Question

A piece of aluminium foil has a mass of ${ 27 }$ grams. About how many atoms does this foil contain?
A.) ${ 1.20\times 10 }^{ 24 }{ atoms }$
B.) ${ 6.02\times 10 }^{ 23 }{ atoms }$
C.) ${ 3.011\times 10 }^{ 23 }{ atoms }$
D.) ${ 27 }$ atoms
E.) ${ 13 }$ atoms

Answer 1

Hint: Mole is the unit for the number of atoms or molecules of a material. One mole is equal to the Avogadro’s number and each element has a different molar mass depending on the weight.

Complete step-by-step answer:

Atomic mass of Aluminium = ${ 27g }$
It means 1 mole of aluminium contains ${ 27g }$ of aluminium.
As we know that 1 mole of any element contains Avogadro’s number of atoms ,i.e,
${ 6.02\times 10 }^{ 23 }{ atoms }$
As we know that,
${ Number\quad of\quad moles\quad =\quad mass/molar\quad mass }$
Now, we have, ${ 27g/27gmol^{ -1 } }$
We get, number of moles = ${ 1 }$ mole of Al

The formula used is: Number of particles/atoms/molecules = number of moles Avogadro’s number
So, number of atoms in one mole of aluminium = ${ 6.02\times 10 }^{ 23 }{ atoms }$
Hence, Number of atoms in ${ 27g } of Al = { 1\times } { 6.02\times 10 }^{ 23 }{ atoms }= { 6.02\times 10 }^{ 23 }{ atoms }$
The correct option is B.

Additional Information:
Avogadro’s Law: According to this law, “each volume of gases contain an equal number of molecules at standard temperature and pressure.”
Importance of Avogadro’s number;
It is used to calculate the actual mass of a single atom of an element or a single molecule of a substance.
It is used in the calculation of actual masses of ${ 1amu }$ or ${ 1u }$.
It is also used to calculate the number of atoms or molecules in the given mass of the element of a compound.
It is used to calculate the number of molecules present in a given volume of the gas under given conditions of temperature and pressure.

Note: The possibility for the mistake is that you can choose the option (a) or (c)
As the number of atoms is equal to the number of moles and Avogadro’s number. Here, the number of moles of Al is ${ 1 }$ not twice or half the Avogadro’s number.