Problem — Moles and molecules in a gas cylinder

Problem

A cylinder contains ideal gas at $T=300$ K, $V=10$ L, $p = 1{,}0$ atm. How many moles of gas does it contain? How many molecules?

Solution

I use the ideal gas equation of state $pV = nRT$, solving for $n$. First I convert the units to the International System: $V = 10\ \text{L} = 10^{-2}\ \text{m}^3$ and $p = 1{,}0\ \text{atm} = 1{,}013\cdot 10^{5}\ \text{Pa}$. $n = \frac{pV}{RT} = \frac{1{,}013\cdot 10^{5}\cdot 10^{-2}}{8{,}31\cdot 300}$ $n = \frac{1013}{2493} \approx 0{,}40\ \text{mol}$ The number of molecules is obtained by multiplying by Avogadro’s number: $N = n\,N_A = 0{,}40\cdot 6{,}02\cdot 10^{23} \approx 2{,}4\cdot 10^{23}\ \text{molecules}$ $\ev{n \approx 0{,}40\ \text{mol}\ ;\quad N \approx 2{,}4\cdot 10^{23}\ \text{molecules}}$

Links

Topics: Kinetic theory of gases Concepts: Ideal gas law Skills: Unit conversion Methods: Conversion factor method