$2.8 imes 10^{-3}$ mol of $\mathrm{CO}_{2}$ is left after removing $10^{21}$ molecules from its '

Question

$2.8 	imes 10^{-3}$ mol of $\mathrm{CO}_{2}$ is left after removing $10^{21}$ molecules from its ' $x$ ' mg sample. The mass of $\mathrm{CO}_{2}$ taken initially is Given $N_{A}=6.02 	imes 10^{23} \mathrm{~mol}^{-1}$\

Professor PC Thomas Classes · Answer

(d): Molecules of $\mathrm{CO}_{2}$ left
$=2.8 	imes 10^{-3} 	imes 6.02 	imes 10^{23}$
$=1.69 	imes 10^{21}$ molecules
Initial molecules of $\mathrm{CO}_{2}=$ Number of $\mathrm{CO}_{2}$ molecules left + Number of $\mathrm{CO}_{2}$ molecules removed $=1.69 	imes 10^{21}+10^{21}$
$
=2.69 	imes 10^{21} 	ext { molecules }
$

Initial moles of $\mathrm{CO}_{2}$
$=\frac{2.69 	imes 10^{21}}{6.02 	imes 10^{23}}=4.468 	imes 10^{-3} \mathrm{~mol}$
Mass of $\mathrm{CO}_{2}=$ Mole $	imes$ Molar mass
$
\begin{array}{r}
=4.468 	imes 10^{-3} \mathrm{~mol} C 44 \mathrm{~g} / \mathrm{mol} \
\left(\because 	ext { Molar mass of } \mathrm{CO}_{2}=44 \mathrm{~g} / \mathrm{mol}ight) \
\quad=0.196592 \mathrm{~g}=196.6 \mathrm{mg}
\end{array}
$