Question

Suppose you have 75 gas-phase molecules of methanol (CH3OH) at T = 470 K. These molecules are contained in a spherical container of volume 0.500 liters.At this temperature, the root mean square speed of methanol molecules is 605 m/sec.What is the average pressure in the container due to these 75 molecules?(The molar mass of methanol is 32.0 g/mol.)

Answer 1

Answer:

The average pressure in the container due to these 75 gas molecules is $P=9.72 \times 10^{-16} Pa$

Explanation:

Here Pressure in a container is given as

$P=\frac{1}{3} \rho$

Here

• P is the pressure which is to be calculated

• ρ is the density of the gas which is to be calculated as below

                                         $\rho =\frac{mass}{Volume of container}$

        Here

                mass is to be calculated for 75 gas phase molecules as

                      $m=n_{molecules} \times \frac{1 mol}{6.022 \times 10^{23} molecules} \times \frac{32 g/mol}{1 mol}\\m=75 \times \frac{1 mol}{6.022 \times 10^{23} molecules} \times \frac{32 g/mol}{1 mol}\\m=3.98 \times 10^{-21} g$

              Volume of container is 0.5 lts

     So density is given as

                         $\rho =\frac{mass}{Volume of container}\\\rho =\frac{3.98 \times 10^{-21} \times 10^{-3} kg}{0.5 \times 10^{-3} m^3}\\\rho =7.97 \times 10^{-21}\, kg/m^3$

• is the mean squared velocity which is given as

                                        $=RMS^2$

      Here RMS is the Root Mean Square speed given as 605 m/s so

                                      $=RMS^2\\=(605)^2\\=366025$

Substituting the values in the equation and solving

$P=\frac{1}{3} \rho \\P=\frac{1}{3} \times 7.97 \times 10^{-21} \times 366025\\P=9.72 \times 10^{-16} Pa$

So the average pressure in the container due to these 75 gas molecules is $P=9.72 \times 10^{-16} Pa$