Question

Which one of the following will have the largest number of atoms?
(A). 1g of Au
(B). 1g of Na
(C). 1g of Li
(D). 1g of ${ Cl }_{ 2 }$

Answer 1

- Hint: We have to calculate the number of moles of every element in the given options and the element which has the maximum number of moles will have the largest number of atoms.

Formula Used: No. of moles = $\dfrac{Weight}{{Gram Atomic/ Molecular mass}}$

Complete step-by-step solution -

The number of atoms in 1 mole of an element is determined by Avogadro's number. The number of atoms in 1 mole is represented by the symbol N and its value is $6.023\times { 10 }^{ 23 }$. So, there are $6.023\times { 10 }^{ 23 }$ numbers of atoms in 1 mole of a substance.
The number of moles of a substance can be calculated as the ratio of the weight of the substance to the gram atomic/molecular mass of the substance. Gram atomic/molecular mass is the same as that of atomic/molecular mass and the only difference is that it has a unit – gram.
The gram atomic mass of Au (Gold) = 197 gm
The gram atomic mass of Na (Sodium) = 23 gm
The gram atomic mass of Li (Lithium) = 7 gm
The gram molecular mass of ${ Cl }_{ 2 }$ (Chlorine gas) = 71 gm
Now, the number of moles of Au $=\dfrac { 1g }{ 197g } =\dfrac { 1 }{ 197 }$ mole.
Number of moles of Na $=\dfrac { 1g }{ 23g } =\dfrac { 1 }{ 23 }$ mole.
Number of moles of Li $=\dfrac { 1g }{ 7g } =\dfrac { 1 }{ 7 }$ mole.
Number of moles of ${ Cl }_{ 2 } =\dfrac { 1g }{ 71g } =\dfrac { 1 }{ 71 }$ mole.
Arranging the number of moles of Au, Na, Li and ${ Cl }_{ 2 }$ in ascending order.
$Au = \dfrac { 1 }{ 197 }, { Cl }_{ 2 } = \dfrac { 1 }{ 71 }, Na = \dfrac { 1 }{ 23 }, and Li = \dfrac { 1 }{ 7 }$
Therefore, Lithium (Li) has the highest number of moles i.e. $\dfrac { 1 }{ 7 }$. Thus, Lithium has the highest number of atoms in 1g of Lithium.

Note: Since the gram atomic/molecular mass is more than the weight, the number of moles will come in fraction. Don’t get confused by selecting the one that has a higher value of gram atomic/molecular mass because that value is in the denominator and higher the value of the denominator in a fraction, lower is the value of the fraction.