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Acceleration in 2D

The density o...

Question

The density of vapours of a substance at 1 atm pressure and 400 K is 0.4 kg m $^{- 3}$ . These vapours effuse through a pin at a rate of 2 times faster than $S O_{2}$ under the same conditions. Is it attractive or repulsive forces operating in the given gas molecule?
(Given 1 atm = 101325 Nm $^{- 2}$ )

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Solution

$\frac{r_{v}}{r_{s o}} = \sqrt{\frac{M_{s o}}{M_{v}}}$
$2 = \sqrt{\frac{64}{M_{v}}}; 4 = \frac{64}{M_{v}}, M_{v} = 16$
Molar volume $¯ ¯¯ ¯ V = \frac{16 \times 10^{- 3}}{0.4} = 40 \times 10^{- 3} m^{3}$
Compressibility factor $Z = \frac{P V}{R T} = \frac{101325 \times 40 \times 10^{- 3}}{8.314 \times 400}$
$= 1218.9 \times 10^{- 3} = 1.219$
Since $Z > 1$ , repulsive forces do operate.

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