Question

How many minutes are required to deliver 3.21×106 coulombs using a current of 500 A? That is used in the commercial production of chlorine.

Answer 1

The current is defined as the rate of flow of electrons in the conductor. As we know mathematically current is given as :
${\text{I = }}\frac{{\text{Q}}}{{\text{t}}}$
Where Q= charge in coulombs
t = time required in the second
I = current produced.
By using the above formula we can calculate time required to deliver the charge as:
${\text{time = }}\frac{{{\text{charge}}}}{{{\text{current}}}}$

Complete step by step answer: Here given charge = 3.21×106 coulombs and Current required = 500 A. As we know
charge= current × time
So,
$3.21 \times {10^6} = 500 \times {\text{time}} \\\ \Rightarrow \frac{{3.21 \times {{10}^6}}}{{500}} = {\text{time}} \\\ \Rightarrow {\text{time}} = 6420\sec \\\$
As we know 60 seconds = 1 minute. Hence 6420 second = $\frac{1}{{60}} \times 6420 = 107\min$
Hence the minute required to deliver 3.21×106 coulombs using a current of 500 A is 107 minutes.

Note: Commercially chlorine can be manufactured by electrolysis of sodium chloride solution which is also known as brine. In this process, the sodium chloride and water get ionized as:
$NaCl(aq) \to N{a^ + }(aq) + C{l^ - }(aq)$
${H_2}O(l) \to {H^ + }(aq) + O{H^ - }(aq)$
Since sodium chloride is a strong electrolyte it gets completely ionized whereas water gets slightly ionized. On passing electricity, sodium and hydrogen ions move towards the cathode while chloride and hydroxide ions move towards the anode.
At cathode:
Since the discharge potential of hydrogen ion is lower than that of sodium-ion hence there is the discharge of hydrogen ion at the cathode.
${H^ + } + {e^ - } \to \dot H \\\ \dot H + \dot H \to {H_2} \\\$
At anode: Since the discharge potential of chloride ion is less than that of hydroxide ion. Hence there is the discharge of chloride ion at the anode as:
$C{l^ - } \to C\dot l + {e^ - } \\\ C\dot l + C\dot l \to C{l_2} \\\$
And hydroxide ions remain in the solution.
Hence we can say during the electrolysis of sodium chloride solution hydrogen gas is obtained at the cathode and chlorine gas obtained at the anode and sodium hydroxide solution remain in the solution.