Question

How much electric charge is required to produce 20.0g of calcium from molten $CaC{{l}_{2}}$?

Answer 1

Hint: Faraday’s first law of electrolysis relates the amount of a substance deposited or liberated at any electrode due to chemical reaction amount of electricity used.
 Mass of one mole of calcium is 40 g. Two electrons are required for the reduction of $C{{a}^{2+}}$ to Ca in the electrolysis of molten $CaC{{l}_{2}}$.

Complete answer:
Calcium (Ca) is electrolytically obtained from molten calcium chloride ($CaC{{l}_{2}}$).
Let us consider the electrolysis of molten $CaC{{l}_{2}}$, i.e.
     \[CaC{{l}_{2}}\to C{{a}^{2+}}+2C{{l}^{-}}\]
 Thus, the reaction taking place at electrode (in this case cathode) is will be
     \[C{{a}^{2+}}+2{{e}^{-}}\to Ca\]
This means that two electrons are required to produce one calcium atom. Therefore, we can say that two moles of electrons produce one mole of calcium.
We know that one mole of calcium contains 40 g of calcium.
Therefore, we can write that two moles of electrons give 40 g of calcium, i.e.
2 moles of electrons = one mole of calcium = 40 g of calcium
Then, if we divide both sides by 2, we get
1 mole electron = 20 g calcium
Now, in order to find the electric charge required to produce 20.0g, we need to find the electron charge on one mole electron.
As it is known that,
Charge carried by one electron = $1.6\times {{10}^{-19}}$ coulombs (C)
One mole of electrons = $6.022\times {{10}^{23}}$ electrons
Therefore, the charge on one mole of electron can be obtained by multiplying the charge on one electron with the total number of electrons in one mole (i.e. Avogadro’s number) which is equal to
     $1.6021\times {{10}^{-19}}C\times 6.022\times {{10}^{23}}=96487C$
96487 C is generally taken as 96500 C. this amount of electric charge is called one faraday such that 1F = 96500 C.
Therefore, the charge is required to produce 20.0g of calcium from molten calcium chloride is one faraday, i.e. 96500 C.

Note:
We can also obtain the answer by simply using Faraday’s first law of electrolysis, i.e.$W=ZQ$, where Z is called the electrochemical equivalent of calcium. It is given as $Z={}^{\text{Equivalent mass}}/{}_{96500}$ . Equivalent mass of Ca will be 20g (i.e. ${}^{40}/{}_{2}$ ). Substituting the values of $Z={}^{20g}/{}_{96500C}$ and W=20g in $W=ZQ$, we will get $Q=96500C$.