Modern vacuum pumps can evacuate a vessel down to a pressure of 4.0 × 1 0 - 1 5 atm. at room temperature (300 K). Taking R = 8.3 JK -1 mole -1 , 1 atm = 10 5 Pa and N Avogadro = 6 × 1 0 2 3 mole - 1 ,

Question

Modern vacuum pumps can evacuate a vessel down to a pressure of 4.0 × 1 0 - 1 5 atm. at room temperature (300 K). Taking R = 8.3 JK -1 mole -1 , 1 atm = 10 5 Pa and N Avogadro = 6 × 1 0 2 3 mole - 1 , the mean distance between molecules of gas in an evacuated vessel will be of the order of :

TestHub · Accepted Answer

Let the inter molecular distance be D
Then in a volume of $\frac{4}{3} π D^{3}$ there is only one molecule.

$\frac{4}{3} π D^{3} P = (\frac{1}{N_{A}}) R T$

$D = {(\frac{3 R T}{4 π N_{A} P})}^{\frac{1}{3}}$

Substituting $P = 4 \times 10^{- 10} P a, R = 8.3, N_{A} = 6 \times 10^{23}, T = 300 K$

$D = 0.2 m m$

Physics - Heat & Thermo Question with Solution | TestHub

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