Question

What is the mass of co2 which contains the same number of molecules as are contained in 40g of oxygen?

Answer 1

$\textsf{\Large{\underline{Solution}}}$ :

Number of moles in of any molecule = $\boxed{ \mathsf{\dfrac{Mass \:of\:that \:molecule} {Molecular\: mass} \:=\:{\dfrac{Number of molecules} {Avagadro\:Number, N_A}}}}$

For Oxygen $\mathsf{(O_2)}$,

$\mathsf{\dfrac{40} {32} \:=\:{\dfrac{Number of molecules} {6.022*{10}^{23}}}}$

$\mathsf{Number of molecules\:=\:{\dfrac{40 *6.022*{10}^{23}}{32}}}$

$\mathsf{Number of molecules\:=\:7.527*{10}^{23}}$

Given, Number of molecules of $\mathsf{O_2}$ = Number of molecules of $\mathsf{CO_2}$

For $\mathsf{CO_2}$,

Let mass of $\mathsf{CO_2}$ be m.

$\mathsf{\dfrac{m}{44} \:=\:{\dfrac{Number of molecules} {6.022*{10}^{23}}}}$

$\mathsf{\dfrac{m}{44} \:=\:{\dfrac{7.527*{10}^{23}} {6.022*{10}^{23}}}}$

$\mathsf{m\:=\:{\dfrac{7.527*{10}^{23}*44} {6.022*{10}^{23}}}}$

$\mathsf{m\:=\: 1.25*44}$

$\mathsf{m\:=\:55}$

$\boxed{\mathsf{Mass\:of\:CO_2\:=\:55\:g.}}$