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Calculate the number of ions, number of oxygen atoms and total charge in $3gms$ of \[C{O_3}^{2 - }\]

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Last updated date: 19th Jul 2024
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Answer
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Hint: We have to remember that the \[C{O_3}^{2 - }\] is known as a carbonate ion. It is an anion since it carries negative charge. To find the number of ions present in carbonate we need to find the number of moles first, thus we can find the number of ions, total charge in $3gms$ of \[C{O_3}^{2 - }\].

Complete answer:
Firstly we need to know the molecular mass of \[C{O_3}^{2 - }\] ion in order to find the number of moles as mass is already given. Molecular mass of \[C{O_3}^{2 - }\] is \[60g/mol\]. Number of moles can be calculated as given mass divided by molar mass thus by putting values we get \[0.05mol\].
\[n = \dfrac{m}{M} = 0.05mol\]
Number of moles in $3gms$ of \[C{O_3}^{2 - }\] is \[0.05mol\].
Next is to find the number of ions, the formula used to find the number of ions is the number of moles multiplied by Avogadro’s number which is \[6.022 \times {10^{23}}\].
Number of ions \[ = no.of moles \times Avogadro's Number\]
Now we can substitute the known values we get,
\[ = 0.05 \times 6.022 \times {10^{23}}\]
On simplification we get,
\[ = 0.3011 \times {10^{23}}\]
So the number of ions in $3gms$ of \[C{O_3}^{2 - }\] is \[0.3011 \times {10^{23}}\].
Now, we need to find number of oxygen atoms in $3gms$ of \[C{O_3}^{2 - }\], there are three oxygen atoms in carbonate ion, we have \[0.3011 \times {10^{23}}\] ions of \[C{O_3}^{2 - }\]
Number of oxygen atoms\[ = 3 \times 0.3011 \times {10^{23}}\]
Number of oxygen atoms\[ = 9.033 \times {10^{23}}\]
So the number of oxygen atoms in $3gms$ of \[C{O_3}^{2 - }\] is \[9.033 \times {10^{23}}\].
Total charge on carbonate ion is $ - 2$ so the total charge on $3gms$ of \[C{O_3}^{2 - }\] ion will be calculated as:
\[Total Charge = moles \times charge \times 2\]
Now we can substitute the known values we get,
\[ = 0.05 \times 96500 \times 2\]
On simplification we get,
\[ = 9650C\]
So, the total charge on $3gms$ of \[C{O_3}^{2 - }\] is \[9650C\].

Note:
We have to remember that the Avogadro’s number is \[6.022 \times {10^{23}}\] which can also be denoted as \[{N_A}\]. The unit of charge is coulombs. Number of moles is represented in moles. The units for molecular mass are \[g/mol\]. The atoms, molecules and other species can be found in the units called moles.