Chapter 13, Problem 41P

To determine

To Calculate:The number of molecules per meter cube.

Answer to Problem 41P

The number of molecules/meter cube is $2.69\times {10}^{25}{\text{molecules/m}}^{\text{3}}$ .

Explanation of Solution

Given info:

Standard temperature is, $T=273.1\text{5}\text{K}$ .

Pressure, $P={10}^5\text{Pa}$ .

Volume at STP, $V=22.4\text{L}$ .

Formula used:

Write the expression for the number of moles.

  $\text{number}\text{of}\text{moles}\text{=}\frac{\text{mass}\text{of}\text{the}\text{water}}{\text{molecular}\text{mass}}$

Calculation:

Volume of the one mole of the ideal gas at STP is $22.4\text{L}$ andthen the number of molecules per meter cube is,

  $\frac{1\text{mole}}{\text{22}\text{.4}\text{L}}\times \frac{6.023\times {10}^{23}\text{molecules}}{\text{mole}}\times \left(\frac{\text{1}\text{L}}{{\text{10}}^{\text{-3}}{\text{m}}^{\text{3}}}\right)=2.69\times {10}^{25}{\text{molecules/m}}^{\text{3}}$

Conclusion:

The number of molecules/meter cube is $2.69\times {10}^{25}{\text{molecules/m}}^{\text{3}}$ .