High Vacuum

Chemistry Level 1

A lot of modern experiments are led in containers where an artificial high vacuum of the order of 1 0 − 8 P a 10^{-8} Pa is produced in order to deal with very clean enviroments because the number of bumbs between atoms, molecules, ions or electrons is very reduced.

How many molecules of gas M are inside such a cointeiner (after the vacuum is produced) every m 3 m^{3} at the temperatue of 27 Celsius degrees?

Enter you answer as ⌊ M 1 0 9 ⌋ \left \lfloor \frac{M}{10^{9}} \right \rfloor


The answer is 2414.

Andrea Virgillito by Andrea Virgillito , 22, Italy

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1 solution

Andrea Virgillito
Jul 11, 2017

Using the ideal gas law we can write that: n V = P R T → n V = 1 0 − 8 P a 8.31 J m o l ∗ K ∗ 300 K = 4.011 ∗ 1 0 − 12 m o l m 3 \frac{n}{V} = \frac{P}{RT} \rightarrow \frac{n}{V} = \frac{10^{-8}Pa}{8.31\frac{J}{mol*K}*300K} = 4.011*10^{-12}\frac{mol}{m^{3}}

Recalling that 1 m o l = 6.02 ∗ 1 0 23 m o l e c u l e s 1mol=6.02*10^{23} molecules

M = 2.41462 ∗ 1 0 12 M=2.41462*10^{12}

⌊ M 1 0 9 ⌋ = 2414 \boxed{\left \lfloor \frac{M}{10^{9}} \right \rfloor=2414}

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