Question

The lowest pressure ever obtained in a laboratory setting is 4.0×10−11 Pa.

At this pressure, how many molecules of air would there be in a 50 ∘C experimental chamber with a volume of 0.020 m3 ?

Express your answer using two significant figures.

Answer 1

From the ideal gas equation,

$$ \begin{aligned} P V &=n R T \\ n &=\frac{P V}{R T} \\ &=\frac{\left(4 \times 10^{-11}\right)(0.020)}{(8.314)(50+273)} \\ &=2.98 \times 10^{-16} \end{aligned} $$

The number of molecules is,

$$ \begin{aligned} N &=n\left(6.023 \times 10^{23}\right) \\ &=\left(2.98 \times 10^{-16}\right)\left(6.023 \times 10^{23}\right) \\ &=1.79 \times 10^{8} \\ &=1.8 \times 10^{8} \end{aligned} $$