Chapter 13, Problem 78GP

To determine

To Find: The number of molecules per cm³.

Answer to Problem 78GP

The number of molecules per ${\text{cm}}^{\text{3}}$ is $265{\text{ molecules / cm}}^{\text{3}}$ .

Explanation of Solution

Given info:

Pressure $P={10}^{-12}{\text{ N/m}}^{\text{2}}$ .

Temperature $T=0\text{°C }=273\text{ K}$ .

Boltzmann constant $k=1.38\times {10}^{-23}\text{ J/K}$ .

Formula used:

  $\begin{array}{l}PV=NkT\\ \frac{N}{V}=\frac{P}{kT}\end{array}$

Here, $P$ is the pressure,

  $V$ is the volume,

  $T$ is the temperature,

  $k$ is the Boltzmann constant,

  $N$ is the no of molecules.

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}\frac{N}{V}=\frac{{10}^{-12}}{1.38\times {10}^{-23}\times 273}=265\times {10}^8{\text{ molecules/m}}^{\text{3}}\\ \frac{N}{V}=265\times {10}^8{\text{ molecules/m}}^{\text{3}}=2.65\times {10}^8\times {10}^{-6}{\text{ molecules/cm}}^{\text{3}}\\ \frac{N}{V}=265{\text{ molecules / cm}}^{\text{3}}\end{array}$

Conclusion:

Thus, the number of molecules per ${\text{cm}}^{\text{3}}$ is $265{\text{ molecules / cm}}^{\text{3}}$ .