Question

Find the charge on 1g-ion of ${{N}^{3-}}$ in coulombs.

Answer 1

Hint : Take into consideration the definition of what a gram-ion is and then associate it with the charge of 1 mole of electrons and carry out calculations accordingly.

Complete step by step solution:
A gram-ion means the number of ions that are present in 1 mole of the substance. $N$ has only 1 gram-ion since it forms only one ion i.e., ${{N}^{3-}}$ at a time.
Therefore, 1g-ion of ${{N}^{3-}}$ means 1 mole of ${{N}^{3-}}$ is present. There are 3 electrons in this ion, hence, 3 moles of electrons are present in 1g-ion or 1 mole of ${{N}^{3-}}$.
The charge present on 1 mole of electrons has already been defined by Faraday, it is known as the Faraday’s constant and it is denoted by $F$. The accepted value of this constant is $96485.33212...Cmo{{l}^{-1}}$ but we will round it off to 96500 for ease in calculation.
Charge present on 1 mole of electrons = $96500$ C
Charge present on 3 moles of electrons = $96500\times 3$ C
Charge on 1g-ion of ${{N}^{3-}}$ = $2.895\times {{10}^{5}}$ C
Therefore, the answer to this question is $2.895\times {{10}^{5}}$C

Additional information:
Another method to solve this problem is to consider the charge on 1 ion of ${{N}^{3-}}$.
Charge on 1 ion of ${{N}^{3-}}$= $3\times 1.6\times {{10}^{-19}}$ C
Where $1.6\times {{10}^{-19}}$ C is the charge present on 1 electron
Charge on 1 ion of ${{N}^{3-}}$= $4.8\times {{10}^{-19}}$ C
Now, we will multiply the charge present on 1 ion of ${{N}^{3-}}$ with the number of ions that are present in 1g-ion of ${{N}^{3-}}$. We already know that 1g-ion of ${{N}^{3-}}$ means 1mol of ${{N}^{3-}}$ is present. The number of atoms/ions that are present in 1mol of a substance is $6.022\times {{10}^{23}}$ which is Avogadro's number. Hence, we will multiply the charge present on 1 ion of ${{N}^{3-}}$ by Avogadro's number.
Charge on 1 mole of ${{N}^{3-}}$ions = charge on 1 ion of ${{N}^{3-}}\times$ number of ions
Charge on 1 mole of ${{N}^{3-}}$ions = $(4.8\times {{10}^{-19}})\times (6.022\times {{10}^{23}})$ C
Charge on 1 mole of ${{N}^{3-}}$ions = $2.89\times {{10}^{5}}$ C

Note : Please do not get confused between 1 gram of X ions and 1g-ion of X. Here, X refers to ${{N}^{3-}}$. Remember that 1g-ion means the number of ions present in 1 mole of a substance. For example, $ZnS{{O}_{4}}$, contains 2g-ions. One of $Z{{n}^{2+}}$ and one of $S{{O}_{4}}^{2-}$. The charge can also be written in terms of Faraday in any problem, in this problem the charge will be 3 Faraday. The charge on 1 mole of electrons is 1 Faraday.