Magnesium metal is produced commercially by the isolation of `MgCl_(2)` from sea water followed by electrolysis of molten salt
`MgCl_(2) to Mg+Cl_(2)`
(a) What mass of Mg can be produced if a current of 430 amperes is passed for 1.0 hour ?
(b) If a current of 500 amperes is used, how many hours will be required to convert all the 1000 kg of `MgCl_(2)` into Mg metal ?

Explanation

(a) Quantity of charge passed (Q)`=Ixxt=(430 A)xx(60xx60 s)=1.548xx10^(6)C`
No.of faradays of charge passed`=((1.548xx10^(6)C))/((96500C))=16.04F`
Gram equivalent mass of mg `=(24.0)/(2)=12.0 g`
On passing charge of 16.04F, mass of Mg produced`=((12.0g))/((1F))xx(16.04F)=192.5 g`
(b) No. of gram equivalents of `MgCl_(2)=("Mass of " MgCl_(2))/("Equivalent mass of " MgCl_(2))=((10^(6)g)/((47.5g))`
Charge needed for this purpose`=((10^(6)g))/((47.5g))xx96500C`
Current used in the electrolysis process =500A
Time required for the process`=((10^(6)g)xx96500C(A-s))/((47.5g)xx(500A))=4.063xx10^(6)s`
`=((4.063xx10^(6)s))/(60xx60)=1128.6 "hours"`