The volume occupied by 1 mole of water vapor | vedclass

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Question

(B) At $STP$,the molar volume of an ideal gas is $22.4 \ L$.
However,the question asks for the volume occupied by the molecules themselves (the actua

Vedclass · Accepted Answer

Less than $1\%$ of $22.4 \ L$

Vedclass · Answer

(B) At $STP$,the molar volume of an ideal gas is $22.4 \ L$.
However,the question asks for the volume occupied by the molecules themselves (the actual volume of the particles).
The radius of a water molecule is approximately $1.5 \ \mathring{A} = 1.5 	imes 10^{-10} \ m $ .
The volume of one water molecule is $V = \frac{4}{3} \pi r^3 = \frac{4}{3} 	imes 3.14 	imes (1.5 	imes 10^{-10} \ m)^3 \approx 1.41 	imes 10^{-29} \ m^3$.
For $1$ mole ($6.022 	imes 10^{23}$ molecules),the total volume is $6.022 	imes 10^{23} 	imes 1.41 	imes 10^{-29} \ m^3 \approx 8.5 	imes 10^{-6} \ m^3 = 8.5 \ mL$.
Since $22.4 \ L = 22400 \ mL$,the ratio is $\frac{8.5}{22400} \approx 0.00038$,which is approximately $0.038\%$.
This is significantly less than $1\%$ of $22.4 \ L$.

The volume occupied by $1$ mole of water vapor molecules at $STP$ is ..... (i.e.,Avogadro number $\times$ volume of one molecule).

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