13.3 The ideal gas law  (Page 3/11)

Calculating the number of molecules in a cubic meter of gas

How many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large $N$ typically is.

Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be $0\text{º}\text{C}$ and atmospheric pressure.

Strategy

Because pressure, volume, and temperature are all specified, we can use the ideal gas law $\text{PV}=\text{NkT}$ , to find $N$ .

Solution

1. Identify the knowns.

2. Identify the unknown: number of molecules, $N$ .

3. Rearrange the ideal gas law to solve for $N$ .

4. Substitute the known values into the equation and solve for $N$ .

Discussion

This number is undeniably large, considering that a gas is mostly empty space. $N$ is huge, even in small volumes. For example, $1{\text{cm}}^3$ of a gas at STP has $2\text{.}\text{68}\times {\text{10}}^{\text{19}}$ molecules in it. Once again, note that $N$ is the same for all types or mixtures of gases.