What is the average molecular speed

Answers may vary slightly. A more accurate answer is 0. The molar mass of oxygen is A precision to two significant digits is enough. Find a the most probable speed, b the average speed, and c the rms speed for nitrogen molecules at K. What is the molar mass of the gas? You might like to figure out what the gas is likely to be.

In the deep space between galaxies, the density of molecules which are mostly single atoms can be as low as and the temperature is a frigid 2. What is the pressure? The air inside a hot-air balloon has a temperature of K and a pressure of Using the composition of air as , find the density of the air inside the balloon. When an air bubble rises from the bottom to the top of a freshwater lake, its volume increases by. If the temperatures at the bottom and the top of the lake are 4.

Use the Van der Waals equation of state to estimate the temperature under the same conditions. Which estimate is better? One process for decaffeinating coffee uses carbon dioxide at a molar density of about and a temperature of about. On a winter day when the air temperature is the relative humidity is.

Outside air comes inside and is heated to a room temperature of. What is the relative humidity of the air inside the room. Does this problem show why inside air is so dry in winter? On a warm day when the air temperature is , a metal can is slowly cooled by adding bits of ice to liquid water in it.

Condensation first appears when the can reaches. What is the relative humidity of the air? Assume that the dry air is an ideal gas composed of molecules with a molar mass of For a fixed air pressure, describe qualitatively how the range of a projectile changes with the relative humidity.

Do those conditions give an advantage or disadvantage to home-run hitters? The mean free path for helium at a certain temperature and pressure is The radius of a helium atom can be taken as. What is the measure of the density of helium under those conditions a in molecules per cubic meter and b in moles per cubic meter?

The mean free path for methane at a temperature of K and a pressure of is Find the effective radius r of the methane molecule. Such volumes are a fundamental idea in the study of the flow of compressible fluids such as gases as well. For the equations of hydrodynamics to apply, the mean free path must be much less than the linear size of such a volume, For air in the stratosphere at a temperature of K and a pressure of 5.

Take the effective radius of air molecules to be which is roughly correct for. Find the total number of collisions between molecules in 1. Use as the effective radius of a nitrogen molecule. The number of collisions per second is the reciprocal of the collision time. Keep in mind that each collision involves two molecules, so if one molecule collides once in a certain period of time, the collision of the molecule it hit cannot be counted.

The molar mass of sodium is A sealed, perfectly insulated container contains 0. The stirring bar is magnetically driven to a kinetic energy of What is the equilibrium temperature? Find the ratio for hydrogen gas at a temperature of Unreasonable results. How could you get a better answer? Its molar mass is According to Figure , the of is significantly different from the theoretical value, so the ideal gas model does not describe it very well at room temperature and pressure, and the Maxwell-Boltzmann speed distribution for ideal gases may not hold very well, even less well at a lower temperature.

An airtight dispenser for drinking water is in horizontal dimensions and 20 cm tall. It has a tap of negligible volume that opens at the level of the bottom of the dispenser. Initially, it contains water to a level 3. When the tap is opened, water will flow out until the gauge pressure at the bottom of the dispenser, and thus at the opening of the tap, is 0.

What volume of water flows out? In theory, this energy can be distributed among the gaseous particles in many ways, and the distribution constantly changes as the particles collide with each other and with their boundaries.

By understanding the nature of the particle movement, however, we can predict the probability that a particle will have a certain velocity at a given temperature. Kinetic energy can be distributed only in discrete amounts known as quanta, so we can assume that any one time, each gaseous particle has a certain amount of quanta of kinetic energy.

These quanta can be distributed among the three directions of motions in various ways, resulting in a velocity state for the molecule; therefore, the more kinetic energy, or quanta, a particle has, the more velocity states it has as well. If we assume that all velocity states are equally probable, higher velocity states are favorable because there are greater in quantity.

Although higher velocity states are favored statistically, however, lower energy states are more likely to be occupied because of the limited kinetic energy available to a particle; a collision may result in a particle with greater kinetic energy, so it must also result in a particle with less kinetic energy than before.

Select the mass of the molecules behind the barrier. Remove the barrier, and measure the amount of time it takes the molecules to reach the gas sensor. When the gas sensor has detected three molecules, it will stop the experiment. Compare the diffusion rates of the lightest, heavier and heaviest molecules. Trace an individual molecule to see the path it takes.

Using the above logic, we can hypothesize the velocity distribution for a given group of particles by plotting the number of molecules whose velocities fall within a series of narrow ranges. This results in an asymmetric curve, known as the Maxwell-Boltzmann distribution.

The peak of the curve represents the most probable velocity among a collection of gas particles. Velocity distributions are dependent on the temperature and mass of the particles.

As the temperature increases, the particles acquire more kinetic energy. When we plot this, we see that an increase in temperature causes the Boltzmann plot to spread out, with the relative maximum shifting to the right. Effect of temperature on root-mean-square speed distributions : As the temperature increases, so does the average kinetic energy v , resulting in a wider distribution of possible velocities. Larger molecular weights narrow the velocity distribution because all particles have the same kinetic energy at the same temperature.

According to Kinetic Molecular Theory, gaseous particles are in a state of constant random motion; individual particles move at different speeds, constantly colliding and changing directions. We use velocity to describe the movement of gas particles, thereby taking into account both speed and direction.

Although the velocity of gaseous particles is constantly changing, the distribution of velocities does not change. Particles moving in opposite directions have velocities of opposite signs. In other words, as the temperature of a sample of gas is increased, the molecules speed up and the root mean square molecular speed increases as a result. Graham's Law states that the rate of effusion of two different gases at the same conditions are inversely proportional to the square roots of their molar masses as given by the following equation:.

In according with the Kinetic Molecular Theory, each gas molecule moves independently. However, the net rate at which gas molecules move depend on their average speed. By examining the equation above, we can conclude that the heavier the molar mass of the gas molecules slower the gas molecules move. And conversely, lighter the molar mass of the gas molecules the faster the gas molecules move.

Graham's Law can only be applied to gases at low pressures so that gas molecules escape through the tiny pinhole slowly. In addition, the pinhole must be tiny so that no collisions occur as the gas molecules pass through. The random and rapid motion of tiny gas molecules results in effusion.

Effusion is the escape of gas molecules through a tiny hole or pinhole. The behavior of helium gas in balloons is an example of effusion. The balloons are made of latex which is porous material that the small helium atom can effuse through. The helium inside a newly inflated balloon will eventually effuse out.

This is the reason why balloons will deflate after a period of time. Molecular speeds are also used to explain why small molecules such as He diffuse more rapidly than larger molecules O 2. That is the reason why a balloon filled with helium gas will deflate faster than a balloon filled with oxygen gas. The effusion rate, r , is inversely proportional to the square root of its molar mass, M. By examine the Graham's law as stated above, we can conclude that a lighter gas will effuse or travel more rapidly than a heavier gas.

Mathematically speaking, a gas with smaller molar mass will effuse faster than a gas with larger molar mass under the same condition.

Similar to effusion, the process of diffusion is the spread of gas molecules through space or through a second substance such as the atmosphere. Diffusion has many useful applications. Here is an example of diffusion that is use in everyday households. Natural gas is odorless and used commercially daily. An undetected leakage can be very dangerous as it is highly flammable and can cause an explosion when it comes in contact with an ignition source.

In addition, the long term breathing of natural gas can lead to asphyxiation. Fortunately, chemists have discovered a way to easily detect natural gas occur leak by adding a small quantity of a gaseous organic sulfur compound named methyl mercaptan, CH 3 SH, to the natural gas. When a leak happens, the diffusion of the odorous methyl mercaptan in the natural gas will serve as a sign of warning.