Answer:
The average pressure in the container due to these 75 gas molecules is [tex]P=9.72 \times 10^{-16} Pa[/tex]
Explanation:
Here Pressure in a container is given as
[tex]P=\frac{1}{3} \rho <u^2>[/tex]
Here
[tex]\rho =\frac{mass}{Volume of container}[/tex]
Here
mass is to be calculated for 75 gas phase molecules as
[tex]m=n_{molecules} \times \frac{1 mol}{6.022 \times 10^{23} molecules} \times \frac{32 g/mol}{1 mol}\\m=75 \times \frac{1 mol}{6.022 \times 10^{23} molecules} \times \frac{32 g/mol}{1 mol}\\m=3.98 \times 10^{-21} g[/tex]
Volume of container is 0.5 lts
So density is given as
[tex]\rho =\frac{mass}{Volume of container}\\\rho =\frac{3.98 \times 10^{-21} \times 10^{-3} kg}{0.5 \times 10^{-3} m^3}\\\rho =7.97 \times 10^{-21}\, kg/m^3[/tex]
[tex]<u^2>=RMS^2[/tex]
Here RMS is the Root Mean Square speed given as 605 m/s so
[tex]<u^2>=RMS^2\\<u^2>=(605)^2\\<u^2>=366025[/tex]
Substituting the values in the equation and solving
[tex]P=\frac{1}{3} \rho <u^2>\\P=\frac{1}{3} \times 7.97 \times 10^{-21} \times 366025\\P=9.72 \times 10^{-16} Pa[/tex]
So the average pressure in the container due to these 75 gas molecules is [tex]P=9.72 \times 10^{-16} Pa[/tex]
