Question

Calculate the number of ions, number of oxygen atoms and total charge in 3gm $C{{O}_{3}}^{2-}$.

Answer 1

Hint: To calculate the above-asked quantities, we have to find the moles of the carbonate ion present in 3 grams of the substance. Moles obtained can be used to determine the number of ions, a number of oxygen atoms and total charge in 3gm $C{{O}_{3}}^{2-}$.

Complete step by step solution:
Given in the question is the mass of $C{{O}_{3}}^{2-}$ ion which is 3grams. To calculate the number of ions, a number of an oxygen atom and total charge in 3gm $C{{O}_{3}}^{2-}$ we will find out the moles of $C{{O}_{3}}^{2-}$ present in this amount of $C{{O}_{3}}^{2-}$.
Moles of $C{{O}_{3}}^{2-}$ can be determined by using a molecular mass of $C{{O}_{3}}^{2-}$.
The molecular mass of $C{{O}_{3}}^{2-}$ is 60g/mol.
Therefore, moles will be ,
\[\begin{align}
& moles=\dfrac{weight}{MolecularMass} \\
& moles=\dfrac{3}{60} \\
& moles=0.05mol \\
\end{align}\]
Moles of $C{{O}_{3}}^{2-}$is equal to 0.05mol.
To find out the number of ions present in the 3gm of $C{{O}_{3}}^{2-}$ we have to multiply the Avogadro number with the moles of $C{{O}_{3}}^{2-}$.
\[\text{Number of ions= n}\times {{\text{N}}_{A}}\]
\[\text{Number of ions= 0}\text{.05}\times \text{6}\text{.022}\times \text{1}{{\text{0}}^{23}}\]
\[\text{Number of ions = 3}\text{.011}\times \text{1}{{\text{0}}^{22}}\]
Therefore, number of ions of $C{{O}_{3}}^{2-}$ is \[\text{3}\text{.011}\times \text{1}{{\text{0}}^{22}}\].
Now we have to calculate the number of oxygen atoms. Since one ion have 3 oxygen atoms, and we have \[\text{3}\text{.011}\times \text{1}{{\text{0}}^{22}}\]ions of $C{{O}_{3}}^{2-}$, therefore, total number of oxygen will be 3 times of number of ions,
\[\begin{align}
& \text{number of Oxygen atoms = 3}\times \text{3}\text{.011}\times \text{1}{{\text{0}}^{22}} \\
& \text{number of Oxygen atoms =}9.033\times \text{1}{{\text{0}}^{22}} \\
\end{align}\]
Therefore, the number of oxygen atoms is $9.033\times \text{1}{{\text{0}}^{22}}$.
Now we have to calculate the total charge on the $C{{O}_{3}}^{2-}$. Since we have -2 charge on a single ions, and we have 0.05mol of ions, also the magnitude of a single charge is 96500C, therefore the total charge will be:
\[\begin{align}
& \text{Total charge = moles }\times \text{ charge }\times \text{ 2} \\
& \text{Total charge =}0.05\times 96500\times 2 \\
& \text{Total charge =}9650C \\
\end{align}\]
Therefore, the total charge on the $C{{O}_{3}}^{2-}$ will be 9650 coulombs.

Note: The number $6.02214076\times {{10}^{23}}~$ is popularly known as the Avogadro constant and is often denoted by the symbol ‘NA’. The elementary entities that can be represented in moles can be atoms, molecules, monatomic/polyatomic ions, and other particles.