Mole to Mass Conversion Using Avogadro Number JEE Chemistry

 

❓ Question

A sample of $CO_2$ has mass $x$ mg. After removing $10^{21}$ molecules from it, $2.8\times10^{-3}$ of $CO_2$ is left.

Given:

$$N_A=6.02\times10^{23}\ \text{mol}^{-1}$$

Find the initial mass of $CO_2$.

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✍️ Solution

Moles of $CO_2$ removed:

$$n=\frac{\text{Number of molecules}}{N_A}$$
$$=\frac{10^{21}}{6.02\times10^{23}}$$
$$=1.66\times10^{-3}\ \text{mol}$$

Moles of $CO_2$ initially:

$$=2.8\times10^{-3}+1.66\times10^{-3}$$
$$=4.46\times10^{-3}\ \text{mol}$$

Molar mass of $CO_2$:

$$=12+2(16)=44\ \text{g mol}^{-1}$$

Mass of $CO_2$ initially:

$$m=n\times M$$
$$=4.46\times10^{-3}\times44$$
$$=0.19624\ \text{g}$$

Converting into mg:

$$0.19624\times1000=196.24\ \text{mg}$$

✅ Final Answer

$$\boxed{196.24\ \text{mg}}$$