Question

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

Answer 1

We know that one mole of any chemical contains Avogadro number of Avogadro number of atoms.
Avogadro number = $6.023\times {{10}^{23}}$ atoms.
There is a formula to calculate the number atoms in 1 g of element and it is as follows.
$\text{Number of atoms in 1 g of an element=}\dfrac{1}{\text{molecular weight of the element}}\text{ }\\!\\!\times\\!\\!\text{ 6}\text{.022 }\\!\\!\times\\!\\!\text{ 1}{{\text{0}}^{\text{23}}}$

Complete step by step answer:
- In the question it was asked to find which element has the largest number of atoms among the given elements.
- Coming to the given options, option A, 1 g of Au.
- The molecular weight of the aurum is 197.
197 g of Au contains $6.023\times {{10}^{23}}$ atoms.
1 g of Au contains

& =\dfrac{1}{197}\times 6.023\times {{10}^{23}} \\\ & =3.06\times {{10}^{21}}atoms \\\ \end{aligned}$$ \- Coming to option B, 1 g Na. \- The molecular weight of the sodium is 23. 23 g of Na contains $6.023\times {{10}^{23}}$ atoms. 1 g of Na contains $$\begin{aligned} & =\dfrac{1}{23}\times 6.023\times {{10}^{23}} \\\ & =26.2\times {{10}^{21}}atoms \\\ \end{aligned}$$ \- Coming to option C, 1 g Li. \- The molecular weight of the lithium is 7. 7 g of Li contains $6.023\times {{10}^{23}}$ atoms. 1 g of Li contains $$\begin{aligned} & =\dfrac{1}{7}\times 6.023\times {{10}^{23}} \\\ & =86.0\times {{10}^{21}}atoms \\\ \end{aligned}$$ \- Coming to option D, 1 g of $C{{l}_{2}}$ . \- The molecular weight of the Chlorine is 71. 71 g of Cl contains $6.023\times {{10}^{23}}$ atoms. 1 gm of Cl contains $$\begin{aligned} & =\dfrac{1}{71}\times 6.023\times {{10}^{23}} \\\ & =8.48\times {{10}^{21}}atoms \\\ \end{aligned}$$ \- Chlorine exists in dimeric form then 1 gm of Chlorine contains = $2\times 8.48\times {{10}^{21}}=16.96\times {{10}^{21}}atoms$ \- Therefore from the above calculations we can say that 1 g of Lithium contains more number of atoms. **\- So, the correct option is C.** **Note:** The number of atoms present in an element is going to depend on the molecular weight of the atoms. If the molecular weight of the atoms is less then it contains more number of atoms. That means molecular weight of the element is inversely proportional to the number of atoms present in that particular atom.