Question

Calculate the total positive or negative charge on a $2.35g$ of copper penny. Given Avogadro’s number $6.022 \times {10^{23}}$ , atomic number of copper $ = 29$ and atomic mass of copper $ = 63.5g$ .

Answer 1

Hint: Number of atoms can be determined since we know the mass of the penny and we know the number of molecules in the molecular mass of copper, which is the Avogadro’s number.
Find out the number of atoms, and then multiply it with the number of electrons in one atom of copper and the charge on one electron to get the total value of charge.
Formula Used:
$Number\,of\,atoms = \dfrac{{given\,mass\,of\,copper}}{{molecular\,mass\,of\,copper}} \times Avogadro's\,numer \times Atomic\,number \times charge\,on\,1{e^ - }$

Complete step by step answer:
Let us understand the structure of a copper atom and what exactly is the question asking us to find.
Copper has atomic number $29$ which means it has 29 electrons and 29 protons.
Now, we know that the charge on one electron is $1.6 \times {10^{ - 19}}C$ .
So, to find out the charge on one atom of copper, all we need to do is multiply the number of electrons with the charge carried by one electron.
Now, when we talk about $2.35g$ of Copper, as it is given in the question, we need to find the number of electrons which will be present in that $2.35g$ of copper. To find the electrons, first we need to find the value of the number of copper atoms present in $2.35g$ of copper.
We know that One Mole has $6.022 \times {10^{23}}$ atoms. So, If we find out the number of moles of copper, and multiply it with Avogadro’s number, we will know the number of atoms present.
$Number\,of\,moles\,of\,Copper = \dfrac{{Given\,mass\,of\,copper}}{{Molecular\,mass\,of\,copper}}$
As given in the question:
$Given\,mass\,of\,copper = 2.35g,Molecular\,mass\,of\,copper = 63.5g$
Substituting these values we get,
$Number\,of\,moles\,of\,copper = \dfrac{{2.35}}{{63.5}} \Rightarrow 0.064$
$\therefore Number\,of\,atoms = Number\,of\,moles \times Avogadro's\,number$
Substituting the values, we get:
$Number\,of\,atoms = 0.064 \times 6.022 \times {10^{23}} \Rightarrow 0.22 \times {10^{23}}$
So 1 atom contains $29$ electrons or protons
Hence, $0.22 \times {10^{23}}$ atoms will contain = $0.22 \times {10^{23}} \times 29$ protons or electrons.
Total number of electrons or protons = $6.38 \times {10^{23}}$ protons or electrons.
Now, we know than charge on 1 electron or proton is $1.6 \times {10^{ - 19}}C$
Hence, the charge on $6.38 \times {10^{23}}$ electrons or protons will be $6.38 \times {10^{23}} \times 1.6 \times {10^{ - 19}}C \Rightarrow 10.208 \times {10^4}C$

Note: The charge on the electron will be $ - 10.208 \times {10^4}C$whereas the charge on proton will be $10.208 \times {10^4}C$. Since Copper is electrically neutral, the magnitude of the charge by the electrons and protons will be the same but they will be opposite in charge so as to there is no net charge on the atom.