Physics
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A nitrogen (N2, molar mass = 28.01 g/mol) molecule in the atmosphere has a root mean square speed of 509 m/s. Determine its momentum as it moves at that speed.
Constant pressure of a gas sample can be attained by fitting a container with a movable piston. A gas in such a container is maintained at a constant pressure of 800 Pa. If the gas is oxygen (molar mass 32.00 g/mol) and its temperature varies between 40°C and -70°C, calculate the range of root-mean-square speeds for oxygen molecules.
Monoatomic gases helium (He), argon (Ar), and xenon (Xe) are isolated from the atmosphere and placed in the same tank. How does the root-mean-square speed vary between these three species?
Nitrogen (N2) is a diatomic gas with a molar mass of 28.01 g/mol. What is its root-mean-square speed (vrms) at room temperature (298K)?
Brownian motion refers to the random motion of particles as they collide with fluid particles. A dust particle of mass 2.15 × 10-17 kg is suspended in air whose temperature is 308 K. Determine the root mean square speed of its Brownian motion.
Oxygen and Chlorine are among the gaseous elements in the periodic table. Determine the temperature when the root-mean-square speed of chlorine molecules is the same as the root-mean-square speed of oxygen molecules at room temperature (25.0°C). Hint: The molar mass of O2 is 32.00 g/mol; Cl2 is 70.90 g/mol.
The molar mass of Nitrogen is 28.01 g/mol. If the root-mean-square speed of the nitrogen molecules is 509 m/s, how many molecules with this speed moving between the left and right faces of a cube of length 0.2 m are required to produce a pressure of 1.5 atm?
A 0.15m long cube filled with nitrogen (N2, molar mass 28.01 g/mol) at a rms velocity of 524m/s. Imagine a molecule repeatedly moving between the left and right faces, then determine the average force exerted on one of the cube's faces. Take the motion to be perpendicular to the left and right faces.
Consider that in the future a very high spatial resolution microscope is developed to study the motion of gas molecules. Suppose that a scientist is using the microscope to study the motion of oxygen molecules at standard atmospheric pressure inside a small container. The microscope detects two oxygen molecules separated by a distance of 22 molecular radii, which then collide head-on after 2.3 seconds. Assume that the oxygen molecules in the container have the same root mean square speed and that there are no other gases present in the container. The molecular radius of oxygen is 1.52 angstroms, and its molecular weight is 32 g/mol. Determine the temperature of the oxygen gas in Kelvin.
A sample of 15 nitrogen molecules has speeds ranging from 36 m/s, 37 m/s, 38 m/s, ....., and 50 m/s. Determine the i) average speed and ii) the root-mean-square speed of the nitrogen molecules in the sample.
Consider a cylindrical container of radius r filled with an ideal gas that has a movable piston. The gas undergoes an isobaric process while the piston is moving at a constant speed v and the gas expands. Determine the expression for the rate of change of the root mean square speed of the gas in terms of v, the instantaneous value of the root mean square speed (vrms), and the instantaneous value of the cylinder's height h.
A sample of hydrogen gas contains hydrogen (11H) and deuterium (21H) atoms. A scientist developed a method to separate the two isotopes based on the technique of isotope separation by gas diffusion. The sample of hydrogen is introduced into a series of diffusion-permeable porous cells at a fixed temperature T. 11H diffuses through the porous membrane more rapidly than 21H, resulting in a separation of the two isotopes. The scientist collects the enriched gas stream, which contains 21H. Calculate the ratio of the root mean square velocities of 11H and 21H (vrms(11H)/vrms(21H)). 11H has a mass of 1.008 u, and 21H has a mass of 2.014 u.
A sealed container has a pressure of 1.5 atm and contains gas molecules with an rms speed of 343 m/s at a temperature of 300 K. Name the gas in the container if it has a number density of 5.8 × 1025 m-3.
The root-mean-square speed of molecules in a gas is 700 m/s. If the volume of the gas is suddenly doubled, what will be the new rms speed of the molecules, assuming the pressure remains constant?
A gas molecule is at a temperature of 15°C and is moving at a random rms speed. Find the ratio of new rms speed to old rms speed if the temperature of the molecule is raised to 2000°C.
Assuming that pollen grains are spherical and have a density of 1100 kg/m3, calculate the rms speed of a pollen grain at a temperature of 25°C if it behaves like an ideal gas. The diameter of a typical pollen grain is 20 μm.