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(C) The ideal gas equation is given by $PV = NkT$,where $P$ is pressure,$V$ is volume,$N$ is the number of molecules,$k$ is the Boltzmann constant,and

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$3.3 	imes 10^{21}$

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(C) The ideal gas equation is given by $PV = NkT$,where $P$ is pressure,$V$ is volume,$N$ is the number of molecules,$k$ is the Boltzmann constant,and $T$ is the temperature in Kelvin.Given: $P = 13.8 \ Pa$,$V = 1 \ m^3$,$k = 1.38 	imes 10^{-23} \ JK^{-1}$,and $T = 27^{\circ}C = 27 + 273 = 300 \ K$.Rearranging the formula for $N$: $N = \frac{PV}{kT}$.Substituting the values: $N = \frac{13.8 	imes 1}{1.38 	imes 10^{-23} 	imes 300}$.$N = \frac{13.8}{414 	imes 10^{-23}} = \frac{13.8}{4.14 	imes 10^{-21}} = \frac{13.8}{414} 	imes 10^{23} = 0.0333 	imes 10^{23} = 3.33 	imes 10^{21}$.Thus,the number of molecules is approximately $3.3 	imes 10^{21}$.

What is the number of oxygen molecules in a cylinder of volume $1 \ m^3$ at $27^{\circ}C$ and $13.8 \ Pa$? (Boltzmann constant $k = 1.38 \times 10^{-23} \ JK^{-1}$)

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