Question

The critical density of the gas co2 is 0.44 g cm–3 at a certain temperature. If r is the radius of the molecule, r3 in cm3 is approximately

Answer 1

Answer : The radius of a molecule is $3.693\times 10^{-23}Cm^3$.

Solution : Given,

Critical density of a gas = $0.44gCm^{3-}$

Molar mass of $CO^2$ = 44 g/mole

Formula used :

$Density=\frac{Mass}{Volume}$

Mass of $6.022\times 10^{23}$ molecules = 44 g of $CO^2$

Mass of 1 molecule = $\frac{44\times 1}{6.022\times 10^{23}}$ = $7.3065\times 10^{-23}$

The volume of 1 molecule = $\frac{4}{3} \pi r^3$ = $\frac{4}{3}\times \frac{22}{7}\times r^3$          ( $\pi =\frac{22}{7}$ )

Now pur all the given values in the formula, we get

$Density=\frac{Mass}{Volume}$

$0.44=\frac{7.3065\times 10^{-23}}{\frac{4}{3}\times \frac{22}{7}\times r^3}$

by rearranging the terms, we get

$r^3=3.693\times 10^{-23}Cm^3$

Therefore, the radius of a molecule is $3.693\times 10^{-23}Cm^3$.

Answer 2

Here you go, mind that instead of using normal volume I've used critical volume.