First slide

Kinetic theory of ideal gases

Question

The highest vacuum attained so far is of the order of 10^-11 mm of Hg. How many molecules are there in 1m³ of a vessel under such a high vacuum at $0 º C$ ?

Moderate

A

$3.5 \times 10^{14}$
B

$6.4 \times 10^{17}$
C

$6.4 \times 10^{27}$
D

$2.2 \times 10^{12}$

Solution

$\begin{array}{l} P V = n R T = \frac{N}{N_{A}} R T = N k T \\ \Rightarrow N = \frac{P V}{k T} = \frac{(10^{- 11}) (13000) (9.8) (1)}{(1.38 \times 10^{- 23}) (273)} = 3.5 \times 10^{14} \end{array}$

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