Question

How many atoms are there in a 36.5 g sample of ${ SF }_{ 6 }$ gas?
(A) $1.51\times { 10 }^{ 22 }$
(B) $1.06\times { 10 }^{ 22 }$
(C) $1.51\times { 10 }^{ 23 }$
(D) $1.06\times { 10 }^{ 24 }$
(E) $1.51\times { 10 }^{ -24 }$

Answer 1

Hint: Mole in Latin means “large mass” or “bulk” and gives us a measure of the amount of a substance. It is equal to the number of atoms present in a 12 g of $^{ 12 }{ C }$ sample which comes out to be equal to $6.022\times { 10 }^{ 23 }$ atoms.

Complete step by step answer:
In order to solve this question we need to understand the mole concept.
Mole is the unit for the amount of a substance. It gives us information about the number of atoms or molecules present in a substance (which is taken in bulk). A mole of a substance contains the same number of species (atoms, molecules, ions etc.) as that of the number of atoms present in 12 g of $^{ 12 }{ C }$ sample. The number of atoms present in 12 g of $^{ 12 }{ C }$ sample is experimentally determined to be $6.022\times { 10 }^{ 23 }$ which is called the Avogadro’s number after the Italian scientist Amedeo Avogadro. Hence one mole of any substance will contain Avogadro number of discrete entities (atoms, molecules, ions etc.) but they will have different molar mass since the mass of individual atoms, molecules, ions etc. is different for different substances. The molar mass of a compound/substance is equal to the mass of one mole of that compound/substance in grams. The molar mass is expressed as grams/mole. Now, the molar mass of a substance/compound is equal to its formula or atomic weight in amu (atomic mass unit). A single $^{ 12 }{ C }$ atom weighs 12 amu and one mole of $^{ 12 }{ C }$ sample weighs 12 g (hence its molar mass is 12 g/mol) which contains Avogadro number of $^{ 12 }{ C }$ atoms. Hence, when this principle is extrapolated on other substances we will see that the molar mass of a substance will be numerically equal to its formula weight in amu.

Now, let us solve the question. The molar weight of ${ SF }_{ 6 }$ in amu is around 146 amu. Hence the mass of 1 mole of ${ SF }_{ 6 }$ should be equal to 146 g.
We will convert 36.5 g of ${ SF }_{ 6 }$ in the number of moles.
Number of moles of ${ SF }_{ 6 }$ = $\cfrac { 36.5\quad g }{ 146\quad g/mol } =0.25\quad mol$

Now, 1 molecule of ${ SF }_{ 6 }$ has 7 atoms. Therefore, 1 mole of ${ SF }_{ 6 }$ will have = $7\times 6.022\times { 10 }^{ 23 }\quad atoms=4.2154\times { 10 }^{ 24 }\quad atoms$

Since, 1 mole of ${ SF }_{ 6 }$ contains $4.2154\times { 10 }^{ 24 }\quad atoms$ therefore, 0.25 moles of ${ SF }_{ 6 }$ will contain = $4.2154\times { 10 }^{ 24 }\times 0.25\quad atoms=1.06\times { 10 }^{ 24 }\quad atoms$
So, the correct answer is “Option D”.

Note: Though atomic mass (in amu) and molar mass are numerically equivalent, they differ in terms of scale. While 1 amu is equal to the mass of one $^{ 12 }{ C }$ atom, molar mass is equal to the mass of one mole of $^{ 12 }{ C }$ sample.