}{{\text{l}}^{-}} ions discharged = 4.6×10164.6\times {{10}^{16}}
The charge on each electron = 1.6×10−191.6\times {{10}^{-19}} coulombs.
Therefore the charge of6.1×10166.1\times {{10}^{16}} sodium cations = 1.6×10−19×6.1×1016=9.76×10−31.6\times {{10}^{-19}}\times 6.1\times {{10}^{16}}=9.76\times {{10}^{-3}} Coulombs.
Similarly, the charge on 4.6×10164.6\times {{10}^{16}} Cl−\text{C}{{\text{l}}^{-}} ions = 4.6×1016×1.6×10−19=7.36×10−34.6\times {{10}^{16}}\times 1.6\times {{10}^{-19}}=7.36\times {{10}^{-3}} coulombs.
We know that the current is equal to the rate of flow of charge. Therefore, the total current passing through the solution is = total chargetotal time\dfrac{\text{total charge}}{\text{total time}}
Total charge = 9.76×10−3+7.36×10−3=17.12×10−39.76\times {{10}^{-3}}+7.36\times {{10}^{-3}}=17.12\times {{10}^{-3}} Coulombs
Total time = 10 seconds
Therefore, total current = 17.12×10−310=1.7×10−3\dfrac{17.12\times {{10}^{-3}}}{10}=1.7\times {{10}^{-3}} mili-Ampere.

Hence, the correct answer is option A.

Note:
The charge carried by one mole of electrons is defined as one Faraday and its value is equal to 96500 coulombs. This can be determined as follows:
One mole of electrons = 6.023×10236.023\times {{10}^{23}} electrons.
The charge of each electron = 1.6×10−191.6\times {{10}^{-19}} coulomb
Therefore the charge on mole of electrons = 1.6×10−19×6.023×1023=965001.6\times {{10}^{-19}}\times 6.023\times {{10}^{23}}=96500 coulombs
This is called one faraday after the great British Physicist and chemist Michael Faraday due to this ingenious contribution to electricity.
The magnitude of the charge of the proton in the nucleus is the same as the magnitude of the charge of the electron, only the sign is different. For protons it is positive and for the electrons it is negative.