Consider three identical flasks filled with different gases. Flask A: \(\mathrm{CO}\) at 760 torr and \(0^{\circ} \mathrm{C}\) Flask \(\mathrm{B}: \mathrm{N}_{2}\) at 250 torr and \(0^{\circ} \mathrm{C}\) Flask C: \(\mathrm{H}_{2}\) at 100 torr and \(0^{\circ} \mathrm{C}\) a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest average velocity?

To convert the temperature from Celsius to Kelvin, we can use the following formula: \(T_K = T_C + 273.15\). Here, all the flasks have the same temperature of \(0^{\circ} \mathrm{C}\), so the temperature in Kelvin is: \(T_K = 0 + 273.15 = 273.15\,\mathrm{K}\). a. Now, let's find out the flask with the greatest average kinetic energy.

Using the average kinetic energy formula \(\frac{3}{2} kT\), we can calculate the average kinetic energy for all the flasks since they have the same temperature of \(273.15\,\mathrm{K}\). Therefore, their average kinetic energies will also be the same. So, the molecules in all the flasks (A, B, and C) will have the greatest (and identical) average kinetic energy. b. Now, let's find out the flask with the greatest average velocity.

First, we need to find the molar masses of CO, N2, and H2 gases. The molar masses are as follows: CO: \(\mathrm{12.01\,g/mol + 16.00\,g/mol} = 28.01\,\mathrm{g/mol}\) N2: \(2 \times \mathrm{14.01\,g/mol} = 28.02\,\mathrm{g/mol}\) H2: \(2 \times \mathrm{1.01\,g/mol} = 2.02\,\mathrm{g/mol}\) Now, use the root mean square velocity formula \(v_{rms} = \sqrt{\frac{3kT}{m}}\) to calculate the average velocities for each gas. For Flask A (CO): \(v_{rms} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 273.15\,\mathrm{J/K}}{28.01 \times 10^{-3}\,\mathrm{kg/mol}}} = 384.4\,\mathrm{m/s}\) For Flask B (N2): \(v_{rms} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 273.15\,\mathrm{J/K}}{28.02 \times 10^{-3}\,\mathrm{kg/mol}}} = 384.3\,\mathrm{m/s}\) For Flask C (H2): \(v_{rms} = \sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 273.15\,\mathrm{J/K}}{2.02 \times 10^{-3}\,\mathrm{kg/mol}}} = 1920\,\mathrm{m/s}\) From these calculations, we can conclude that the molecules in Flask C (H2) will have the greatest average velocity.