Question

How long (in hours) must a current of 5 ampere be maintained to electroplate 60g of calcium from molten $\text{CaC}{{\text{l}}_{\text{2}}}$ ?
A.27 hours
B.8.3 hours
C. 11 hours
D. 16 hours

Answer 1

Hint : The question here talks about the time required for decomposition,so, by calculating the the charge (Q) ,we will be able to substitute in the given formula ,and find the time taken.Our main emphasis must be on calculating the total number of moles required by the compound.

Complete solution step by step:
By the concept of electrochemistry, and following the faraday’s law,the formula for charge Q passed is given by:
Q=It
Where I= is the current in ampere
T= is the time in seconds required to be deposited
Let’s see the reaction of calcium:
{ Ca }\xrightarrow { Ca }^{ 2+ } + { 2e }^{ - }\\\ (oxidation)
{ Cl }_{ 2 } +{ 2e }^{ -}\xrightarrow { 2Cl }^{ - }\\\ (reduction)
$Ca +{ Cl }_{ 2 }+ { 2e }^{ - }\xrightarrow { Ca }^{ 2+ }+ 2{ e }^{ - }+ { 2Cl }^{ - }$ (net redox reaction)
Therefore the number of moles=2
Now,the molar mass of calcium= 40g/mol
So, for calculating the number of moles we have the formula as :${ given weight }/{ molecular weight }$
Then number of moles for 60 grams of calcium will be=${ 60 }/{ 40 }$ = 1.5
Now we know that 1 mole of electron requires 96500 C
So, 2 moles of electron will require = 193000 C
Therefore, 1.5 moles will require : $1\cdot 5\times 193000$
=289500 C
Now,in order to find the time, t= ${ Q }/{ I }$
${ 289500 }/{ 5 }$= 57900 s
In order to convert it in hours,we will divide by 3600,which gives us : 16 hours

So the correct option is D.

Note : In order to find the number of electrons, we must always try to write the full oxidation and reduction reaction.So,it is always important to find the total number of loss and gain in electrons,so that we could balance the redox reaction.